# The Concept of Abstraction on the GMAT

The concept of abstraction involves taking things from specific values to general ideas. On the GMAT, abstraction is one of the simplest ways to turn an easy problem into a difficult one. A simple example would be to ask someone what “5 times 6” would be, and then to expand that to “x times y” or “odd number times even number.” Abstraction helps by giving broad strokes to concepts, but it also requires a deeper understanding of the underlying principles. (This is the same principle as abstract art… apparently).

The GMAT is known for employing abstraction to make simple questions harder to grasp. Sometimes, a concrete problem using specific numbers can be very difficult, but the difficulty lies in the execution of the solution. An abstract problem, however, introduces an entirely different level of complexion, where even understanding the question at hand isn’t obvious (think of a Georgia O’Keefe painting). Once you’ve figured out what the problem is asking, then you can go about solving it. But until then you’re scratching your head wondering what the next step could be.

There is a lot of value in understanding the abstract, overarching theme of a question. After all, instead of saying that 2 + 2 gives you an even number, and 2 + 4 gives you an even number, and 2 + 6 gives you an even number, you can summarize that the sum of any two even numbers will be even. Once you understand this principle, it makes all future questions on this topic easier to solve. However, if you happen to see something on test day that you’re unfamiliar with, you might be better off concentrating on the question at hand than the unbreakable rule that guarantees the consistency of the answer.

As such, digging into why problems work is important during the time you prepare for the GMAT, so that problems seem easier on test day. Let’s explore one such relatively simple problem, made difficult by the abstract phrasing of the question:

If the operation ∆ is one of the four arithmetic operations addition, subtraction, multiplication, and division, is (6 ∆ 2) ∆ 4 = 6 ∆ (2 ∆ 4)?

1. 3 ∆ 2 > 3
2. 3 ∆ 1 = 3

A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
B) Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
C) Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
D)
Each statement alone is sufficient to answer the question.

Data sufficiency questions tend to be somewhat abstract on their own because they are asking whether something is sufficient or not. There aren’t specific values you are being asked to evaluate, but rather the entire spectrum of possibilities. To make things even more abstract, the question is asking about some equation (which looks isosceles to me), which could represent any of the four basic operations. This question is very abstract, and contains a pitfall or two if you’re not careful.

Before even looking at the statements, let’s revisit the equation in the question:

(6 ∆ 2) ∆ 4 = 6 ∆ (2 ∆ 4)

This equation is actually asking about the commutative property of operations, because the numbers are all the same, but the order of operations is different. Replace all the operations by +, and we quickly see that the answer is 12 on both sides. You may already know that addition and multiplication are commutative, whereas subtraction and division are not (and this holds for all problems, so it’s a great shortcut). However, we may as well demonstrate it to ourselves here:

(6 + 2) + 4 = 6 + (2 + 4) –> 8 + 4 = 6 + 6 –>  12 = 12. This holds, meaning the operation is commutative.

(6 x 2) x 4 = 6 x (2 x 4) –> 12 x 4 = 6 x 8 –> 48 = 48. This holds, meaning the operation is commutative.

(6 – 2) – 4 = 6 – (2 – 4) –> 4 – 4 = 6 – (-2) –> 0 = 8. This doesn’t hold, meaning the operation is not commutative.

(6 ÷ 2) ÷ 4 = 6 ÷ (2 ÷ 4) –> 3 ÷ 4 = 6 ÷ ½ –> ¾ = 12. This doesn’t hold, meaning the operation is not commutative.

This means that we will have sufficient data if a statement can narrow down the choices to any one operation or to either multiplication & addition or division & subtraction. The data will be insufficient if we cannot narrow down the operations or have at least one commutative operation (x or +) and a non-commutative operation (- or ÷) as possibilities.

Next, we must look through the statements and see what information we can glean. For simplicity’s sake, I’m going to begin by evaluating statement 2. This is because the equation will yield less abstraction than the inequality of statement 1. If the equation can satisfy this equation, it’s a possible answer. If it cannot, we can remove it from the list of potential equations.

Statement 2 says that 3 1 = 3. We can replace this by the four basic equations and see which ones hold:

3 + 1 = 3 –> This should give 4. Doesn’t hold. Eliminate addition.

3 – 1 = 3 –> This should give 2. Doesn’t hold. Eliminate subtraction.

3 x 1 = 3 –> This should give 3. Holds. Keep multiplication.

3 ÷ 1 = 3 –> This should give 3. Holds. Keep division.

You may be able to quickly ascertain that addition and subtraction do not hold for this equation, so only multiplication and division could work. Since we have two operations that could work, one of which is commutative and one of which is not, we can definitely say that this statement is insufficient.

Moving on to statement 1, we approach it in the same way and see if the operations can hold (i.e. the answer is greater than 3):

3 + 2 > 3  –> This gives 5. Holds. Keep addition.

3 – 2 > 3 –> This gives 1. Doesn’t hold. Eliminate subtraction.

3 x 2 > 3 –> This gives 6. Holds. Keep multiplication.

3 ÷ 2 > 3 –> This gives 1.5. Doesn’t hold. Eliminate division.

For this statement alone, we see that addition and multiplication both work, but the other two equations don’t. This means that we don’t know exactly which operation this represents, but either way it will give the same answer to the question given. The two operations left standing (last operation standing?) both yield the same answer to the statement, which means we don’t need to narrow down the choices or put the statements together. A common pitfall on this question is to put the statements together, because then only multiplication can work for both statements. However, that’s a trap, as you don’t need statement 2 at all. The correct answer is A, because statement 1 is sufficient on its own to answer the question posed.

For abstract problems, it’s easy to get lost in the generalization of the problem. What happens whenever I add two even numbers together? The magnitude of the scope is almost overwhelming, and as such the best strategy is to turn it concrete using simple examples. If no numbers are provided, try picking small, useful numbers like 2, 3 and 10. If the numbers are given but other variables, such as the operations, are left blank, then just go through all the possibilities until the rule becomes clear. The best way to overcome abstraction is to make it concrete.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# 99th Percentile GMAT Score or Bust! Lesson 2: If the Answers Smell the Same, They Stink

Veritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99thvideo series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

Lesson Two:

If Answers Smell the Same, They Stink.  GMAT verbal problems all carry the same basic instruction: select the best answer from this list of five; while that may sound straightforward enough, it actually lends itself to a powerful strategy.  Since there cannot be two correct answers, if two answer choices are too similar, you can infer that neither is correct.  In this video, Ravi explains how to leverage that strategy to save yourself from trap answers and ensure that your decision process takes place on the proper grounds.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Want to learn more from Ravi? He’s taking his show on the road for one-week Immersion Courses in San Francisco and New York this summer, and teaches frequently in our new Live Online classroom.

By Brian Galvin

# Planning for Retirement (& the GMAT)

When preparing for the GMAT, most prospective students start thinking about the schools they want to attend, the jobs they want to land and the opportunities they want to seize. After all, embarking on a new degree is an adventure that must be carefully prepared and thought out. Some students with long term thinking even begin thinking about something that most people dream of regularly: retirement.

Now, if you’re studying for an advanced degree, perhaps retirement is still many decades (or centuries) off. However, the day will likely come when you at least want to consider retirement, even if you don’t opt to do it for various reasons. Sometimes your economic reality keeps you gainfully employed, but often it becomes an issue of boredom, trepidation and even fear. Why would anyone fear retirement? Isn’t it supposed to be the culmination of your hard work so that you can enjoy your golden years without worrying about work and money? It is, at least in theory. However, in practice, it is a project that should be prepared for just like any other major life change.

In North America, many people retire and move to a sunny, warm climate such as Arizona or Florida. The temperate weather allows many people to enjoy outdoor activities regularly, sometimes in stark contrast to the cooler northern climates. (Winter is coming.) Many people are even opting to retire in other countries to take advantage of the increased buying power of their home currency. No matter whether you plan on retiring tomorrow or in 50 years, it is something you must consider at one point or another in your life.

The GMAT often features questions that discuss relevant topics and that arouse your own interests in order to make the questions more relatable. This is also a double-edged sword because the question must be solvable with only the information contained within the stimulus. Any outside information can’t help you, but the topic may still concern something you’ve contemplated in the past. Let’s look at an example that plays into the retirement theme:

In the United States, of the people who moved from one state to another when they retired, the percentage who retired to Florida has decreased by three percentage points over the past ten years. Since many local businesses in Florida cater to retirees, these declines are likely to have a noticeably negative economic effect on these businesses and therefore on the economy of Florida.

Which of the following, if true, most seriously weakens the argument given?

A) People who moved from one state to another when they retired moved a greater distance, on average, last year than such people did ten years ago.

B) People were more likely to retire to North Carolina from another state last year than people were ten years ago.

C) The number of people who moved from one state to another when they retired has increased significantly over the past ten years.

D) The number of people who left Florida when they retired to live in another state was greater last year than it was ten years ago.

E) Florida attracts more people who move from one state to another when they retire than does any other state.

This problem is a Critical Reasoning Weaken problem, which means that we should be able to identify the conclusion, examine the supporting evidence and find the gap between the two. The conclusion is that the economy of Florida will suffer based on shifting demographics. The evidence is that a smaller percentage of people are retiring to Florida than 10 years ago, coupled with the fact that Florida’s economy is dependent on these retirees. (Nothing about hurricanes or floods, though.)

If we had to predict an answer to this question, it would likely hinge on the fact that the evidence is a 3% decrease of all retirees who choose to move to Florida. Whenever you see a percentage as evidence, it should make you think that you may need to consider the absolute value as well (the reverse is also often true). Just because the percentage went down by 3%, that doesn’t mean that fewer people are actually going. You might still be growing, just growing slower than you were 10 years ago. Let’s look at the answer choices and see if any of them match our expectations.

Answer choice A, people who moved from one state to another when they retired moved a greater distance, on average, last year than such people did ten years ago, discusses the distance of these moves. This is clearly out of scope, as the question is only interested with the destination state, not in the original state. One mile (maybe you’re right on the border?) or one thousand miles are identical in this regard, so the distance travelled won’t matter. We can eliminate A.

Answer choice B,  people were more likely to retire to North Carolina from another state last year than people were ten years ago, is only concerned with North Carolina. There are clearly many other states that people can move to, but none of them are pertinent to the question about Florida. This answer choice is thus incorrect as well (and paid for by the North Carolina tourism board).

Answer choice C, the number of people who moved from one state to another when they retired has increased significantly over the past ten years, plays right into our prediction. Just because a smaller proportion than before is moving to Florida does not mean that there is economic collapse on the horizon. If 20% of one million people moved to Florida ten years ago, we could have more immigration by reducing the percentage to 17% but increasing the number of people to two million. As such, answer choice C weakens the argument significantly, as it could justify a sizable increase in relocations to the sunshine state. Let’s look at the other choices to confirm.

Answer choice D, the number of people who left Florida when they retired to live in another state was greater last year than it was ten years ago, turns the argument on its ear by discussing the number of people leaving Florida. While there is some merit in arguing that people are leaving the state in bigger numbers, it would actually support the argument that local businesses are in trouble. This answer choice is a 180° because it strengthens the argument instead of undermining it.

Finally, answer choice E, Florida attracts more people who move from one state to another when they retire than does any other state, is most likely true in the real world, but doesn’t help us in this question. If I have the most water in a drought, I may still not have much water at all. This answer choice doesn’t weaken the argument because it’s still entirely possible that the economy of Florida will suffer. Answer choice E can be eliminated. We now can confirm that it must be answer choice C.

For strengthen and weaken questions, it’s often best to attempt a logical guess at the answer choice based on the disconnect between the conclusion and the supporting evidence. Some statistical errors appear frequently on the GMAT, such as percentage and absolute number data that can be interpreted differently depending on the context. Like anything else in life, preparation is the key to success. Once you’ve mastered the finer elements of the GMAT, you can even start preparing your own retirement plan.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Simplifying Algebraic Equations on Data Sufficiency GMAT Questions

In the past few weeks, I’ve written a couple of posts extolling the virtues of using strategies in lieu of doing difficult algebra. But over the course of the quant section, there’s no getting around it: at times, algebra will be an effective tool that you’ll want to deploy. The key is for us to use this tool judiciously.

Because the GMAT is largely a test of pattern recognition, it’s worthwhile to first discuss the structural clues that we’ll want to be on the lookout for when determining whether algebra will be the most effective approach. My older posts discussed two scenarios when algebra would be problematic: the first was problem-solving questions involving difficult quadratic simplification, and the second was problem-solving percent questions that involved variables. In both cases, we’re better off either picking numbers or back-solving. Alternatively, when we see Data Sufficiency word problems, algebra serves a much more useful function, allowing us to distill complex information in simpler, more concrete form.

Once we recognize that we’ll be attacking a question algebraically, the next step is to consider how we can make our equations and expressions as simple as possible. Say, for example, that we’re told that the ratio of men to women to children in a park is 6 to 5 to 4. One way to depict this information is to write M:W:C = 6:5:4. The problem with this approach is that it leaves us with three variables. Hardly the simplicity and elegance that we’re looking for if we’re dealing with a time constraint. The alternative is to use only one variable and depict the information in terms of x:

Men:  6x

Women: 5x

Children: 4x

Now when we receive additional information about how these values are related, the equations we can assemble will be far more straightforward. Let’s try a GMATPrep* question to see this in action.

A certain company divides its total advertising budget into television, radio, newspaper, and magazine budgets in the ratio of 8:7:3:2 respectively. How many dollars are in the radio budget?

(1) The television budget is \$18,750 more than the newspaper budget

(2) The magazine budget is \$7,500.

We’ve got a Data Sufficiency word problem, so let’s start by putting all of the relevant information into algebraic form. Rather than using four different variables, we’ll organize our information like so:

Television: 8x

Newspaper: 3x

Magazine: 2x

Our ultimate goal is find the radio budget, which is 7x. Clearly, if we have the value of x, we can find 7x, so we can rephrase the question as: ‘What is the value of x?’

Statement 1 tells us that the television budget, 8x, is 18,750 more than the newspaper budget, 3x. In algebraic form, that will be: 8x = 18750 + 3x. Obviously, we can solve for x here, so SUFFICIENT.

Statement 2 tells us that the magazine budget, or 2x, is 7500. So 2x = 7500. Again, we can clearly solve for x, so SUFFICIENT.

And the answer is D; either statement alone is sufficient to answer the question.

Let’s try another.

Of the shares of stock owned by a certain investor, 30 percent are shares of Company X stock and 1/7 of the remaining shares are shares of Company Y stock. How many shares of Company X stock does the investor own?

(1) The investor owns 100 shares of Company Y stock.
(2) The investor owns 200 more shares of Company X stock than of Company Y stock.

Same drill: we recognize that we’re dealing with a Data Sufficiency word problem, so let’s convert the initial into algebraic form.

If we designate our total shares of stock ‘T,’ and we know that 30% of those are Company X, we’ll have .3T shares of company X. We’re told that 1/7 of the remaining shares are Company Y. If .3T shares are company X, we’ll have .7T shares left over. If 1/7 of those .7T shares belong to Company Y, we can designate Company Y’s shares as (1/7) * .7T =   .1T.

Summarized, we have the following information:

Company X: .3T

Company Y: .1T

We’re asked about Company X, so we want .3T. Clearly, if we have T, we can solve for .3T, so our rephrased question is just: “What is the value of T?”

Statement 1 tells us there are 100 share of Y, so .1T = 100. We can solve for T, so SUFFICIENT.

Statement 2 tells us that the investor has 200 more shares of X than Y. Algebraically: .3T = 200 + .1T. Again, we can solve for T, but no need to actually do the math. SUFFICIENT.

The answer is D; either alone is sufficient to answer the question.

Takeaway: preparation for the GMAT is not about learning which strategies are ‘best.’ Different strategies will work well in different scenarios, and for some test-takers, it will be a matter of taste to determine which they prefer. If you do decide to approach a question algebraically – and again, in Data Sufficiency word problems, this will often work nicely – try to diminish the complexity of the problem by minimizing the number of variables you use to depict the relevant information.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# 99th Percentile GMAT Score or Bust! Lesson 1: Drywall vs. Door

Veritas Prep’s Ravi Sreerama is the #1-ranked GMAT instructor in the world (by GMATClub) and a fixture in the new Veritas Prep Live Online format as well as in Los Angeles-area classrooms.  He’s beloved by his students for the philosophy “99th percentile or bust!”, a signal that all students can score in the elusive 99th percentile with the proper techniques and preparation.   In this “9 for 99th” video series, Ravi shares some of his favorite strategies to efficiently conquer the GMAT and enter that 99th percentile.

Lesson One:

Drywall vs. Door.  Many GMAT quantitative problems resemble an everyday situation you see frequently: you need to get out of this room, so are you going to break through the drywall you might be facing, or will you look for a door for easy exit? As Ravi demonstrates in this video, too often students are inclined to break through the proverbial drywall on quant problems, when looking at them from a slightly different angle would show them an open door and a cleaner exit.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Want to learn more from Ravi? He’s taking his show on the road for one-week Immersion Courses in San Francisco and New York this summer, and teaches frequently in our new Live Online classroom.

By Brian Galvin

# Start from the Beginning of GMAT Questions to Understand the Pattern

If you’ve ever walked into a conversation that was in progress, you know how hard it can be to figure out what’s going on without starting at the beginning. People often timidly ask “What are we talking about?” or “Could you please start over?” in such situations. This is because being parachuted into an ongoing conversation can be quite disorienting.

Most of the time, you can eventually figure out what’s happening, but sometimes you missed an important point near the beginning and just can’t understand the situation. As frustrating as this situation may seem, imagine if, at the end of the conversation, everyone turned to you and asked you to give your detailed opinion on the debate!

On the GMAT, you will frequently be parachuted into a situation that is already in progress. This type of scenario discombobulates most people, because we’re used to a gradual progression starting from the beginning. Since you won’t be at the beginning, you will need to figure out the beginning and the end given what you know from your position in the middle. (In essence, you’re Malcolm). You may not immediately know how to solve the issue, but you can deduce the beginning by seeing where you are in the middle and attempting to reverse engineer the process.

In many ways, this is similar to the dichotomy between multiplication and division. They are, in effect, the exact same operation (multiplying by 2 is dividing by ½ and vice versa). However, people tend to find multiplication easier because you’re going forward. Going backwards is typically harder, in no small part because your brain is not used to going in that (one) direction. When you do something a hundred times a day, it becomes second nature. If you start something for the first time on the GMAT, it may seem almost impossible to solve.

Let’s look at an example of a problem that starts you off in the middle of the action:

A term an is called a cusp of a sequence if an is an integer but an+1 is not an integer. If a5 is a cusp of the sequence a1, a2,…,an,… in which a1 = k and an = -2(an-1 / 3) for all n >1, then k could be equal to:

• 3
• 16
• 108
• 162
• 243

Sequences are excellent examples of this parachuting phenomenon because you typically need to have the previous entry in order to find the next element (like a scavenger hunt!). If you find a3, you should be able to find a4. But if you have a4, it’s a lot harder to identify a3. Since you tend to have the pattern, you have to start at the beginning to uncover the progression.

This particular sequence is made easier if you manipulate the algebra a little to get a more manageable form. Instead of the way the sequence is defined, change the pattern to an = -2/3 an-1. This small change highlights the fact that the new element is just the old element multiplied by -2/3. And since the question hinges on when the sequence changes from integers to non-integers, it’s really the denominator that will be of interest to us.

Since this is fairly abstract, let’s go through plugging in answer choice A to see what happens to the series. If k = 3, then the second element of the series would be -2/3 (3). This gives us just -2, and is still an integer. However, the next iteration, a3, would call for -2/3 (-2), which is 4/3, and not an integer. Indeed, this sequence is just calling for us to continually divide by 3, and then determine when the result will no longer be an integer. Clearly, answer choice A won’t be the right choice, as we just found that a3 was not an integer, and thus a2 would be the “cusp” as defined in the question.

Now, using the brute force approach of plugging in each answer choice will eventually yield the correct answer, but it can be tedious and time-consuming. A more logical approach would involve determining that we need a number that has many 3’s in its prime factors. Every time we divide by 3, we will get another integer, provided that we still have 3’s in the numerator. Once we’re left with a number that is not a multiple of 3, the sequence will spit out a non-integer, and the previous number will be the cusp.  Using the prime factorization of the four remaining answer choices, we get:

16 = 2^4

108 = 2 * 54 –) 2 * 2 * 27 –) 2^2 * 3^3

162 = 2 * 81 –) 2 * 3 * 27 –) 2 * 3^4

243 = 3 * 81 –) 3^5

So as we can see, one answer choice has three 3’s, the other has four and the final one has five (the seventh would be Furious). How many 3s do we actually need? Well if the fifth one must be the cusp, then we need to divide by 3 four separate times to get rid of all the 3s. After that, the fifth element will be an integer (also, an action movie), and the sixth element will be a non-integer. Since answer choice D is our educated guess, let’s double check our answer by executing the sequence on 162.

A1 = 162

A2 = -2/3 (162) = -108

A3 = -2/3 (-108) = 72

A4 = -2/3 (72) = -48

A5 = -2/3 (-48) = 32

A6 = -2/3 (32) = -64/3.

This is exactly what we wanted. We can see that each time we are multiplying the previous item by 2/3 and changing the sign. Once we get to 32, that is just 2^5 and dividing it by 3 will no longer yield an integer.

If you’d gone through the complete trial and error process, you’d quickly see that answer choices A and B are incorrect. Answer choice C, 108, comes pretty close, but cusps at A4, not A5. If you then pick answer choice D, 162, you find that you get to 108 on the second iteration, and you can skip the next four steps because you just did them. Finally, answer choice E is a tempting number to start testing with, because it is a perfect exponential of 3. However, you will get to an integer at A6, and thus you need a number with fewer 3s in the numerator.

On test day, you might be able to recognize patterns or you might have to bite the bullet and try each answer choice one by one. However, if you recognize that you need to determine what happens at the beginning before moving on to the middle and the end, you’ll have more success. You always need to understand the pattern, and that starts at the beginning. If you keep this strategy in mind, you won’t find yourself stuck in the middle (with you).

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Simplify Your Calculations on Data Sufficiency GMAT Questions

In a previous post, I emphasized the importance of minimizing the number of variables we assign when tackling word problems in Data Sufficiency. This philosophy also works quite well when dealing with complicated geometry questions. Let’s say, for example, that you had an isosceles triangle. We know that in isosceles triangles, two sides will be equal and the angles opposite those sides will be equal to each other. Rather than call the angles ‘x,’ ‘y,’ and ‘z,’ we can designate the two equal angles as ‘x.’ Because these two angles sum to 2x, the remaining angle must be 180-2x, as the interior angles of a triangle always sum to 180.  Now we have one variable to deal with, rather than three, and this greatly simplifies any future calculations we’ll have to make.

Let’s apply this logic to an extremely challenging 700+ level Data Sufficiency question*:

We’re given the following:

In the figure shown, point O is the center of the circle and points B, C, and D lie on the circle. If the segment AB is equal to the length of line segment OC, what is the degree measure of angle BAO?

• The degree measure of angle COD is 60
• The degree measure of angle BCO is 40

That is a complicated-looking figure. Your instinct might be that you don’t have time to draw it, but these kinds of questions will be designed specifically to thwart our intuition if we attempt to do too much work in our heads. So the first thing to do is draw the figure on our scratch pad, and mark the relationships we’re given. We’re told that segment CO is equal to AB, so we’ll designate that relationship. We’ll also call angle BAO, which we’re asked about, ‘x.’ Now we have the following:

Fight the impulse to jump to the statements now. In a harder question like this, we’ll benefit from taking more time to derive additional relationships from the question stem. Psychologically, this is often a struggle for test-takers. You’re conscious of your time constraint. You want to work quickly. The trick is to trust that this pre-statement investment of time will allow you to evaluate the information provided in the statements more efficiently, ultimately saving time.

Now the name of the game is to try to label as much of this figure as we can without introducing a new variable. Notice that segments CO and BO are both radii of the circle, so we know those are equal. Our diagram now looks like this:

Next, look at triangle ABO. Notice that segments AB and BO are equal. If angles opposite equal angles are equal to each other, we can then designate angle AOB as ‘x’ because it must be equal to angle BAO, as those two angles are opposite sides that are of equal length. Moreover, if the three interior angles of a triangle will sum to 180, the remaining angle, ABO, can be designated 180-2x. This gives us the following.

No reason to stop here. Notice that angles ABO and CBO lie on a line. Angles that lie on a line must sum to 180. If angle ABO is 180-2x, then angle CBO must be 2x. Now we have this:

Analyzing triangle CBO, we see that sides BO and CO are equal, meaning that the angles opposite those sides must be equal. So now we can label angle BCO as ‘2x.’ If angles CBO and BOC sum to 4x, the remaining angle, BOC, must then be 180-4x, so that the interior angles of the triangle will sum to 180.

We’ve got enough at this point that we can very quickly evaluate our statements, However, there is one last interesting relationship. Notice that angle COD is an exterior angle of triangle CAO. An exterior angle, by definition, must be equal to the sum of the two remote interior angles. So, in this case, Angle COD is equal to the sum of angles BCO and BAO. Therefore COD = 2x + x = 3x, which I’ve circled in the figure. (Triangle CAO is outlined in blue in the figure below to more clearly demarcate the exterior angle.)

That’s a lot of work. Determining all of these relationships will likely take close to two minutes. But watch how quickly we can evaluate our statements if we’ve done all of this preemptive groundwork:

Statement 1: Angle COD = 60. We’ve designated angle COD as 3x, so 3x = 60. Clearly we can solve for x. Sufficient. Eliminate BCE.

Statement 2: Angle BCO  = 40. We’ve designated angle BCO as 2x, so 2x = 40. Clearly we can solve for x. Sufficient. Answer is D.

Notice, all of the heavy lifting for this question came before we even so much as glanced at our statements.

Takeaway: For a challenging Data Sufficiency question in which you’re given a lot of information in the question stem, the best approach is to spend some time taming the complexity of the problem before examining the statements. When you work out these relationships, try to minimize the number of variables you use when doing so, as this will simplify your calculations once you’re ready to go to the statements. Most importantly, don’t do too much work in your head. There’s no need to rely on the limited bandwidth of your working memory if you have the option of putting everything into a concrete form on your scratch pad.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# GMAT Tip of the Week: Writing the AWA Without Engaging Your Brain

Writing a Friday GMAT Tip of the Week post on a tight deadline is a lot like writing the AWA essay in 30 minutes.

30 minutes is not a lot of time, many say, and because an effective essay needs to be well-organized and well-written it is therefore impossible to write a 30-minute essay.

Let’s discuss the extent to which we disagree with that conclusion, in classic AWA style.

In the first line of a recent blog post, the author claimed that writing an effective AWA essay in 30 minutes was impossible. That argument certainly has at least some merit; after all, an effective essay needs to show the reader that it’s well-written and well-organized. But this argument is fundamentally flawed, most notably because the essay doesn’t need to “be” well-written as much as it needs to “appear” well-written. In the paragraphs that follow, I will demonstrate that the conclusion is flawed, and that it’s perfectly possible to write an effective AWA essay in 30 minutes or less.

Most conspicuously, the author leans on the 30-minute limit for writing the AWA essay, when in fact the 30 minutes only applies to the amount of time that the examinee spends actually typing at the test center. In fact, much of the writing can be accomplished well beforehand if the examinee chooses paragraph and sentence structures ahead of time. For this paragraph, as an example, the transition “most conspicuously” and the decision to refute that claim with “in fact” were made long before I ever stopped to type. So while the argument has merit that you only have 30 minutes to TYPE the essay, you actually have weeks and months to have the general outline written in your mind so that you don’t have to write it all from scratch.

Furthermore, the author claims that the essay has to be well-written. While that’s an ideal, it’s not a necessity; if you’ve followed this post thus far you’ve undoubtedly seen a number of organizational cues beginning and then transitioning within each paragraph. However, once a paragraph’s point has been established the reader is likely to follow the point even if it’s a hair out of scope. Does this sentence add value? Maybe not, but since the essay is so well-organized the reader will give you the benefit of the doubt.

Moreover, while the author is correct that 30 minutes isn’t a lot of time, he assumes that it’s not sufficient time to write something actually well-written. Since the AWA is a formulaic essay – like this one, you’ll be criticizing an argument that simply isn’t sound – you can be well-prepared for the format even if you don’t see the prompt ahead of time. Knowing that you’ll spend 2-3 minutes finding three flaws in the argument, then plug those flaws into a template like this, you have the blueprint already in place for how to spend that time effectively. Therefore, it really is possible to write a well-written AWA in under 30 minutes.

As discussed above, the author’s insistence that 30 minutes is not enough time to write an effective AWA essay lacks the proper logical structure to be true. The AWA isn’t limited to 30 minutes overall, and if you’ve prepared ahead of time the 30 minutes you do have can go to very, very good use. How do I know? This blog post here took just under 17 minutes…

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

# Exploit the Gap in Logic on Critical Reasoning GMAT Questions

When dealing with strengthen or weaken Critical Reasoning questions, it’s important to have a rough idea of what the correct answer should look like. This process is often called “predicting” the correct answer, and it helps tremendously to avoid tempting but incorrect answer choices. It’s important to note that you won’t always be able to guess the exact answer choice provided, but you can get within the ballpark. After all, the correct answer is something that will hinge on the inevitable disconnect between the conclusion stated and the evidence provided in the passage.

Let’s focus on this disconnect first. If the GMAT provided you airtight arguments that were absolutely perfect, there would be no simple way to strengthen or weaken them. As such, the arguments provided inevitably have some kind of gap in logic contained between the conclusion and the evidence that theoretically supports that conclusion. Your goal is to identify that gap and either attempt to seal it up (strengthen) or rip it apart (weaken).

Of course, a dozen different answers could all weaken the same conclusion, so it’s not always possible to predict the exact answer ahead of time. However, all the answers that weaken the conclusion stem from the same gap (not banana republic) in logic, whereby the evidence provided does not quite support the conclusion stated. If you can identify the conclusion and the gap in logic, you tend to do quite well on these types of questions.

Let’s look at an example to illustrate this point:

Researchers have recently discovered that approximately 70% of restaurant lemon wedges they studied were contaminated with harmful microorganisms such as bacteria and fungal pathogens. The researchers looked at numerous different restaurants in different regions of the country. Most of the organisms had the potential to cause infectious disease. For that reason, people should not order lemon wedges with their drinks.

Which of the following, if true, would most weaken the conclusion above?

A. The researchers could not determine why or how the microbial contamination occurred on the lemon wedges.

B. The researchers failed to investigate contamination of restaurant lime wedges by harmful microorganisms.

C. The researchers found that people who ordered the lemon wedges at restaurants were equally likely to contact the diseases caused by the discovered bacteria as were people who did not order lemon wedges.

D. Health laws require lemons to be handled with gloves or tongs, but the common practice for waiters and waitresses is to handle them with their bare hands.

E. Many factors affect the chance of an individual contracting a disease by coming into contact with bacteria that have nothing to do with lemons. These factors include things such as health and age of the individual, as well as the status of their immune system.

There is a lot of text to review for this question, so let’s begin by identifying the conclusion. (Pauses an appropriate amount of time for review). The final sentence “For that reason, people should not order lemon wedges with their drinks” is the conclusion. In fact, the first three words can be removed, as they simply point to the fact that everything previous to that sentence is evidence to back up the ultimate conclusion. The passage concludes that we should not order lemon wedges (Antilles).

Let’s examine the evidence provided to back this up: 70% of the wedges observed are contaminated, and this contamination can lead to infectious diseases. Furthermore, the study was conducted in various locations across the country. This means we can’t weaken the conclusion by simply going two towns over. Apart from that, the sky’s the limit.

At first blush, this passage seems like a classic causation/correlation problem. The majority of lemon wedges are contaminated, so we shouldn’t order the lemon wedges in order to avoid falling ill. Well what if something else (say the water) was contaminated, leading to tainted lemon wedges. Then we’d avoid the wedges without avoiding the underlying cause of the diseases. In the general sense, avoiding the lemon wedges may not have the desired effect because there is nothing guaranteeing that it is solely the wedges that cause infectious diseases.

Now let’s look at the answer choices, keeping in mind that the correct answer choice should weaken the conclusion that the wedges are somehow responsible for any potential illness.

Answer choice A, “the researchers could not determine why or how the microbial contamination occurred on the lemon wedges”, doesn’t help in any real way. Just because you don’t understand how a virus works doesn’t make it any less dangerous to you (e.g. the Walking Dead). The problem is still the lemon wedges, even if no one is sure why. This answer choice can be eliminated.

Answer choice B, “the researchers failed to investigate contamination of restaurant lime wedges by harmful microorganisms” is quite obviously out of scope. Lime wedges have very little to do with lemon wedges (despite what Sprite says), so the cleanliness of the lime wedges is irrelevant to avoiding the lemon wedges. It is possible to be tempted by this answer choice if you conflate lemon with lime, especially if you’re tired, but a thorough analysis convincingly knocks this choice out.

Answer choice C, “the researchers found that people who ordered the lemon wedges at restaurants were equally likely to contact the diseases caused by the discovered bacteria as were people who did not order lemon wedges” is spot on. We had predicted that the problem was about lemon wedges being correlated to infectious disease without necessarily causing them. This answer choice tells us that people who didn’t order the lemon wedges were exactly as likely to fall sick as those who did. Therefore, avoiding the lemon wedges (the conclusion) will have no effect on your likelihood of feeling sick. This will be the correct answer, but we should look through the remaining two choices nonetheless.

Answer choice D, “health laws require lemons to be handled with gloves or tongs, but the common practice for waiters and waitresses is to handle them with their bare hands.” is almost certainly true, but does not weaken the conclusion. Newsflash: Not everyone follows health code guidelines. (I’ve seen Ratatouille). If anything, knowing such an uncouth practice is commonplace would strengthen the idea of not ordering lemon wedges. Answer choice D is incorrect, as our goal is to weaken the conclusion.

Finally, answer choice E, “Many factors affect the chance of an individual contracting a disease by coming into contact with bacteria that have nothing to do with lemons. These factors include things such as health and age of the individual, as well as the status of their immune system” is also true, but orthogonal to the issue of lemon wedges. Perhaps you could claim that healthy people have fewer risks in ordering lemon wedges, but still it would be a health risk. This answer does not weaken the conclusion in any way, and must therefore be discarded as well.

As indicated before, your prediction might not match exactly the correct answer choice, but it will exploit the gap in logic between the conclusion and the evidence. There will inevitably be (at least) one disconnect between the conclusion and the supporting evidence presented, your goal is to identify and elaborate upon that gap. If you successfully do that on test day, you can go toast your score with a celebratory drink, lemon wedges and all.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# A Simple Shortcut to Help You on the Quantitative Section of the GMAT

There are certain strategies that we all know, and yet, for whatever reason, sometimes hesitate to use during the exam. Some students are unusually skilled in algebra, for example, and so when we discuss the option of picking numbers, they dutifully nod and decide that this approach isn’t for them, that picking numbers is an unsatisfying shortcut that robs them of the opportunity to display their algebraic virtuosity.

The problem with this line of thinking is that our goal on the test isn’t simply to answer the questions correctly, but to do them within the confines of a challenging time constraint. So while it might feel more satisfying for the quantitatively-inclined to solve a complicated system of equations than it would feel to use a strategy, a strictly algebraic approach can be counterproductive, even if done correctly.

Take this Official Guide* question, for example:

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine’s average speed for the entire trip?

A. (1800 – x) /2
B. (x + 60) /2
C. (300 – x ) / 5
D. 600 / (115 – x )
E. 12,000 / ( x + 200)

Here’s what happens if we do this algebraically: let’s say that the total distance traveled is ‘D.’ If x% of the trip is spent traveling 40mph, then this distance can be represented as (x/100)*D. This means that the remaining distance, during which Francine will be traveling at 60mph, will be [1 – (x/100)]*D.

Here’s what this will look like in a standard rate table:

 R T D Part 1 40 [(x/100) * D]/40 (x/100) * D Part 2 60 [[1 – (x/100)]*D]/60 [1 – (x/100)]*D Total Ugh D

Well, good luck. Incidentally, this is how the Official Guide solves this question in their explanations. This approach will get you to the answer. But it will likely be difficult and time-consuming.

So rather than suffer through the brutal algebra required above, we can pick numbers. I always appreciate symmetry in my math problems, so let’s say that Francine went the same distance at 40mph as she did at 60mph. If this is the case, then she went 50% of the distance at 40mph, and x = 50.

Next, we can pick any distance we like for both parts of the trip. To make the arithmetic as simple as possible, let’s pick a number that’s a multiple of both 40 and 60. 120 will work nicely. Now our table will look like this:

 R T D Part 1 40 120 Part 2 60 120 Total

Life is much improved. We can see that Francine spent 3 hours going 40mph and 2 hours going 60mph, so now we can fill in the rest of the table:

 R T D Part 1 40 2 120 Part 2 60 3 120 Total R 5 240

Solving for R, we get R*5 = 240. R = 48.

Not so bad. So we know that if x = 50, the average rate should be 48. Now all we have to do is plug 50 in place of ‘x’ in all the answer choices, and once we get to 48, we’ll have our answer.

Before we proceed, let’s think about this from the perspective of the question-writer for a moment. If we were trying to make this question more challenging, where would we put the correct answer? Considering that the average test-taker will start with A and work her way down, it makes sense to put the correct answer towards the bottom of our options, as this will require more work for the test-taker. Let’s get around this by starting with E and working our way up.

E. 12,000 / (x + 200)

Substituting 50 in place of ‘x’ we get:

12,000 / 250

Rather than doing long division, I’ll rewrite 12,000 as 12*1000 to get

12*1000/250

That becomes 12 * 4 = 48. That’s what we want. We’re done. The answer is E.

Takeaway: There are no style points on the GMAT. We don’t want the approach that would most impress our fellow test-takers, we want the approach that gets us the right answer in the shortest amount of time. Percent questions that involve variables are excellent opportunities for simplifying matters by picking numbers.

Moreover, when we find ourselves in a situation that requires testing the answer choices, we want to remember that the problem will be more challenging if the correct answer is D or E, so while this won’t always be true, it is the case often enough that it’s beneficial to start by testing E and systematically working our way up. As soon as we have our answer, we’re finished. We can save the impressive mathematical flourishes for our finance classes.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# When Do You Have Enough Information on Data Sufficiency GMAT Questions?

Habitually, data sufficiency questions give students cause for concern on the GMAT quantitative section. This is primarily due to the fact that data sufficiency questions are rarely seen in high school and college, and are therefore relatively unknown to most prospective test takers.  If you remember the first data sufficiency question you encountered while studying for the GMAT, it may have looked like it was written in another language.

In many ways, data sufficiency questions are like being in a foreign land. Even if you understand the rules, you’re often not as comfortable as in your native environment that you’ve acclimated to over many years (e.g.  an Englishman in New York). It is normal to feel a little discombobulated, especially at first. However, once you’ve done a few (hundred) data sufficiency questions, you tend to get a feel for the question type. One issue still eludes a lot of test takers: When is it enough?

Data sufficiency is asking about (drum roll, please) when the data is sufficient. It’s pretty easy to disprove something if you can find a counter-example right away, but if you struggle with finding definitive proof, how long should you try to work at it.

Suppose a question asks whether X^2 = Y^3, that is asking whether any perfect square is also a perfect cube, you could spend a lot of time meandering towards a solution. What if we try 2^3, which gives 8? Well 8 isn’t a perfect square of any number, so we keep going. 3^3 is 27, which isn’t a perfect square of any number either. How far should we go? The next number, 4^3, gives 64, which is a perfect square, so we found an example relatively quickly, but we could conceivably spend several minutes calculating various permutations. Imagine a question asking if X^2 = Z^5 and see how long it would take to find an example.

The good news is that the question is almost always solvable using logic, algebra and mathematical properties. The bad news is it’s not always obvious how to proceed with these definitive approaches, and the brute force strategy is often employed. We can try various options and see if any of them work, while at the same time looking for patterns that tend to repeat or signal the underlying logic of the situation. While this strategy certainly has its place, it can sometimes be very wearisome.

Let’s look at a data sufficiency question that highlights this issue:

W, X, Y and Z represent distinct integers such that WX * YZ = 1,995. What is the value of W?

WX

* YZ

_____

1,995

• X is a prime number
• Z is not a prime number
• Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
• Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
• Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
• Each statement alone is sufficient to answer the question.

This question can be very tempting to start off with brute force. We can limit our choices by looking at the unit digits. If the unit digit of the product is 5, then there are only a few digits that are possible for X and Z. They all have to be odd, and, more than that, one of them must be exactly 5, as no other digits combine to give a 5. If one of them is 5, the other one is some odd number, 1, 3, 5, 7 or 9. Unfortunately, multiple options exist at both prime (3, 5 and 7) and non-prime (1, 9) for these digits, so it will be hard to narrow down the choices (where’s a dart board when you need one?)

Let’s look at this problem another way, which is: these two numbers must multiply to 1,995. We know one number ends with a 5, so we arbitrarily set it to be 25 and see what that gives if we set the other number to be 91. That comes to 2,275, which is way above what we need. How about 25 * 81, that yields 2,025. That’s too big, but just barely. How about 25 * 79? That will give us 1,975, which is slightly too small. We can’t get 1,995 with 25, but that’s all we’ve demonstrated so far. We can eliminate some choices as number like 15 can never be multiplied by a 2-digit number and yield 1,995, but there are still numerous choices to test.

It’s pretty easy to see how the brute force approach when you have dozens of possibilities will be very tedious. There’s another element that’s even worse, which is let’s say you manage to find a combination that works (such as 21 * 95), how can you be sure that this is the only way to get this product? Short of trying every single possibility (or calling the Psychic Friends hotline), you can’t be sure of your answer.

This problem thus requires a more structured approach, based on mathematical properties and not dumb luck. If two numbers multiply to a specific product, then we can limit the possibilities by using factors. We thus need to factor out 1,995 and we’ll have a much better idea of the limitations of the problem.

1,995 is clearly divisible by 5, but the other number might be hard to produce. The easiest trick here is to think of it as 2,000, and then drop one multiple of 5. Since 2,000 is 5 x 400, this is 5 x 399. Now, 399 is a lot easier than it looks, because it’s clearly divisible by 3 (since the digits add up to 21, which is a multiple of 3). Afterwards, we have 133, which is another tough one, but you might be able to see that it’s divisible by 7, and actually comes to 7 x 19. Finally, since 19 is prime, we have the prime factors of 1,995: 3 x 5 x 7 x 19.

How does this help? Well there may be 16 factors of 1,995, but the limitations of the problem tell us that we only have two two-digit numbers. Thus something like 15 * 133 breaks the rules of the problem. Our only options to avoid 3-digits are 19*3 and 5*7 or 19*5 and 3*7. This gives us either 57 * 35 or 95 * 21. At least at this point we’re 100% sure that these are the only two-digit permutations that combine to give 1,995.

Let’s get back to the problem. Statement 1 tells us that X (the unit digit of the first number) is prime, which knocks out 21 from the running. However the three other options all end with a prime unit digit, meaning that any of them are still possible. At this point it’s very important to note that the problem specified that W, X, Y and Z were all distinct integers. Since they must all be different, the option of 57 * 35 is not valid because the 5 is duplicated. As such, the only option is 95*21, and the prime number restriction confirms that it’s really 95 * 21 (and not 21 * 95). Variable W must be 9, and thus this statement ends up being sufficient.

Statement 2 essentially provides the same information, as Z is not a prime number and thus necessarily 1 given our choices. This confirms that the multiplication is 95 * 21 and W is still 9. Either statement alone is sufficient, so answer choice D is the correct option here. It’s important to note how close this question was to being answer choice B, as the non-prime limitation ensured we knew where the 1 was. But the fact that these digits had to be distinct changed the answer from B to D, reinforcing the adage that you should read the questions carefully.

This question can be solved without factors, but it is very hard to confidently answer it using only a brute-force approach. Solving through mathematics and number properties is not always the easiest route to success on data sufficiency. Sometimes you can write down a few options and see exactly how the problem will unfold, but if you use concrete concepts, you’ll know when it’s been enough.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Take Notes on Critical Reasoning Questions to Increase Your GMAT Score

Imagine that you were tasked with writing questions for the GMAT. You have to produce questions that have a clear answer but will trip up a certain percentage of test-takers. How do you do that reliably? The most straightforward way I can think of is to simply inundate the test-taker with information. What elicits the loudest groans during Reading Comprehension? Long, technical passages. What is the most unpleasant thing to see in a Data Sufficiency question? Lots of complex information in the question stem.

It’s not that these questions are asking you to do hard things, but the information overload makes it hard to determine what it is that you have to do. In fact, there is a vast body of literature demonstrating that the human brain has fairly circumscribed limits when it comes to working memory. Certain questions are designed to exploit this hard-wired deficit.

So how do we combat the brain’s working memory limitations? As we learn more and more about how working memory functions, researchers have discovered effective techniques for improving it. One technique, which I mentioned in a previous post, is mindfulness meditation. Another proposed technique is the judicious use of certain kinds of brain-training games. (Note that the research on the efficacy of brain training is decidedly mixed. Some studies show a robust improvement in general fluid intelligence. Other studies conclude that the improvements participants make in the game are not transferrable to other realms. I’ll explore this in more detail in a future post.)

Though I am a proponent of practicing mindfulness – both for improving standardized test scores and for boosting our mental and physical health – and I certainly have nothing against brain-training, the best way to combat the strain that the GMAT puts on our working memory is simply to write things down. There’s no need to juggle all the dizzying elements in a complex question in your head. Break hard questions into smaller, more manageable bites.

Consider the following GMATPrep* Critical Reasoning argument.

Kernland imposes a high tariff on the export of unprocessed cashew nuts in order to ensure that the nuts are sold to domestic processing plants. If the tariff were lifted and unprocessed cashews were sold at world market prices, more farmers could profit by growing cashews. However, since all the processing plants are in urban areas, removing the tariff would seriously hamper the government’s effort to reduce urban unemployment over the next five years.

Which of the following, if true, most seriously weakens the argument?

1. Some of the by-products of processing cashews are used for manufacturing paints and plastics
2. Other countries in which cashews are processed subsidize their processing plants
3. More people in Kernland are engaged in farming cashews than in processing them
4. Buying unprocessed cashews at lower than world market prices enables cashew processors in Kernland to sell processed nuts at competitive prices
5. A lack of profitable crops is driving an increasing number of small farmers in Kernland off their land and into the cities

When I read this and try to internalize all the information, I can actually feel the strain. It’s unpleasant. So let’s boil this way down. When there is a tariff, domestic farmers are forced to sell to domestic producers. This is bad for farmers because they don’t have access to all relevant markets, and it’s good for domestic producers, because they’re competing against fewer potential buyers. As an arrow diagram, it might look like this:

Tariff –> hurt farmers –> helps domestic producers

The argument is about removing the tariff, which would, presumably, produce the opposite result. Now the farmers benefit because they have an additional market to sell to, and the domestic producers are harmed because they have to compete with foreign producers to buy the raw cashews. Our new arrow diagram would look like this:

No Tariff –> helps farmers –> hurt domestic producers.

The argument’s conclusion is that because removing the tariff will harm the domestic producers, the end result will be rising unemployment in cities. So we can tack that on to the arrow diagram:

No Tariff –> helps farmers –> hurt domestic producers –> rising unemployment in cities

If we want to weaken this argument, we want an answer choice that shows that removing the tariff will not cause unemployment to rise in cities, but rather, that not having a tariff might be good for the urban employment rate. (And note the scope here: we’re talking about urban unemployment. Attention to language detail is always crucial in CR questions).

1. Hard to see how the use of the by-products will shed much light on urban unemployment. Out of Scope.
2. Other countries? We’re talking about urban unemployment in Kernland. Out of scope.
3. This one is interesting. We know that removing the tariff benefits farmers. If more people are farming than processing, it stands to reason that more people benefit from the tariff’s removal. But does this tell us anything about urban unemployment? The farmers don’t live in the city. The producers do. So if those producers are hurt, urban unemployment can still go up, even if they’re outnumbered by farmers. No good.
4. We’re told specifically that if the tariff were lifted, cashews would sell “at world market prices.” Any benefit from selling at below market prices could only be realized if there were a tariff. But we’re trying to show that removing the tariff is a good thing! This answer choice does the exact opposite.
5. This is correct, but requires a little unpacking. Remember that the tariff hurt the farmers. So back in the tariff days, the farmers were struggling, and, according to this answer choice, were forced to flee to the cities. There’s no reason to believe that these farmers had jobs waiting for them, so this chain of events would raise urban unemployment. But, if we remove the tariff, the farmers benefit, and if farmers are doing well, they won’t have to flee to the city, which would actually reduce Exactly what we want. (Note also that we’re talking about urban employment. This is the only answer choice that even mentions cities.)

This was a tough one. The point here is that the best way to grapple with complexity is to distill information into digestible bits. Write down what you want in a single phrase or two. A full paragraph laden with terminology can be hard to work with. A simple arrow diagram, like “No tariff –> lower urban unemployment” is far more manageable. You have a scratch pad for a reason – to give your working memory a break.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here.

# Find Logical Meaning in Sentence Correction Questions on the GMAT

One of the hardest things about Sentence Correction is that it tests so much more than just grammar. Many students erroneously conflate Sentence Correction problems with high school grammar problems, and this can lead to avoidable mistakes on test day. Indeed, the rules you learned in high school still apply, but you must be able to recognize them among various other potential problems.  It’s fairly simple to spot an agreement error on a verb (there are one problem) or a misplaced comma (good, job bro), but sometimes you have to eliminate an answer choice because the sentence just doesn’t make sense.

Think about a sentence like “This table has four arms.” Grammatically, the sentence is flawless (although I use the term loosely). However, from a logical point of view, it doesn’t make any sense at all. Tables are colloquially said to have “legs,” even if these don’t exactly fit the Darwinian definition of the term, but they are not typically said to have “arms”. On the GMAT, this sentence is as incorrect as “This table have four arms,” but it’s much harder to see for most people. The error lies not in the grammar, but in the meaning.

In fact, there are two broad categories of illogical meanings on the GMAT. The first is the type described above: A sentence that just doesn’t make sense. The second type can be more subtle, as it constitutes the array of answer choices that change the meaning of the sentence. This error often occurs when the structure of the sentence is changed and no longer meshes with the rest of the sentence. A typical example would be changing from “Human beings have skulls…” to “The skulls of human beings”… Within the underlined portion, everything can seem fine. But if the rest of the sentence is discussing how human beings are remarkable adaptable creatures, this simple switch can have serious ramifications as it changes the meaning dramatically. Originally, human beings were remarkable creatures. Now only their skulls are remarkable creatures, which is completely nonsensical and thus not a valid sentence on the GMAT.

Let’s look at an example and see if we can keep the meaning of this sentence.

The Buffalo Club has approved tenets mandating that members should volunteer time to aid the community.

A) that members should volunteer time

B) that time be volunteered by members

C) the volunteering of time by members

D) members’ volunteering of time

E) that members volunteer time

This sentence is not particularly long, and the underlined portion is only five words, so each word should be weighed carefully. Most of the words are not underlined, so the sentence tells us that the Buffalo Club is mandating something specific, and the goal of this endeavor is to aid the community. The only options we have are the few words (Malcolm) in the middle of the sentence.

Using the original sentence (answer choice A) as a benchmark, we see that the club is mandating that members should volunteer their time. This sentence doesn’t have a glaring grammatical error, but the logical error here is quite noticeable. Mandating something means that it is required, so the verb “should” is illogical within the sentence. It’s like telling someone that they’ve arrived late to work for the past two weeks, and that they’re definitely fired. Maybe. Answer choice A is illogical because the word “should” contradicts the logic of the sentence and undermines the entire message.

Answer choice A is the only one to use the word “should”, so we cannot use that decision point to knock out any other choices. However, A does correctly begin with the word “that”, which is a correct idiom to be used with mandated. When something is mandated, it must either be “The club mandated that Ron win” or “the club mandated the victory be awarded to Ron”. Either way, the directive must be clear, and Ron must be declared the victor (now that’s what I call a win-win situation). Answer choices C and D can be eliminated because they do not follow either idiom of the verb, and the meaning of the sentence is distorted.

This only leaves answer choices B and E. Let’s evaluate answer choice B first, and we quickly notice that the sentence is more verbose than it needs to be. Furthermore, the sentence is switched to the passive voice because “time” is now the subject of the sentence, not “members”. Since the members are being mandated to do something, they must be the subject of the sentence, not the time they are volunteering. Answer choice B can be eliminated.

This leaves only answer choice E, and it is indeed the correct answer. Comparing it with answer choice A, it is exactly the same, except that it removes the superfluous “should”. In reality, the members are being mandated to help out the community, and this is non-negotiable (House of Cards’ Victor Petrov style) so there is no room for ambiguity by adding in a rider.

On the GMAT, the difference between a correct answer and an incorrect answer often comes down to which selection actually makes sense. Nowhere is this more common than on sentence correction problems, where the inclusion or exclusion of one word can dramatically alter the meaning of a phrase. Indeed, if you master the strategies of logical meaning on the GMAT, you will (not should) do well on the exam.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Succeed on Critical Reasoning GMAT Questions with This Causation Tip

Oh, causation on the GMAT.  Why do you cause so much stress in people’s lives?

Success on many Critical Reasoning questions really comes down to understanding whether one thing (“X”) causes another thing (“Y”) or not. For example, I moved to New York in 2007. Shortly thereafter, there was a huge drop in the New York stock market. Did I cause the crash (Y) simply by moving to New York (X)?

Of course I did! But that’s beside the point.

Take a look at the following question from an MBA.com practice CAT:

The growing popularity of computer-based activities was widely predicted to result in a corresponding decline in television viewing. Recent studies have found that, in the United States, people who own computers watch, on average, significantly less television than people who do not own computers. In itself, however, this finding does very little to show that computer use tends to reduce television viewing time, since_______.

Which of the following most logically completes the argument?

Let’s not even look at the answer choices yet. We can do quite a bit of “pre-work” on a question like this before the answer choices begin to sway us in various directions.

In the simplest terms, the argument states that some believe:

An Increase in Computer Usage (ICU) causes a Decrease in Television Watching (DTW).

And this makes some logical sense, right? We only have a certain number hours per day, and if we spend some time on our laptops, we might not have as much time to catch up on Girls and Shark Tank.

The argument then goes on to state a bit of evidence that seems to support the initial prediction:

Computer Owning (not quite the same as ICU, but in the same ballpark) actually correlates with Watching Less Television (DTW).

However, the argument then, a bit paradoxically, states that even though “Computer Owning and DTW” seem to happen at the same time, it is not the case that “ICU causes DTW.” Interesting.

Well, whenever you see a case like this on the GMAT, you’re better off coming up with a possible answer or two before checking out the answer choices. When the GMAT says that “X and Y happen together, but X did not cause Y,” a very strong possibility is that “Z” actually caused Y. What is Z? Z is anything else that might have caused Y.

Here are some possible answer choices that would work:

• People can generally only afford either one computer or one television (implying that ICU doesn’t cause the DTW, but the price of a computer might).
• Computer owners tend to be overworked professionals who have very little leisure time (implying that ICU doesn’t cause DTW, but a pre-existing condition of computer owners is strongly correlated with DTW before the computer usage is even mentioned).
• Computers create an electromagnetic field that disables televisions from turning on (implying that ICU doesn’t cause DTW, but the physical properties of owning a computer might).
• Computer owners, at the point of purchase, were forced by the Illuminati to sign a document swearing never to watch television under the penalty of jail time (implying that ICU doesn’t cause DTW, but intense pressure from an underground fraternity might).

At this point, you might be saying, “Whoa, those answers were totally out of left-field.” Indeed, you’re right. When the argument concerns X’s and Y’s, and we’re looking for a Z (something else that might have caused Y), then the correct answer might very well be out of left-field. Do not eliminate an answer simply because it seems random or unexpected. Instead, simply focus on the chain of logic. If your out-of-left-field Z supersedes X as the primary cause of Y, you’ve done a great job of weakening the causal link between X and Y.

Now let’s look at the real answer choices:

(A) many people who watch little or no television do not own a computer.

(B) even though most computer owners in the United States watch significantly less television than the national average, some computer owners watch far more television than the national average.

(C) computer owners in the United States predominately belong to a demographic group that have long been known to spend less time watching television than the population as a whole does.

(D) many computer owners in the United States have enough leisure time that spending significant amounts of time on the computer still leaves ample time for watching television.

(E) many people use their computers primarily for tasks such as correspondence that can be done more rapidly on the computer, and doing so leaves more leisure time for watching television.

Boom. Answer choice C basically says that ICU doesn’t necessarily cause DTW, because the demographics of computer users correlate strongly with DTW independently of actually using the computer. While this answer choice does not exactly provide a direct cause of DTW, it does strongly weaken the causal link between ICU and DTW, and that should be your main goal.

Does a “Z” always represent the answer on GMAT causation weakeners? Not always, but it occurs frequently enough that it’s worth spending 5-10 seconds coming up with one or two Z’s on a question like this. If nothing else, doing so can help solidify a more complete understanding of the argument.

Hopefully this Blog Post (BP) will cause you to Do Well on Your GMAT (DWYG). When was the last time BP caused something good to happen?

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Ingber

# How a 99th Percentile GMAT Instructor Approaches Sentence Correction Questions

The other night, in class, I had a student come up to me and ask how I really approached Sentence Correction. We’d done our Sentence Correction lesson a few weeks before, so the implication was that there was a little more to it than the framework we’d covered. The mundane truth is that there isn’t. Not really.

When I’m evaluating an SC problem, and nothing jumps out at me immediately, I really do run through the mental checklist we discuss in the lesson: is the meaning logical? Are the modifiers placed appropriately? Is there an issue with parallel construction? Etc. But I saw what this student was saying. In class, we move systematically from one kind of error to another, so they’re much easier to classify than when you’re taking a test and the sentence’s errors either aren’t terribly conspicuous or encompass multiple categories.

As much as I like to preach that it’s best to attack these questions systematically, no test-taker is an algorithm, so I thought it would be worthwhile to go through a few official examples and discuss how my approach, while always rooted in the framework I teach in class, leaves some room for instinctive adjustments. Put another way, the GMAT is a test of pattern recognition. If the pattern is immediately apparent, I think about a question one way, and if it isn’t obvious, my strategy shifts accordingly.

Here’s one example from the Official Guide where the pattern is pretty conspicuous.

Published in Harlem, the owner and editor of The Messenger were two young journalists, Chandler Owen and A. Philip Randolph, who would later make his reputation as a labor leader.

(A) Published in Harlem, the owner and editor of The Messenger were two young journalists, Chandler Owen and A. Philip Randolph, who would later make his reputation as a labor leader.

(B) Published in Harlem, two young journalists, Chandler Owen and A. Philip Randolph, who would later make his reputation as a labor leader, were the owner and editor of The Messenger.

(C) Published in Harlem, The Messenger was owned and edited by two young journalists, A. Philip Randolph, who would later make his reputation as a labor leader, and Chandler Owen.

(D) The Messenger was owned and edited by two young journalists, Chandler Owen and A. Philip Randolph, who would later make his reputation as a labor leader, and published in Harlem.

(E) The owner and editor being two young journalists, Chandler Owen and A. Philip Randolph, who would later make his reputation as a labor leader, The Messenger was published in Harlem.

In this case, the ol’ lizard brain jumps immediately into action. Anytime a sentence begins with an –ing or –ed verb, I’m immediately thinking about participial modifiers. This sentence begins with a the participal “published” so I know right away that I want who or what is published to immediately follow the phrase.  Well, it makes most sense to say that The Messenger was published, so I want The Messenger to come right after that initial participial phrase. The answer is C. In this case, after you’ve done dozens and dozens of examples that involve misplaced participles, the issue is glaring. For many test-takers, there’s no need to systematically go through that internal checklist. You’ll still want to read your answer choice with the original sentence and make sure the meaning is logical, etc. but you don’t have to process this problem with the kind of comprehensive rigor you’ll need for more challenging problems.

Now consider this Official Guide problem, which, to me, isn’t categorized nearly as easily as the previous example:

Over 75 percent of the energy produced in France derives from nuclear power, while in Germany it is just over 33 percent.

(A) while in Germany it is just over 33 percent

(B) compared to Germany, which uses just over 33 percent

(C) whereas nuclear power accounts for just over 33 percent of the energy produced

in Germany

(D)whereas just over 33 percent of the energy comes from nuclear power in Germany

(E) compared with the energy from nuclear power in Germany, where it is just over 33 percent

The original sentence doesn’t feel right to me, but it’s not as immediately evident what the problem is. So now I have to be a bit more systematic. Okay, maybe the answer choices will offer some clues. Still not obvious, but I do notice that B and E have the word “compared,” which means one potential issue is an inappropriate comparison. I also notice that the word “it” appears in A and E, so maybe there’s a pronoun issue. With these notions in mind, I’ll start going through my mental checklist. First, is the meaning logical, and if not, is a faulty comparison or inappropriate pronoun to blame?

The first thing I ask myself is “what does the “it” refer to?” Is the original sentence really saying, “Over 75 percent of the energy produced in France derives from nuclear power, while in Germany the energy produced in France is just over 33 percent?” That doesn’t make sense. So A is out because of illogical meaning/inappropriate pronoun.

Now in B, we see “compared.” Read literally, the sentence seems to be comparing the percent of energy produced in France to Germany, the country. That’s no good. We’d like to compare energy to energy and country to country. B is out.

C jumps out at me because we’ve eliminated both “compared” and “it.” “Whereas” signals a new clause entirely. So I have the first clause: Over 75 percent of the energy produced in France derives from nuclear power. And then I get a second clause: nuclear power accounts for just over 33 percent of the energy produced in Germany. The meaning is clear. Additionally, there seems to be a nice parallel construction, both clauses containing a variation of: X% of energy produced in Y. Not something I noticed initially, but a promising development. Hold onto C.

D also eliminates “compared” and “it,” so I need to focus on meaning here. If I read this literally, it seems to say 33% of the energy in France comes from nuclear power in Germany. Well, that would be an awfully generous gesture by Germany, but I can’t imagine this is the intended meaning of the sentence. D is out.

E We see “compared” again. Here, we seem to be comparing the percent of energy produced in France to the energy in Germany. So that’s not really logical. We’d want to compare the percent of energy produced in France to the percent of energy produced in Germany. And then that last phrase, ”where it is just over 33 percent” is a bit mystifying. 33% of what? Is “it” referring to Germany or to energy? E is out.

And we’re left with C.

Notice that on a superficial level, I’m using the same general principles for both of these questions, but my thought process looks a lot different when the problem is obvious than when the underlying issue is a bit more obscure. So our goal as test-takers is first, to do enough practice problems that we become adept at recognizing conspicuous patterns like the one we saw in the first example. And second, we want to have a systematic approach to address more complicated questions when they arise. A single approach or mindset just won’t work for every single question – the GMAT isn’t that kind of test.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# How to Avoid Tedious Calculations on the Quantitative Section of the GMAT

One of the hardest things for people to get used to on the GMAT is that there is no calculator for the quantitative section. The reasoning behind this is simple: human beings will not be faster than machines at pure calculations. Human beings, however, will be better at logic, reasoning and deduction than a machine (at least until Skynet is developed).

The GMAT wants to determine how good the test taker is at solving problems through logic and analytical reasoning, not brute strength. Despite this stated goal, the GMAT frequently features questions that can turn students into mindless calculators. The goal is to avoid falling for this sinister trap and solving the problem with sound strategy and logical applications of mathematical theory.

The quintessential large calculation will be something like “Multiply all the integers from 1 to 10” (or more succinctly, find 10!).  Now, such a calculation is possible within the 2 minutes we typically have to solve a question, but even when you get the result, there is often another portion to the question that must be solved. Even if the end goal is just to find one number, the brute force approach is time-consuming and error-prone (and frequently cramps up my hand). You are much better off approaching the problem using either order of magnitude or unit digit properties.

Generally speaking, asking someone to compute 10! can be tedious. However, the GMAT is in fact asking you which of the five choices provided is 10! The answer choices provided are typically fairly far apart, so an approach that cares only about the order of magnitude of the answer will help narrow down the possibilities tremendously. Sometimes there may still be two contending answer choices, and additional calculations may be required to confirm which one is correct.

For 10!, we can calculate the small numbers easily and approximate the rest. You can get much more detailed than this, but 5! = 120, and then multiplying by 6 and then 7 is like multiplying by 5 and then 5 again, so 120 x 25 = approximately 3,000. Multiplying by 8, 9, and then 10 is like multiplying by 10 thrice, so the answer will be somewhere around 3,000,000. I approximated a couple of numbers up and a couple of them down to somewhat balance out. You can approximate more closely to reality but you should still get an answer in the same ballpark (actual retail price: 3,628,800).

Another potential shortcut is to consider only the unit digit. The answer choices will tend to be far apart and have different unit digits, so if you can calculate which number should be the unit digit, you can eliminate several answers quickly. In our case, we know we’re multiplying by 10, so the unit digit will be zero. Furthermore, we are multiplying by 5 as well, and there are many 2’s (including 2 itself), so there will be a second zero as a tens digit. In this case knowing factors simplified the process, but even trying to figure out the unit digit of 2^88 is simply an exercise in pattern recognition.

The above example may have been somewhat abstract as there were no answer choices to compare, so let’s look at an actual GMAT question and apply these same strategies:

A small cubical aquarium has a depth of 1 foot. In the small aquarium there is a big fish with volume 44 cubic inches. A big cubical aquarium has a depth of 2 feet and 88 fish, each with a volume of 2 cubic inches. What is the difference in the amount of water between the two aquariums if they are both completely filled? (Note: 1 foot = 12 inches)

• 246 cubic inches
• 300 cubic inches
• 11,964 cubic inches
• 13,824 cubic inches
• 16,348 cubic inches

This question is considered geometry because it’s dealing with a 3-dimensional shape, but the question is primarily concerned with converting cubic feet to cubic inches. As such, the question is really asking for a laborious calculation. Therefore, we need to find a shortcut to avoid spending the rest of the hour calculating cubic inches in our aquarium. (Hey, fishy fishy fishy!)

A cubical aquarium with three sides of 1 foot is 1 cubic foot (or foot^3), but that doesn’t help much in terms of cubic inches. The easiest thing is to convert to inches from the get go, which leaves us with a cube that has height, width and depth of 12 inches. Since the formula for the volume of a cube is side^3, we know that the volume of the aquarium is 12^3 cubic inches. 12^2 is easy, so now we must multiply 144 by 12. It might take a few seconds, but we can break it down to 144 x 10 + 144 x 2, which yields a total of 1,728 cubic inches.

At this point, a lot of people would think about removing the volume that is being filled by the big fish. While this is technically correct, if we’re considering this problem from an order of magnitude point of view, it will be a drop in the bucket (or aquarium), taking the total volume from 1,728 down to 1,684 if you subtract 44 cubic inches. Both of these numbers are essentially 1,700, so there’s not much value in taking the time to remove the fish. I’m more concerned with shortcutting the calculation for the big aquarium.

The big aquarium has sides of 2 feet, or 24 inches. This means that it will be twice as wide, twice as tall and twice as deep as the small aquarium, leading to an overall eight-fold increase from the original aquarium. This means that I can take the 1,728 I calculated earlier and multiply it by 8 to get the total volume (sans fish) of the big aquarium. However, the problem eventually asks for the difference in water between the two aquariums (or aquaria), which means I’ll have to take the 8Y volume and subtract the original Y volume. This means we’re better off shortcutting the calculation and just multiplying the original volume by 7. It’s tantamount to saying I’ll lend you 100\$ then you lend me 20\$. I think we can just make one transaction for 80\$ and call it a day.

Multiplying 1,728 by 7 isn’t necessarily trivial, but remember that we’re mostly interested in the order of magnitude of the answer. This means we can ignore some digits and think of it as approximately 1,700 x 7, which is (1,000 x 7 =) 7,000 + (700 x 7=) 4,900, yielding a total of about 11,900. It should be a little higher than this because we rounded 1,728 downward. This is almost exactly answer choice C, with answer choice D looking about 1,700 bigger and thus likely the volume of the bigger aquarium only. The other three answer choices are way off.

At this point we’re essentially done, but you can confirm the number, particularly with the consideration of the fish (plural but hard to tell). The volume of the small aquarium is 1,728, and of the big aquarium is indeed 13,824 cubic inches. If we subtract the 44 cubic inch fish from the small aquarium, we get 1,684. If we subtract the 176 cubic inches (88×2) of the big aquarium fish, we get 13,648. Finding the difference of these two numbers yields exactly 11,964 cubic inches. Answer choice C is correct, but you don’t have to meticulously calculate every element in order to know it given the five choices provided.

It’s worth noting that unit digits don’t help much on this problem. The smaller aquarium has a volume of 12^3, and the 2^3 unit digit will yield an 8. Subtracting the 44 cubic inches for the fish (which we must do if we’re being precise), the water in the small aquarium should end with a 4. The big aquarium has a total volume of 24^3, which will give a unit digit of 4. Subtracting the 176 cubic inches for the fish leaves us with a unit digit of 8. Finally, subtracting the 4 of the little aquarium from the 8 of the big aquarium means the answer choice must end with a 4. Despite all that abstract and confusing math, we still can’t choose between answer choices C and D, and must therefore perform additional calculations.

Sometimes the GMAT likes to ask questions that would take 15 seconds if you had a calculator, but 5 minutes if you stubbornly decided to use an inflexible brute force approach. Sometimes unit digits will be faster, and sometimes order of magnitude will be faster, but both have their place in your tool belt. Each question on the GMAT is like a door, and you may be able to knock down the door with brute strength, but you’ll go faster with a deft touch (also: fewer shoulder surgeries).

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# The Pitfalls of Confusing Correlation and Causation on GMAT Critical Reasoning Questions

In Stephen Pinker’s book, The Blank Slate, there’s an entertaining discussion illustrating the pitfalls of confusing correlation and causation. Pinker cites an old Russian folktale in which a Tsar discovers that, of his many provinces, the one that has the highest disease rate also has the most doctors. So he orders all the doctors killed. I’ll often make reference to this passage when I’m teaching Critical Reasoning because the absurdity of the argument is immediately apparent. Just because two variables are correlated, it doesn’t mean that one is necessarily causing the other.

Causality arguments show up frequently on the GMAT and they can be quickly encapsulated with a simple arrow diagram. So the above discussion involving the Tsar could be depicted on scratch paper like so:

Doctors –> Disease

x –> y

Typically, if we need to weaken one of these arguments, we’ll do so in one of two ways. First, it’s possible that cause and effect are reversed. Here it would mean that the disease was causing the doctors to come to the province. In arrow diagram form, it would look like this:

Disease –> Doctors

y –> x

Secondly, there may be a different underlying cause. In the case of our folktale, maybe it’s the case that poor sanitation is causing the disease.

Poor sanitation –> Disease

z –> y

To summarize: whenever we see a causality argument that needs to be weakened, we can distill it into an arrow diagram and then search for one of the two above scenarios.

Here’s an example from the Official Guide:

In the last decade there has been a significant decrease in coffee consumption.  During this same time, there has been increasing publicity about the adverse long-term effects on health from the caffeine in coffee.  Therefore, the decrease in coffee consumption must have been caused by consumers’ awareness of the harmful effects of caffeine.

Which of the following, if true, most seriously calls into question the explanation above?

A. On average, people consume 30% less coffee than they did 10 years ago.
B. Heavy coffee drinkers may have mild withdrawal symptoms, such as headaches, for a day or so after, significantly decreasing their coffee consumption.
C. Sales of specialty types of coffee have held steady, as sales of regular brands have declined.
D. The consumption of fruit juices and caffeine-free herbal teas has increased over the past decade.
E. Coffee prices increased steadily in the past decade because of unusually severe frosts in coffee-growing nations.

This one is straightforward enough to diagnose – we actually get the phrase “caused by” in the argument! As an arrow diagram, it looks like this:

Awareness of harmful effects of caffeine –> decrease in coffee consumption

According to our earlier analysis, this can be weakened in one of two ways. If cause and effect were reversed, the diagram be:

Decrease in coffee consumption –> Awareness of harmful effects of caffeine

Well, that doesn’t make sense. How could a decrease in coffee consumption cause a heightened awareness of the ill effects of caffeine? So we must be looking for an alternative cause:

Something else –> decrease in coffee consumption.

So that’s what we’re after: that alternative underlying cause.

A. On average, people consume 30% less coffee than they did 10 years ago.

There’s no different underlying cause here. In fact, this is reiterating the notion that coffee consumption has decreased. We already knew this. Eliminate A.

B. Heavy coffee drinkers may have mild withdrawal symptoms, such as headaches, for a day or so after, significantly decreasing their coffee consumption.

This isn’t an alternative reason for why people are drinking less coffee. In fact, the unpleasant withdrawal symptoms would be a pretty compelling reason to continue drinking plenty of coffee! Eliminate B.

C. Sales of specialty types of coffee have held steady as sales of regular brands have declined.

Again, no real alternative cause presented here. And, logically, this doesn’t weaken the argument at all. It’s certainly possible that while many coffee drinkers have cut back on their coffee consumption, the kind of aficionados who drink specialty coffee will continue to drink their double latte espressos without reservation. Eliminate C.

D. The consumption of fruit juices and caffeine-free herbal teas has increased over the past decade.

This one is often tempting. Students sometimes argue that it’s the appeal of fruit juices that is the alternative underlying cause we’re looking for. The problem is that we’re trying to weaken the argument, and this answer choice really isn’t incompatible with the conclusion. To see why, imagine that the argument is true: people find out that caffeine is bad for them, and so drink less coffee. It would be perfectly reasonable for them to then replace that morning coffee with alternatives like fruit juice and herbal tea. In other words, the increase in the consumption of other beverages wouldn’t be a cause of the decrease in coffee, but rather, a consequence of that decrease. D is out.

E. Coffee prices increased steadily in the past decade because of unusually severe frosts in coffee-growing nations.

Now we have our alternative cause. Perhaps it’s not the awareness of the ill effects of caffeine that’s caused this drop in coffee consumption, it’s an increase in price. The new arrow diagram looks like this:

Increase in price –> Decrease in consumption

And this makes perfect sense. E is our answer.

The takeaway: A simple arrow diagram can powerfully simplify the logic of any causality argument.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here

# What Figure Skating Can Teach You about GMAT Sentence Correction Questions

Like many Americans, I get caught up in figure skating for exactly two weeks every four years. It’s a fascinating sport, but because I don’t follow it consistently, as I do with the NBA and NFL, I really have no idea how the figure skaters are being judged.

I see what appears to a be hiccup in the routine; the announcer says that it was a flawless set-up for an impressive jump. I see what appears to be a perfect routine; the scores come back and the skater is firmly in 13th.

When you see a GMAT question, you need to know exactly what criteria to use to “judge” a question, even if your first instinct is not correct. Check out the following question from a GMAC practice pack:

At first, I thought “We do need the structure to be parallel!” Why did I think this? Because I saw the word whereas. When I see a comparison word like that, the first thing I look for is consistency between the two things we’re comparing. “Language areas” comes after the comma and is not underlined; like it or not, that phrase is not going anywhere.

Wanting to retro-fit my comparison to match my non-underlined portion, I hope and pray that I see something like, “Whereas language areas in adult brains are X, language areas in a child’s brain are Y.” Clearly, we can compare language areas to other language areas, so my next thought is that I’ll eliminate any answers that don’t satisfy this rule.

However, a quick scan of the underlined terms of comparison in each answer choice reveals that we don’t have such an opportunity.

1. A) each language
2. B) (ignorable prepositional phrase) each language
3. C) each language
4. D) each language
5. E) each language

Whoa. I guess we’re going to have to go with “each language.”

What’s really going on here? “Whereas in some situations X happensthere are other situations in which Y occurs.” We aren’t comparing a thing to a thing; we’re comparing a situation to an analogous situation.

So, what do I focus on next? Simply making a complete sentence that comes right after a semicolon, and eliminating any answer choice that fails to make a sentence. If the answer doesn’t make a grammatical sentence anyway, then why should we care what it’s comparing?

Answer choice B just blows through the existence of a two-part comparison: “Whereas Situation X is a thing and Situation Y is a thing.” That’s not a sentence! We need it to say “Whereas Situation X is a thing <COMMA> Situation Y is also a thing.”

Answer choice C misuses a pronoun by having the plural word “they” refer to the singular noun “language.”

Answer choice D wrongly employs the past tense “occupied,” as the language ceased to exist before the study ended. (Or the adults all tragically died during the study.)

Answer choice E wrongly tries to pass off “Incomplete sentence + comma + AND + Complete sentence” as a grammatical structure to put after a semicolon. Nope.

So let’s recap. In a question that seems to be about comparisons, we just eliminated four answer choices on the basis of No Verb, Bad Pronoun, Bad Verb Tense, and Bad Sentence Structure. None of the wrong answers had anything to do with comparisons!

Meanwhile, I haven’t yet said a word about the correct answer A, and that’s because truthfully, I didn’t love A when I read it for the first time. When you don’t love A, but you can’t identify a tangible error, you just let it hang around. If you can drop four answer choices like the bad habits they are (as we did in B through E), then Mr. Lingering Around Answer A becomes your default champion.

Congrats, Answer Choice A. You’re the “Only Figure Skater Who Didn’t Fall on His Butt So He Wins By Default” of answer choices.

I don’t know much about figure skating, but I know that falling on your butt is not ideal.

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By David Ingber

# Solving Inference Questions in Reading Comprehension on the GMAT

One of the most common things you’re going to do on the GMAT is to infer things. Inferring things is something we inherently do on a daily basis as human beings. If your friend tells you they’re preparing for a big presentation, you generally automatically infer they’re presenting to an audience and are nervous about public speaking. However, on the GMAT, inferring carries a little more baggage than in your everyday life. What if your friend is in charge of logistics for the presentation, or running the slideshow behind the presenter? Perhaps they are being presented in the debutante ball definition of the term? (niche, I know). On the GMAT, inferences have a high threshold they must always attain: the inferences must be true.

After preparing countless Critical Reasoning inference questions, this “must be true” mantra should already be indoctrinated into most GMAT test takers. However, this type of question also shows up in Reading Comprehension, offering a rare opportunity to excel at two different question types using the same concept. By the same token, it’s a concept that’s sure to show up on your test, and you shouldn’t lose easy points because you assumed something that wasn’t explicitly stated.

The approach I always use with students is to ask them: “Is this always true?” If it’s Thursday or a solar eclipse or you pass on the 1 yard line or Venus is in Scorpio… is this still true? Imagine every obscure, unlikely scenario, and make sure the answer choice still holds in that situation. (Seriously, who passes on the 1 yard line?) If this is the case for any scenario you can dream up, your inference holds. If you can imagine even one nice corner case (e.g. a prime number being even) where this doesn’t hold, then it cannot be the correct answer.

Let’s delve into this further using a Reading Comprehension passage. (note: this is the same passage I used previously for function and specific questions)

Nearly all the workers of the Lowell textile mills of Massachusetts were unmarried daughters from farm families. Some of the workers were as young as ten. Since many people in the 1820s were disturbed by the idea of working females, the company provided well-kept dormitories and boarding-houses. The meals were decent and church attendance was mandatory. Compared to other factories of the time, the Lowell mills were clean and safe, and there was even a journal, The Lowell Offering, which contained poems and other material written by the workers, and which became known beyond New England. Ironically, it was at the Lowell Mills that dissatisfaction with working conditions brought about the first organization of working women.

The mills were highly mechanized, and were in fact considered a model of efficiency by others in the textile industry. The work was difficult, however, and the high level of standardization made it tedious. When wages were cut, the workers organized the Factory Girls Association. 15,000 women decided to “turn out”, or walk off the job. The Offering, meant as a pleasant creative outlet, gave the women a voice that could be heard by sympathetic people elsewhere in the country, and even in Europe. However, the ability of the women to demand changes was severely circumscribed by an inability to go for long without wages with which to support themselves and help support their families. The same limitation hampered the effectiveness of the Lowell Female Labor Reform Association (LFLRA), organized in 1844.

No specific reform can be directly attributed to the Lowell workers, but their legacy is unquestionable. The LFLRA’s founder, Sarah Bagley, became a national figure, testifying before the Massachusetts House of Representatives. When the New England Labor Reform League was formed, three of the eight board members were women. Other mill workers took note of the Lowell strikes, and were successful in getting better pay, shorter hours, and safer working conditions. Even some existing child labor laws can be traced back to efforts first set in motion by the Lowell Mill Women.

The author of the passage implies that the efforts of the women workers at the Lowell Mills ________________?

(A) Were of less direct benefit to them than to other workers.

(B) Led to the creation of child labor laws that benefited the youngest workers at the Lowell mills.

(C) Forced the New England Labor Reform League to include three women on its board.

(D) Were addressed in the poetry included in the Offering.

(E) Were initially organized by Sarah Bagley.

The question is phrased in such a way that you must complete the sentence. Looking over the sentence, the active verb is “implies”, which means that we’re dealing with an inference question. This means that the correct conclusion to this sentence must be unimpeachable with regards to the passage. We must go through all the answer choices because inference questions inherently have multiple answers that could be correct. Our advantage is that four of the answer choices will be flawed and only one unassailable choice shall remain.

Let’s begin with option A. It essentially reads: “…the efforts of the women workers at the Lowell Mills were of less direct benefit to them than to other workers”. This seems about right because the passage states that the Lowell Mills workers couldn’t go on strike for long (paragraph 2). Conversely, it is also mentioned that “other mill workers took note of the Lowell strikes, and were successful in getting better pay, shorter hours and safer working conditions”. This makes it pretty hard to argue with answer choice A, but let’s continue and see if any other answer choices seem like contenders.

Answer choice B reads “…the efforts of the women workers at the Lowell Mills led to the creation of child labor laws that benefited the youngest workers at the Lowell Mills.” This seems like it could be correct, because the passage ends with a sentence about how some child labor laws can be traced back to the efforts of these women. However, there is no indication that these laws benefitted anyone at the Lowell Mills, and in fact were likely only instituted many years later. This answer choice affords a positive outcome to the situation, but is unfortunately unsupported by the passage.

Answer choice C reads “…the efforts of the women workers at the Lowell Mills forced the New England Labor Reform League to include three women on its board.” This might be the easiest answer choice to eliminate. Three members of the Reform League were women, but it is not guaranteed that this is due entirely to the worker strife. It is likely correlated, but it is impossible to defend that it is caused by the conflict. If we’re looking for bulletproof arguments, this one is full of holes.

Answer choice D reads “…the efforts of the women workers at the Lowell Mills were addressed in the poetry included in the Offering”. This is another strong candidate. The Lowell Offering was established as a journal written by the workers that contained at least some poetry in the first paragraph. Would it then be logical that the Offering would address worker malcontent during a strike? Likely, yes, but not guaranteed. Furthermore, would worker dissatisfaction necessarily show up as poetry versus an opinionated peace or an invitation to protest? It is likely that this happened, but there is no guarantee, and therefore this type of answer is incorrect for a GMAT inference question.

Answer choice E reads “…the efforts of the women workers at the Lowell Mills were initially organized by Sarah Bagley”. This answer choice is similar to answer choice D. It is quite possibly true, as Sarah Bagley seemingly had a powerful voice at the Lowell Mills, but there is no indication that she spearheaded the movement in any way. Had this been mentioned somewhere, it would have been unsurprising given the situation. However, on its own, it’s plausible at best, speculation at worst.

Since we’ve systematically eliminated answer choices B through E, the correct answer must be answer choice A. This makes sense because answer choice A seemed completely supported by the passage. Inference questions are typically exercises in process of elimination. If four answer choices can be purged (:anarchy), the remaining answer choice must be correct. If you can accomplish this task on the GMAT, you can infer with absolute certainty that you’ll select the correct answer.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# What the White & Gold, Blue & Black, Periwinkle & Whatever Dress Can Teach You About the GMAT

Over the past week, the online world has been consumed with discussions about one of the most mundane topics anyone could conceivably imagine. Indeed, for several days, the only discussion reasoned people seemed to be having was: “What color is this dress”?

Doctors, lawyers, engineers, (GMAT geeks), people of all walks of life were discussing the same basic concepts that toddlers learn in kindergarten. Is this dress blue and black, or white and gold? It seems preposterous even as I type it out, and yet people entrenched themselves into one camp or another with such certainty and vitriol that it seemed the other faction must be comprised of color blind philistines. Reportedly, some people saw the same picture differently in the morning and at night. Indeed, what was happening is that people were seeing the same thing from different perspectives.

People habitually see the same thing and reach different conclusions. If the middle-aged man next door buys a new sports car, some people assume he got a big raise, while others attribute it to a midlife crisis.  Other people might surmise he’s trying to impress someone new or perhaps he inherited a significant windfall. While seeing things from different perspectives is normal in everyday life, it is rare for multiple people to see the same thing and describe it completely differently. If I showed you the new red sports car, you wouldn’t likely tell me it’s a green bicycle or a blue toaster. At some point very early in our lives, we learn to associate certain words with certain elements, be they nouns, adjectives or colors.

Colors are such a fundamental part of life because so many things depend on them. We go on green lights, we stop for yellow school buses, we wear dark colors to appear more professional, and we wear our favorite team’s colors to show our support. Disagreeing about colors seems as basic as disagreeing that 2+2=4 (or 5 if you’re Orwellian). However the same thing can be seen from many different perspectives, and the variable is simply who is actually observing the phenomenon.

This happens a lot on the GMAT, and I wanted to discuss a problem that many people see one way, but others see in a completely different way:

The number of baseball cards that John and Bill had was in the ratio of 7:3. After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2. After the gift, John had how many more baseball cards than Bill?

• 15
• 30
• 45
• 60
• 90

The way most people would look at this problem is that it’s an algebra problem. The ratio of two numbers is 7:3, and after an exchange of 15 cards, the ratio is now 3:2. I can set up two equations and solve for the two unknowns in this equation, which will give me the number of cards Bill has and the number of cards John has. After that, it’s simply a question of subtracting the two in order to answer the question. Let’s run through the algebra because it’s somewhat time-consuming but otherwise fairly basic (the white-and-gold approach).

The initial ratio, before the gift, can be describes as J / B = 7 / 3.

The final ratio, after the gift, would then be J – 15 / B + 15 = 3 / 2.

Note that we are defining J and B to be the initial values of John and Bill, so we’ll have to keep that in mind for the final calculation.

Cross-multiplying the first equation gives us 3 J = 7 B. This should make sense as John has many more cards than Bill.

Cross-multiplying the second equation gives 2 (J – 15) = 3 (B + 15),

We can expand this to 2J – 30 = 3B + 45.

Finally we can move the constants to one side and get 2 J = 3 B + 75

You can use either the elimination method or the substitution method to solve for the two variables. I prefer the elimination method so I’d multiply the first equation by 2 and the second equation by 3 to isolate J.

6 J = 14 B

6 J = 9 B + 225

Since the left hand sides are the same, we can simplify to 14 B = 9 B + 225.

Subtracting 9 B from both sides gives 5 B = 225.

Dividing 225 by 5 gives 45.

If B is 45, and 3 J = 7 B, then 3 J must be 315, and so J is equal to 105.

We’re still not done, because these are the initial values: 105 and 45. If John gave Bill 15 cards, then the new totals would be 90 for John and 60 for Bill, which is where the 3/2 ratio comes in. The difference in cards is 30 after the gift, so the answer is B.

Other people see this ratio problem and don’t even think about the algebra, they solve it using the underlying concept (the blue-and-black approach). To illustrate this concept, suppose I had 199 cards and you had 101 cards. Since no simplification is possible, the ratio of our cards would be 199:101. But if you then gave me one card, our ratio would suddenly be 2:1. This reduced fraction does not change the fact that I still have 200 cards and you have 100. Simply because the fraction can be simplified, that does not mean that the totals have changed in any way.

Let’s apply that same logic here. The ratio was 7:3. After the gift, the new ratio is 3:2, but the total number of cards has stayed the same. This means that if I can get a new ratio that’s in the same proportions as the old ratio, the problem will seem much simpler. The ratio 7:3 has 10 total parts. The ratio of 3:2 has only 5 total parts, so they are not in the same proportions. However, if I recognize that I can simply multiply 3:2 by 2 to get a ratio of 6:4, I discover a shortcut that can help on ratio problems.

If the ratio used to be 7:3 then became 6:4 after a transfer of 15 cards, then each unit of the ratio must represent 15 cards. This would mean that 7 would drop to 6 and 3 would increase to 4 because of the same 15 card transfer. Thus the old ratio was (7×15): (3×15), or 105:45. The new ratio is similarly (6×15): (4×15), or 90:60.  The difference in cards after the gift is still 30, answer choice B, but for some it’s much easier to see using a little logic than a lot of algebra.

On the GMAT, similar to the chameleon dress, your perspective is what’s going to dictate how you approach problems. Not every question will have a shortcut or an instant solution, but every problem can be approached in multiple ways. The only limit is your understanding of the concepts and your skill at analyzing the presented problem. Hopefully, on test day, these strategies will help you avoid feeling blue (and black).

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

“Trust, but Verify” is an important piece of advice for diplomatic relations. It seems a contradiction at first: if you trust, why do you need to verify? The answer is that some things are important enough to take the extra time and effort to check. Even the small chance that your trust is misplaced is reason to investigate the situation in enough detail to confirm that what you believe to be true is actually true.

Reading comprehension on the GMAT does not rise to the level of international trade pacts, or arms reduction agreements, but the same principle applies. In most instances, when you think you know the answer to a reading comprehension question, take the time and effort to go back to the passage and verify.

After all, the correct answer to most reading comprehension questions on the GMAT is based closely on something actually written in the passage. While an extra minute spent on a sentence correction question may not make the sentence any clearer, an extra minute spent going back to the passage to verify a reading comprehension answer can drastically improve your chances of answering correctly.

Two Types of Reading Comprehension Questions

1) Questions with a specific enough question stem to guide you back to a particular portion of the passage, which you can then re-read to find the answer.

For the first type of question, you should almost always use the question stem to guide you back to a single paragraph and then to a particular portion of that paragraph. Even if you feel that you remember that portion of the reading well enough to simply answer the question, it is still in your best interest to take a few moments to return to the passage and make sure that you have the answer to the actual question that is asked.

• Many reading comprehension questions that appear easy actually have a very high level of difficulty. For these questions, the answer choice that at first appears obvious based on your memory of the passage is usually an answer that requires you to make an assumption that, in reality, is not supported by the passage.
• Take a few seconds and put forth a little effort to check that “obvious answer” against what is actually said in the passage. If the answer really is that easy you will quickly find the portion of the paragraph that supports it. If it is not so simple, you will have saved yourself from choosing the incorrect answer.
• Trust that you remember the passage accurately, but verify your answer.

2) Questions that have a more general question stem and are based on the entire passage as a whole.

The second type of question has a more general question stem and it is not as clear where in the passage to return to confirm your answer. An example of the more general question stem is, “the author of the passage would most likely agree with which of the following?” You can see that there is nothing in the question stem to guide you back to a particular portion of the passage.

• For these questions you should begin with process of elimination. Eliminate any answer choices that you are sure are wrong based on important characteristics of the passage such as the scope of the passage or the tone that the author uses.
• Even on these questions you can still return to the passage to verify! The difference is that since the question stem does not guide you back to a particular portion of the paragraph, you need to use the answer choices themselves to help you return to the passage. You can go back to the passage to check the answer choices that remain after you have eliminated. The correct answer should be well-supported by the passage, while the incorrect answers are not.

With the proper techniques and effort, reading comprehension is an area of the GMAT that you can improve on quickly. If you want to become great at reading comprehension remember to “trust, but verify.”

Plan on taking the GMAT soon?  We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

David Newland has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.

# Identifying the Correct Answer on GMAT Quant Questions

One way in which the GMAT differs from most tests is that you only need to find the correct answer to the given question. There are absolutely no points for your development, your reasoning or indeed anything you decide to write down. This is completely contrary to much of what we learned in high school and university, where you could be rewarded for having the correct algorithm or approach even if you didn’t get the correct answer. On most math problems, if you got the wrong answer but demonstrated how you got there, you could at least get partial credit, especially if your approach was perfect but the execution lacked (like passing on the 1 yard line).

The GMAT will give you 100% credit for selecting the correct answer, even if you got there by flipping a coin, taking a wild guess or only selecting an answer choice based on the letters of your last name (I tend to pick either A or D if I’m making a complete guess). In class, I’ve asked many students how they get to the answer choice they provided me, and often their reasoning is wrong but they still land on the correct square. The GMAT has no way of differentiating sound logic from blind luck (or false positives, as they’re often called), so sometimes you get answers right purely by chance.

Of course, you can often determine which answer choice is correct without necessarily knowing exactly why. Especially on a multiple choice exam, you can often backsolve using the answer choices and find that answer choice A is correct even if the reasoning is hazy. On test day, there is no incentive to spending undue time to determine why the answer must be correct, no trophy for your approach. While preparing for the exam, you can certainly take time to investigate patterns and paradigms that seem to repeat regularly.

As a simple example, you probably know that a number is divisible by 3 if the sum of its digits is divisible by 3 (hence 93 or 1335 would be divisible by 3 because the sum of the digits is 12 in each case). You don’t necessarily need to know why; simply recognizing that it always works is enough on the GMAT.

However, sometimes it’s interesting to delve deeper into number properties as mathematics has so many interesting (well, interesting to me) properties that help you understand math better. Let’s look at an example:

If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?

• 0
• 1
• 2
• 3
• 5

This type of question shouldn’t take you too long to figure out. Even if the question seems somewhat arbitrary, it is simply asking you to take a prime number, square it, and divide the product by 12 to find the remainder. Picking any prime number (greater than 3) should solve this problem, but we’ll want to look at a few just to make sure the pattern holds.

Since the prime numbers 2 and 3 are excluded from consideration, we can begin at the next prime number, which is 5. 5^2 is 25, and 25 divided by 12 gives us 2 with remainder 1 (remember that the remainder is what’s left over after you find the quotient). Since we picked one prime number and got the result of 1, we could already select that answer choice and move on. However, it’s probably cautious to at least consider a couple of other options before hastily selecting answer choice B.

The next prime number would be 7, and 7^2 is 49. If you divide 49 by 12, you get 4, remainder 1. The pattern seems to hold. The next one is 11? 11^2 is 121, which divided by 12 gives 10, remainder 1. The pattern seems pretty solid here. Let’s pick a random bigger prime number just to be sure: say 31. 31^2 is 961, which divided by 12 gives 80, with remainder 1 again. At this point we’re pretty sure that the remainder will always be 1, and can pick answer choice B with confidence. (Feel free to do a dozen more if you’d like, it always holds).

Again, though, on test day, you might make this selection after checking only one or two numbers. But since we’re still preparing for the exam (if you’re reading this during your GMAT they will undoubtedly cancel your score), let’s dive into why this pattern holds. It certainly seems odd that for any prime number, this property will hold, especially considering that prime numbers can be hundreds of digits long.

To see why this holds, let’s consider what this pattern means. The square of the number n, less 1, is divisible by 12. This can be expressed as (n^2 – 1) is divisible by 12. This might remind you of the difference of squares, because it’s of the form n^2 – x^2, where x happens to be 1. We can thus transform this equation to: (n-1) * (n+1) is divisible by 12. This form will be more helpful in detecting the underlying pattern.

For a number to be divisible by 12, it must be divisible by 2, 2 and 3. If I were to take three consecutive numbers n-1, n and n+1, one of these three must necessarily be divisible by 3. Remember that multiples of 3 occur every third number, so it is impossible to go three consecutive numbers without one of them being a multiple of 3. And since n has been defined to be a prime number greater than 3, it cannot be n. Thus either n+1 or n-1 must be divisible by 3.

Similarly, if n is a prime greater than 3, then it must be odd. Clearly, then, n-1 must be even, and n+1 must be even. Since both of these numbers are divisible by 2, their product must be divisible by 4.  This means that for any two numbers (n-1) * (n+1) where n is a prime greater than 3, the product will be divisible by 2, by 2 and by 3, and therefore by 12.

On test day, figuring out the correct answer to the question is your main priority (not taking too long and not soiling yourself are two other big ones). Recognizing a pattern and making a decision based on the pattern is sufficient to get the question right, but it’s an interesting exercise to look into why certain patterns hold, why certain truths are inescapable. There’s no trophy for understanding math properties (not even a Nobel Prize), but identifying things that must be true goes a long way towards getting the right answer.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Using Algebra vs. Logic on GMAT Quant Questions

In pretty much every class I teach, at some point I’ll get the algebra vs. strategy question. Which is better? How do you know? I sympathize with the students’ confusion, as we’ll use the two approaches in different scenarios, but there doesn’t seem to be any magic formula to determine which is preferable. In many instances, both approaches will work fine, and the choice will mostly be a matter of taste and comfort for the test-taker.

In other cases, the question seems to have been specifically designed to thwart an algebraic approach. While there’s no official litmus test, there are some predictable structural clues that will often indicate that algebra is going to be nothing short of hemorrhage-inducing.

Here’s my personal heuristic; if an algebraic scenario involves hideously complex quadratic equations, I avoid the algebra. If, on the other hand, algebra leaves me with one or two linear equations to solve, it will almost certainly be a viable option. You might not recognize which category the question falls under until you’ve done a bit of leg-work. That’s fine. The key is not to get too invested in one approach and to have the patience and flexibility to alter your strategy midstream, if necessary.

Let’s look at some scenarios with unusually complex algebra. Here’s a GMATPrep® question:

A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800

Simple enough. Let’s say the sides of this rectangular park are a and b. We know that the perimeter is 2a + 2b, so 2a + 2b = 560. Let’s simplify that to a + b = 280.

The diagonal of the park will split the rectangle into two right triangles with sides a and b and a hypotenuse of 200. We can use the Pythagorean theorem here to get: a^2 +b^2 = 200^2.

So now I’ve got two equations. All I have to do is solve the first and substitute into the second. If we solve the first for a, we get a = 280- b. Substitute that into the second to get: (280 – b)^2 + b^2 = 200^2. And then… we enter a world of algebraic pain. We’re probably a minute in at this point, and rather than flail away at that awful quadratic for several minutes, it’s better to take a breath, cleanse the mental palate, and try another approach that can get us to an answer in a minute or so.

Anytime we see a right triangle question on the GMAT, it’s worthwhile to consider the possibility that we’re dealing with one of our classic Pythagorean triples. If I see root 2? Probably dealing with a 45:45:90. If we see a root 3? Probably dealing with a 30:60:90. Here, I see that the hypotenuse is a multiple of 5, so let’s test to see if this is, in fact, a 3x:4x:5x triangle. If it is, then a + b should be 280.

Because 200 is the hypotenuse it corresponds to the 5x. 5x = 200 à x = 40. If x = 40, then 3x = 3*40 = 120 and 4x = 4*40 = 160. If the other two sides of the triangle are 120 and 160, they’ll sum to 280, which is consistent with the equation we assembled earlier.

And we’re basically done. If the sides are 120 and 160, we can just multiply to get 120*160 = 19,200. (And note that as soon as we see that ‘2’ is the first non-zero digit, we know what the answer has to be.)

Here’s one more from the Official Guide:

A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by \$1, 10 fewer of the towels could be bought for \$120, excluding sales tax. What is the current price of each towel?

1. \$1
2. \$2
3. \$3
4. \$4
5. \$12

First the algebraic setup. If we want T towels that we buy for D dollars each, and we’re spending \$120, then we’ll have T*D = 120.

If the price were increased by \$1, the new price would be D+1, and if we could buy 10 fewer towels, we could then afford T -10 towels, giving us (T-10)(D+1) = 120.

We could solve the first equation to get T = 120/D. Substituting into the second would give us (120/D – 10)(D + 1) = 120. Another painful quadratic. Cue hemorrhage.

So let’s work with the answers instead. Start with D. If the current price were \$4, we could buy 30 towels for \$120. If the price were increased by \$1, the new price would be \$5, and we could buy 120/5 = 24 towels. But we want there to be 10 fewer towels, not 6 fewer towels so D is out.

So let’s try B. If the initial price had been \$2, we could have bought 60 towels. If the price had been \$1 more, the price would have been \$3, and we would have been able to buy 40 towels. Again, no good, we want it to be the case that we can buy 10 fewer towels, not 20 fewer towels.

Well, if \$4 yields a gap that’s too narrow (difference of 6 towels), and \$2 yields a gap that’s too large (difference of 20 towels), the answer will have to fall between them. Without even testing, I know it’s C, \$3.

This is all to say that it’s a good idea to go into the test knowing that your first approach won’t always work. Be flexible. Sometimes the algebra will be clean and elegant. Sometimes a strategy is better. If the algebra yields a complex quadratic, there’s an easier way to solve. You just have to stay composed enough to find it.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston.

# How to Attack GMAT Sentence Correction Questions Like a Boss

Many people think that finishing the GMAT verbal section on time hinges on quickly solving Sentence Correction problems. This is because these questions tend to have the shortest stimuli of any question type. Even if you’re a speed reader (hopefully you never ordered Mega Reading by Kevin Trudeau), it will still take a minute or so to sift through a passage that’s a few hundred words long. Sentence Correction problems sometimes have stimuli that are two or three lines, and therefore are prime candidates for quick dispatching.

However, sometimes you encounter Sentence Correction passages that are as long as paragraphs. Your job is the same no matter the length of the text, but Sentence Correction problems require you to evaluate every decision point among the answer choices. The longer the sentence, the more decision points you may have to consider. The number of false decision points also tends to increase as the sentence length increases. False decision points are differences between answer choices in which both options are acceptable, so making a choice based on such a decision point could erroneously eliminate a valid answer choice. Indeed, picking between an alternative and a substitute is an exercise in futility.

Another issue that comes up is mental fatigue. Conventional grammatical wisdom postulates that sentences longer than 20-25 words begin to lose their effectiveness, as the human brain struggles to process all the information. Run-on sentences can cause readers to disengage as they find themselves apathetic to the point that the author is trying to make. Often students report a lack of interest on longer passages, and an increased urge to simply select an answer choice (sometimes at random) to move on to a different question.

Let’s look at an example, which clocks in at an impressive 51 words.

The first trenches that were cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence for centrally administered complex societies in northern regions of the Middle East that are arising simultaneously with but independently of the more celebrated city-states of southern Mesopotamia, in what is now southern Iraq.

(A)   that were cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence for centrally administered complex societies in northern regions of the Middle East that are arising simultaneously with but

(B)   that were cut into a 500-acre site at Tell Hamoukar, Syria, yields strong evidence that centrally administered complex societies in northern regions of the Middle East were arising simultaneously with but also

(C)   having been cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence that centrally administered complex societies in northern regions of the Middle East were arising simultaneously but

(D)   cut into a 500-acre site at Tell Hamoukar, Syria, yields strong evidence of centrally administered complex societies in northern regions of the Middle East arising simultaneously but also

(E)    cut into a 500-acre site at Tell Hamoukar, Syria, have yielded strong evidence that centrally administered complex societies in northern regions of the Middle East arose simultaneously with but

The first thing you might notice is that, not only is this sentence way too long, most of it is underlined. That means it will take a fair amount of time just to peruse the answer choices. Our best strategy will probably not be to read through the five similar answer choices without any specific goal.

With run-on sentences, you want to be methodical and review each decision point as it comes up. As noted before, some may be false decision points and you cannot eliminate any choice. However, some words are low hanging fruit, such as verbs or pronouns, which have to be in specific forms (i.e. singular vs. plural). Connectors to and from the underlined portion are often significant as well, since they serve as springboards from one section to the next.

Looking at the original sentence (answer choice A) and going through the words, we’re looking for verbs and pronouns that can help guide our decisions. The first verb encountered is “were cut”, but the verb cut is tricky because it has the same form in the past, the present and the future. Answer choice C’s “having been cut” seems unnecessarily wordy, but that is not necessarily enough to eliminate it outright, so we’ll keep it with an asterisk and continue looking for other verbs.

The next verb encountered is “have yielded”, and a cursory comparison of the other answer choices reveals a 3-2 split between “have yielded” and “yields”. The subject of the verb is “The first trenches”, which is plural. The verb formulation of “yields” only works if the subject is singular, and thus we can eliminate these answer choices with 100% certainty as they contain agreement errors. Answer choices B and D can both be eliminated.

Continuing on, the second verb we encounter is “are arising”. Everything else about specific locations, sizes of land and other minutiae can be ignored using the slash-and-burn technique. We’re on a mission to compare specific terms that can help illuminate errors in various answer choices. Answer choice C has “were arising” and answer choice E has “arose”. The subject of the verb is “societies”, and therefore any of the three could be correct from an agreement standpoint. However, the timelines vary from present to past continuous to simple past, and the rest of the sentence began with the past-tense verb “have yielded”, meaning that the present tense would be erroneous. Answer choice A can be eliminated because of a timeline error.

At this point, only answer choices C and E remain. The verbs are not identical in the two options, but either one could conceivably make sense, so we must look for other differences in order to differentiate between the two. Looking through the answer choices, there are no pronouns to compare, but the first and last words are not the same. These connectors often cause answer choices to be eliminated because they make sense with the underlined portion but they do not fit nicely into the rest of the sentence (like merging onto the highway on a horse and buggy).

Answer choice C is already on our radar because of the wordy verb choice, but let’s examine how it fits back into the sentence at the end. The societies “were arising simultaneously…” is missing the word “with” in order to make grammatical sense. You arise simultaneously with something else. The original sentence had this word, but answer choice C omits the key words, and it’s difficult to see because the text is so verbose. This incorrect construction dooms answer choice C. Only answer E remains as the correct choice.

As with any Sentence Correction question, process of elimination is the name of the game. However, when the sentences get very long, very technical, or otherwise disengaging, you have to go through the text in a methodical manner. The best words to compare are the verbs, the pronouns and the connectors to and from the underlined portion. If you have a sound strategy, you’ll be able to execute the run on sentence correction.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# How to Make the GMAT Quant Section Easier on Test Day

In my decade of teaching the GMAT, perhaps no single group has found the quant section on the test more exasperating than math nerds. Yep, math nerds. Engineers, financial analysts, Physics majors, etc.

This may seem somewhat paradoxical, but the quant section on the GMAT isn’t testing your math ability. The skills that allowed the quantitatively-inclined to ace their tests in high school and college not only have limited value on the GMAT, but actually undermine test-takers, prompting them to grind through calculations when the question is really about how to avoid those very calculations.

Take this * GMATPrep® question, for example.

Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was \$150,000 and the median sale price was \$130,000. Which of the following statements must be true?

I. At least one of the homes was sold for more than \$165,000.

II. At least one of the homes was sold for more than \$130,0000 and less than \$150,000

III. At least one of the homes was sold for less than \$130,000.

A. I only

B. II only

C. III only

D. I and II

E. I and III

Perhaps you were tempted to do it algebraically. Maybe you thought you had to evaluate every scenario independently. If that was the case, you’re in good company. Most of the students I’ve taught over the years have had the same instinctive response. But we need to keep reminding ourselves about the aforementioned axiom: the GMAT isn’t testing math ability. It’s testing fluid thinking ability under pressure. So let’s take a deep breath and think about this for a moment.

How can I make this easier? What if I could construct a very simple scenario that violates two of the three statements?

The simplest possible scenario I can think of involves a set where the first 14 terms are equal to 130,000 exactly. (Clearly, in this case, the middle term, or median will be 130,000.) Then the last member will have to be enormous in order to increase the average to 150,000.  (If you were so inclined, you could do 14*130,000 + x = 15*150,000 and solve for x. x would be 430,000. But there’s no need to actually do this. It’s enough to see that x will be way more than 165,000.)

Well, this set {130, 130, 130, …430} proves that we don’t HAVE to have anything below 130,000. Kill Statement III. And it also proves that we don’t HAVE to have anything between 130,000 and 150,000. Kill II. We’re done. Only I has to be true, and there’s no need to test another scenario, because we’ve already logically disproved the other statements. The answer must be A, I only. All we needed was one simple scenario.

Now let’s look at a second GMATPrep® problem that, on the surface, appears to have absolutely nothing to do with the previous one.

Which of the following lists the number of points at which a circle can intersect a triangle?

1) 2 and 6 only

2) 2,4 and 6 only

3) 1,2,3 and 6 only

4) 1,2,3,4 and 6 only

5) 1,2,3,4,5 and 6

Again, the default response is to just start grinding through scenarios with the hope that, eventually, you’ll hit all of them. But that’s not a very efficient approach. Let’s slow down and think strategically. How can we save time? Well, look at the statements. Notice that there’s plenty of overlap, but only choice E has ‘5’ as a possibility. So if we can draw a triangle that intersects a circle at 5 points, I’ll know that’s the answer.

So, I’ll draw a circle:

Now I’ll draw 5 points on the circle, and try to draw a triangle through those points.

Looks like I can do it. I’m done. E is the answer.

(Interesting Parenthetical Note: if you were the question writer and were trying to concoct a question/answer that would that would be most difficult and time consuming for a test-taker, wouldn’t you have the correct answer contain the greatest number of possibilities? That’s another clue that E is where we want to start.)

The big takeaway here is that it’s good if we can keep reminding ourselves that the GMAT isn’t interested in our raw computational ability.  What the GMAT is interested in is our ability to make good decisions under pressure. So when you see a tough question, slow down. Look at the answers. Then think of the simplest possible scenarios that will allow you to test those answers in the fewest number of steps.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston.

# WTF! Leverage Your Assets on These GMAT Questions

When preparing to take the GMAT, you often solve hundreds or even thousands of practice problems. As you solve more and more of them, you start to realize that almost every question is testing something specific. There’s a geometry question about right angle triangles that’s really all about Pythagoras’ theorem, and an algebra problem that is easy to solve if you expand the difference of squares. However, there are some questions that make you scratch your head and wonder: “What in the world?” Some questions make you think you missed a section of material that you need to review (are there triple integrals on the GMAT?), or at the very least that you don’t know the correct strategic approach. I will euphemistically call these “WTF” questions, which of course stands for “Want To Finish”.

On questions where the entire goal of the question remains a mystery even as you try and come to a conclusion, the best strategy is to leverage all the information provided to you. As an example, if the question asks you about a specific property of an odd number, then try plugging in a few odd numbers to see what’s going on. You can then plug in a few even numbers to contrast the two; this often sheds some light on why only odd figures were selected in the premise. Exploiting seemingly inconsequential hints like these might be the difference between getting the right answer and wasting copious amounts of time on a single question, so look for hints in the set up.

Another important thing to remember is that you are just looking for a single answer choice. On the GMAT, there are no part marks for development, and a single incorrect calculation can sink an otherwise flawless algorithm. So you’re going for the correct answer more than a perfect understanding of what the question is testing. Understanding the question generally leads to a correct answer, but stumbling on the correct choice is worth exactly the same number of points on the GMAT (The Maxwell Smart approach). This also means that eliminating incorrect answer choices is valuable, as worst case you can take an educated guess that’s 50/50 instead of one out of five.

Let’s look at one of these WTF (Want To Finish) questions and see if we can figure out a solution:

If x and y are both prime, is x*y = 323?
(1) x is the first prime number after 18
(2) y is the last prime number before 180

(A) Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
(B) Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
(C) Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
(D) Each statement alone is sufficient to answer the question.

So the first thing that came to my mind is “Wow, that’s random”. The premise seems so arbitrary that it makes many approaches seem irrelevant. Even knowing that the two numbers are prime, we cannot quickly determine whether they must multiply to 323 without some more analysis and manipulation. Luckily, this is a Data Sufficiency question, so we have two additional statements that can help guide our analysis.

It’s important to note that in Data Sufficiency, we are trying to determine whether we can say with certainty that the two numbers multiply together to 323. This also means that if we can determine with certainty that the two numbers cannot multiply to 323, we have sufficient data. The uncertainty arises when we don’t know either way (i.e. maybe), so that provides a good framework for our analysis.

The first statement gives us a big hint, telling us that x is the first prime number after 18. This very quickly implies that x must be 19. We now have a hint as to why the number 323 was chosen (perhaps the author drove a Mazda in the ‘90s). If 323 is not a multiple of 19, then statement 1 will provide definitive evidence that x*y cannot possibly equal 323. Short of using a calculator, we can find multiples of 19 that are nearby and iterate manually until we find the correct answer. 19 x 20 would be easy to calculate as we can consider it as 19 x 2 x 10, or 38 x 10, or 380. From there, we can drop 19s until we get in the correct range.
380 – 19 is 361
361 – 19 is 342
342 – 19 is 323

You might be able to get there faster than by using this strategy, but after a few seconds of calculations, you can determine that 19 * 17 yields exactly 323. The question indicated that x and y would both be prime numbers, and 17 is indeed a prime number, so the possibility exists. However, it’s important to note that we know nothing (John Snow) about the value of y, other than it is a prime number. It could just as easily be 2, or 7, or 30203 (yes that’s a prime; I like palindromes). Since y could have any prime value, there’s insufficient evidence to determine that the product of x and y must be 323. Statement 1 is insufficient, and we can eliminate answer choices A and D.

Statement 2 indicates that y is the last prime number before 180, but it is important to remember that we must evaluate this statement alone. We now have no information about the value of x, other than it is a prime number. Statement 2 gives us a specific value of y, even if we’re not exactly sure what it is. We could do a little math and check to see if 179 (the number right before 180) is a prime, and in this case it is. The verification process is somewhat tedious, you have to check to see if it’s divisible by any prime number smaller than the square root of the number, so once you check 2, 3, 5, 7, 11 and 13, you’re confident than 179 is a prime number.

Knowing only that x is a prime number, we must now try and determine whether 179 and any prime could yield a product of 323, and the answer is very quickly no. The smallest prime number is 2, and 179 * 2 is already 358. You can also visually determine that 179 is more than half of 323, so there’s no need to even formally calculate the result. This statement on its own guarantees that x * y can never be 323, and thus is sufficient information to answer the question. The correct selection is answer choice B, as this statement alone is sufficient.

It is important to point out that these statements, taken together, give very clear numbers for both x and y. When this happens, you know that you can combine the statements and get only one value. That value may or may not be 323 (in this case it’s really, really not), but either way it provides sufficient information to definitively answer the question. However, it is almost always going to be the wrong answer, as it simply provides too much information. There’s no mystery or intrigue left, everything is laid out on the sheet in front of you. In business, as in life, if something seems too good to be true, it usually is.

Indeed, this question is essentially testing to see whether you’ll overpay for information on Data Sufficiency. However, at first blush, it just seems like an arbitrary collection of numbers with a question attached. When faced with similar head-scratchers, keep in mind that the statements (and/or answer choices) will provide hints. Trying to factor out 323 without any hints is a challenging endeavour, so look for hints and exploit them as much as possible. Hopefully, on test day, the only head scratching you’ll do is wondering which school you’ll go to with your outstanding score.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Should You Purchase The New Enhanced Score Report?

For anyone who has ever underperformed their goals on the GMAT, the first question they’ve asked is usually “where did it all go wrong?”. And for those who have asked that question since October 1, 2013, or will ask it soon, there may be an answer waiting for you.

The GMAT Enhanced Score Report is here.

This new add-on report, which costs \$24.95 USD, will provide you with diagnostic feedback from your official GMAT exam, including such information as:

-Performance (percentile ranking) by question type, with question types including Data Sufficiency vs. Problem Solving; Arithmetic vs. Algebra/Geometry; Critical Reasoning vs. Sentence Correction vs. Reading Comprehension

-Time management by question type, broken down by the same categories above

-Time management by correct vs. incorrect answers for Integrated Reasoning

-Percent of Integrated Reasoning questions answered correctly

So those are the features, but the question remains…is this worth \$25? And the answer is a little less concrete than you might like: it depends. Why?

*The report won’t give you question-by-question feedback, so you’ll never know if you got that crazy coordinate geometry problem at #17 right or wrong, and you won’t know which individual problems you spent way too much time on. You’ll get much more aggregate data, which may or may not help.

*If your performance was pretty similar to that of your practice tests – which ought to be the case for most examinees who have taken several practice tests – the report should likely match your expectations. If you’ve prepared well for the test, there shouldn’t be many surprises in that report.

*However, some users will see some VERY enlightening information. Say, for example, you were quite strong on Critical Reasoning and Reading Comprehension (~80th percentile each) but significantly less adept on Sentence Correction (

So who will benefit from the report? Those who have some outliers or anomalies in their performance. If you were 60th percentile on quant, and a combination of 55th, 62nd, 63rd, and 59th on DS, PS, Arith, Alg/Geo, you’re not going to learn very much from that report. But if one area is significantly higher or significantly lower than the others, you’ll learn something.

-If you’re going to retake the exam, the Enhanced Score Report is essentially a 10% increase on your next registration fee, and has the potential to be pretty enlightening. Especially if you’re likely to spend \$25 over the next month on Starbucks or Amazon impulse purchases or anything else extraneous, it’s a good idea to put that \$25 toward the score report. You might not learn anything, but the chance that you’ll learn something is substantial enough that you should leave no stone unturned.

-But if you have \$25 left in your GMAT budget and the choice is between the Enhanced Score Report or a tool like the GMAT Question Pack or one of the Official Guide supplements, choose the extra practice. If you’ve prepared thoroughly there shouldn’t be too many surprises on that report, and whatever you’d learn you’d have to improve by practicing anyway.

So in sum, GMAT retakers should probably pony up the \$25 because the more you know about your performance, the higher the likelihood that you can improve it. Almost all Veritas Prep instructors agree – we want to see those reports from our students! But don’t be surprised if the report only confirms what you suspected. The Enhanced Score Report is a tool to guide your hard work, not a substitute for the effort required to improve.

Are you studying for the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

By Brian Galvin

# What You Need to Know about Assumption Questions in GMAT Critical Reasoning

When it comes to Critical Reasoning on the GMAT, one question that continues to frustrate people is the assumption question. Quite simply, the question is asking you which answer choice is required to support the conclusion that has been drawn in the passage. To successfully navigate these questions, you should use the Assumption Negation Technique, which requires a negation of the answer choice to determine whether or not it was actually required. More than that, though, the correct answer choice must be within the scope of the question. An answer choice that goes too far will not be the correct answer to the question.

As an example, think about a passage that deals with the Super Bowl. It’s very possible that the passage will discuss how good the Seahawks’ defense is, or how good Tom Brady is as a quarterback. The conclusion could then be something like how the Patriots will likely win (disclaimer: this was written before the Super Bowl). If a question was asked about what assumption is needed to reach the conclusion, the correct answer choice must be about Tom Brady or the Seahawks’ defense, given that’s what was discussed as evidence. If an answer choice discusses the catching ability of Rob Gronkowski or the Patriots’ (alleged) (systemic) pattern of cheating, then it is going outside the scope of the question and cannot be the correct selection.

It is important to note that strengthen and weaken questions may sometimes provide new information, so you should be on the lookout for things that weren’t written verbatim in the text. Nonetheless, for assumption questions, it’s easy to select an answer choice that provides new information but goes outside the scope of what was discussed. A choice that has no basis in the passage is usually a clear indicator of a trap answer.

Let’s look at an example to demonstrate scope in assumption questions:

It is a mistake to give post office employees individual discretion as to when to inspect or open suspicious packages. If individual employees are allowed to open “suspicious” packages without first following a strict protocol, it is only a matter of time before all packages will arrive having already been opened due to some postal employee’s idle curiosity.

The conclusion above is based on which of the following assumptions?

(A)   Postal service managers are the only people with the authority to open suspicious packages.

(B)   Suspicious packages are indistinguishable from all other kinds of packages.

(C)   The efficiency of the postal service will be greatly reduced if more packages are inspected.

(D)   There is currently no protocol in place for the inspection of suspicious packages.

(E)    Postal employees desire to open packages out of curiosity.

This question is asking about which assumption is required for the conclusion, which warns that all parcels will eventually be opened by overzealous mail carriers. While it’s somewhat understandable to be concerned about the privacy of your mail, the author’s fears may be unfounded (I’m more concerned about the NSA). The evidence provided in the passage is about when packages are allowed to be opened and verified. The passage mentions that only suspicious packages are allowed to be opened, but there are protocols in place that dictate when this verification can occur.

For assumption questions, the best strategy is to employ the Assumption Negation Technique and negate each answer choice to see if the conclusion falls down without the negated assumption. This approach is similar to the strategy of knocking down beams in a home to see which one was load-bearing. (Not something I’d recommend). If the conclusion falls down without this assumption, then it was absolutely required. If it changes nothing, then it was purely decorative and can be ignored.

Beginning with answer choice A, let’s negate them and see if the author’s paranoia is still defensible. The negation will be underlined to differentiate the negated form from the original assumption:

(A)   Postal service managers are not the only people with the authority to open suspicious packages.

If this were true, then there might be even more people who could open errant parcels. This makes the author’s argument more likely to be true, as seemingly random people could have authority to open packages. If nothing else, it certainly doesn’t lessen the chances of the author’s prediction coming to be, so this assumption is not required.

(B)   Suspicious packages are not indistinguishable from all other kinds of packages.

This double negation is saying that suspicious packages are easy to distinguish from other kinds of packages. If this were true, the employees would be able to tell which packages were suspicious, but they would nonetheless have the authority to open any package. Therefore, the fact that they can ascertain in most instances what constitutes a “suspicious” package would not necessarily stop them opening other packages. The passage is arguing that postal workers would open everything if given unilateral power, whether the package was deemed suspicious or not. This answer choice is probably the closest incorrect choice, but the scope alerts us to the superfluous nature of this assumption.

(C)   The efficiency of the postal service will not be greatly reduced if more packages are inspected.

This answer choice is discussing how the efficiency of the postal office (which many people think is an oxymoron) would not be affected by increasing the number of inspected packages. While this may quell the fears of some people who assume that more inspections would slow down the service, the author’s argument is primarily concerned with the privacy aspect of the inspections. This answer choice is thus out of scope, as the efficiency of the post office was (somehow) never in question.

(D)   There is currently no a protocol in place for the inspection of suspicious packages.

This answer choice, negated, indicates that there is already a protocol in place for suspicious packages. If this were true, it would actually strengthen the argument, as there would be no reason to give postal workers additional power to open packages. The system would indeed be working fine the way it is, and this argument only demonstrates the author’s point, it does not weaken it.

(E)    Postal employees do not desire to open packages out of curiosity.

This answer choice, by process of elimination, must be the correct choice. However, let’s confirm that it makes sense. If postal employees did not want to open packages out of (idle) curiosity, then the author’s entire argument would fall apart. Indeed, the entire argument relies on the fact that the postal employees will open every package they possibly can. If we could ensure that this was not the case (say with a hypnotic suggestion or some Borg nanoprobes), then the whole argument would become moot. Answer choice E is an assumption required by the conclusion, because without it, the argument falls apart.

On questions such as these, it’s entirely possible to get reeled in by an enticing answer choice. Remember to use the Assumption Negation Technique to verify whether an assumption is actually necessary or whether it just sounds important. The incorrect answer choices provided are designed to tempt you, so keep an eye on the evidence provided in the passage as well. If the answer sounds good, but isn’t based on the evidence provided, then much like the guy at my gym with halitosis, it is out of scope.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Why You Felt Good on the GMAT Quant Section but Didn’t Score Well

This is a problem that I have seen many times before. It leaves students bewildered because all of the signs that would lead them to expect a lower score are absent. They did not run out of time, they did not have to guess at lots of questions, and they did not feel overwhelmed. Even I have suffered from this a bit, my lowest Quant score came on the exam where I felt most comfortable – and my highest score on Quant came on the exam that felt the worst.

How is it that you can confidentially answer question after question while obviously missing quite a few questions that felt “easy?”

One culprit is the subtlety of the official GMAT questions overall. No other questions do as good a job of luring you into confidently choosing the wrong answer. This can happen on problem solving, but today I would like to focus on Data Sufficiency.

I sometimes refer to Data Sufficiency as “the Silent Killer” because the very structure of the Data Sufficiency question invites you to choose the wrong answer. This is because you do not know that you have forgotten to consider something. There are no values in the answer choices to help you see what you might have overlooked. That is why the person choosing the incorrect answer is often more confident than is the one who got the question right.

As you can see it is often difficult to gauge how you are doing on Data Sufficiency. And because the Quantitative section adapts as a whole, missing these data sufficiency questions results in the computer selecting lower-level questions in problem solving. So the problem solving questions may have seemed easier because they actually were at a lower level.

This is a pattern that I have seen repeated many times on practice exams. Students miss mid-level data sufficiency questions in the first part of the exam. This results in lower level questions being offered, and the student keeps missing just enough problems (of both Data Sufficiency and Problem Solving) to keep the difficulty level from increasing.

The result? A quant section that felt comfortable because most of the questions were below the level that would really challenge the student. This may be what happened to you.

How to avoid this fate:

With Data Sufficiency questions there are no answer choices to provide a check on your assumptions or calculations. You must be your own editor and look for mistakes before you confirm your answer. Fortunately, there are several things you can do:

1. Think with your pen. Do not presume that you will remember what the question is asking, the facts you are given, or the hidden facts that are implied by the question stem. Note these things on your scratch paper so that you do not forget them. It may seem unnecessary to write “x is integer” or “must be positive” but just think of how dangerous it would be to forget this information!

1. Do your work early. Rewording the question is a great way to make data sufficiency more fool-proof. For example, it is much easier to comprehend the question “Is x a multiple of 4” than it is to wrestle with the questions “Is x/2 a multiple of 2?” Think about what the question is really asking and re-word it when you can.

1. Catch mistakes before you submit. Always keep in mind the most common number properties, “positive/ negative” “integer/ non-integer” and “the numbers 0 and 1.” The test makers can really hide these number properties so that even experts could overlook them, so just run through these three number properties on every problem and you will catch lots of your mistakes before you submit.

Plan on taking the GMAT soon?  We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

David Newland has been teaching for Veritas Prep since 2006, and he won the Veritas Prep Instructor of the Year award in 2008. Students’ friends often call in asking when he will be teaching next because he really is a Veritas Prep and a GMAT rock star! Read more of his articles here.

# Use This Strategy for Fractions and Save Time on GMAT Test Day

One of the most uncomfortable aspects of the GMAT is that you are not allowed to use a calculator for the quantitative section. This is uncomfortable because, throughout your everyday life, you are never more than about 5 feet from a calculator (yes, even in Death Valley). Almost everyone has a cell phone, a laptop, a desktop or a GMAT guru nearby to compute difficult calculations for them. Even high school students are generally allowed their calculators on test day. However, the lack of a calculator allows the GMAT to test your reasoning skills and time management skills much more easily than if you had access to electronic help.

As an example, remember open-book tests. These tests always seemed easier when they were discussed in theory than when they were attempted in practice. An open book test must necessarily test you on more obscure and convoluted material, otherwise the test becomes too easy and everyone gets 100. Closed-book tests, by contrast, can concentrate on the core material and gauge how much preparation each student has put in. Adding more tools only serves to make the test more difficult in order to overcome these enhancements.

With a calculator, asking you to calculate the square root of an 8 digit number or the 9th power of an integer is trivial if you only have to plug in some numbers. However, if you need to actually reason out a strategic approach in your head, you have accomplished more than a thousand brute force calculations would. On the GMAT, the mathematics behind a question will always be doable without a calculator, but the strategy chosen and the way you set up the equations will generally be the difference between the correct answer in two minutes and a guess in four.

Let’s look at a question where the math isn’t too difficult, but can get tedious:

Alice, Benjamin and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8 and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?

(A)   3 / 140

(B)   1 / 28

(C)   3 / 56

(D)   3 / 35

(E)    7 / 40

This is a probability question, and therefore we must calculate the chances of any one event occurring. However, the question is asking about several possibilities, specifically any occurrence where two players win and the third loses (think of any romantic comedy). This means that we have to calculate several outcomes and manually add these probabilities. This is entirely feasible, but it can be somewhat tedious. Let’s look at the best way to avoid getting bogged down in the math:

Firstly, the three players’ are suitably abbreviated as A, B and C (convenient, GMAT, convenient). We therefore want to find the probability that A and B occur, but that C does not occur (denoted as A, B, ⌐C). This represents one of our desired outcomes. However, this is not the only possibility, as any situation where two occur and the other doesn’t is acceptable as well. Thus we can have A and C but not B (A, ⌐B, C), or B and C but not A (⌐A, B, C). The sum of these three outcomes is the desired fraction, so only some math remains.

Let’s do them in order. For (A, B, ⌐C), we take the probability of A, multiplied by the probability of B, and then multiplied by the probability of 1-C. If the chances of C are 2 / 7, then the probability of them not occurring must be the compliment of this, which is 5 / 7. The calculation is thus:

1 / 5 * 3 / 8 * 5 / 7.

In a multiplication, we only care about multiplying the numerators together, and then multiplying the denominators together. There is no need to put these elements on common denominators. The math gives us:

(1* 3 * 5) / (5 * 8 * 7). This is 15 / 280.

There is a strong temptation to cancel out the 5 on the numerator and on the denominator to make the calculation easier, but you should avoid such temptation on questions such as these. Why? (I’m glad you asked). If you simplified this equation, you would get the equivalent fraction of 3 / 56, which is easier to calculate, but since we still have to execute two more multiplications, we will end up adding fractions that have different denominators. This is not a pleasant experience without a calculator, and likely will cause us to revert to our common denominator for all three fractions, which is 5 * 8 * 7 or 280. Additionally, now that we’ve calculated it once, we don’t need to worry about the denominator for the following fractions, it will always be the same. Let’s continue and hopefully this strategy will become apparent.

The next fraction is (A, ⌐B, C), which is equivalent to

1 / 5 * 5 / 8 * 2 / 7. Note that ⌐B is (1 – 3/8)

Executing this calculation yields a result of 10 / 280.

Finally, we need (⌐A, B, C), which is equivalent to

4 / 5 * 3 / 8 * 2 / 7. Note that ⌐A is (1 – 1/5)

Executing this last fraction gives us 24 / 280.

Once we have these three fractions, we must add them together in order to get the probability of any one of them occurring (“or” probability, as opposed to “and” probability”). This is simple because they’re all on the same denominator, so we get 15 / 280 + 10 / 280 + 24 / 280 which is 49 / 280.

Now that we have this number, we can try to simplify it. 49 is a perfect square that is only divisible by 1, 7 and 49, whereas 280 has many factors, but one of them fairly clearly is 7. We can thus divide both terms by 7, and get 7 / 40. Since the numerator is a prime number, there is no additional simplification possible. 7 / 40 is answer choice E, and it is the correct pick on this question.

Had we simplified each probability as much as possible, we would have ended up with 3 / 56, 2 / 56 and 3 / 35. While the addition would not be impossible, it would become much more difficult. In fact, to correctly add these numbers together, you’d have to put them on their least common multiple, which would be 280 again. There is usually no point in simplifying fractions in questions like this because they must usually be recombined at the end. Save time and don’t convert once only to convert back.

The math on this question is not difficult, but having to add together multiple fractions and simplifying expressions can be quite time-consuming. With a calculator, you could simply add the decimals together, regardless of their fractional equivalents. However, the GMAT doesn’t allow you that shortcut on test day (unless you approximate in your head), so you must find a better tactic. The difference between solving all the questions and running out of time on the math section is often the approach you take on each question. Keep up a consistent strategy and you’ll solve a large fraction of the questions you face on test day.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Ariana Grande’s Real Problem with the GMAT

As a GMAT aficionado, I often find GMAT themes in everyday things. This is what happened last week when I was listening to the radio and Ariana Grande’s “Problem” started playing. I’d heard the song before, and despite its catchy melody, there is a glaring grammatical error in the chorus. This may not be that surprising: songs in general are dubious sources of grammar to begin with, and R&B songs often take additional liberties with their lyrics (Timbaland’s “The Way I Are” jumps to mind). However this error is the kind a lot of people make in their daily speech, so I figured I’d use it as an opportunity to improve our grammatical skills beyond what we hear on the radio.

Firstly, if you’ve never heard the song, please feel free to listen to it now. The chorus is discussing how Ariana would have “one less problem” without the person she’s currently serenading (surprisingly this isn’t a Taylor Swift song). The issue with the lyric is that problems are countable, and as such she should actually be singing “one fewer problem without you”. Perhaps the extra syllable messed up the harmony, or perhaps the songwriter hadn’t brushed up on their grammar prior to writing the song, but this is the type of issue students often struggle with because they don’t understand the underlying rule.

When it comes to counting things, there are two broad categories: items that are countable, and items that are not countable. The former comprises most tangible things we can imagine: computers, cars, cats, cookies, cans of Coke and countless conceivable commodities (This sentence brought to you by the letter C). The latter comprises things that are uncountable, such as water, sand or hair. You can count grains of sand or strands of hair, but you cannot count actual sand or hair, so these words get treated a little differently.

The rule is that for any noun that is countable, you must use “fewer” if you are going to decrease it. For any noun that is not countable, you must use “less” to decrease it. As an example, I want less water in my cup; I do not want fewer water in my cup. That example makes sense to most people. However, the converse is just as true: I want fewer bottles of water, not less bottles of water. If the item in question is scarce, similar words will be used. You can say that there is little water, but you wouldn’t say that there is few water left. Note how these words have the same etymology as “less” and “fewer”, respectively.

If the sentence calls for an increase, more is acceptable for both countable and uncountable elements. As an example, you can say that you want more water in your cup, or you can say that you want more bottles of water. Other synonyms exist as well, of course, but the delineation is much cleaner for decreases than for increases, so that structure appears more often on the GMAT. If the item in question is in abundance, similar words will also be used. You can say that there is much water, but you can’t say that there is many water. Much and many follow these same countable/uncountable rules.

The difference between items that are countable or uncountable is not unique to the GMAT, these rules apply to everyday language, they are simply enforced more rigorously on this test. Failure to choose the proper word in a Sentence Correction problem will result in an incorrect answer choice. As such, it behooves us to be aware of the grammatical difference between countable and uncountable elements, as it regularly comes up on the GMAT.

Let’s look at an example to illustrate the point:

The controversial restructuring plan for the county school district, if approved by the governor, would result in 20% fewer teachers and 10% less classroom contact-time throughout schools in the county.

A)     in 20% fewer teachers and 10% less

B)      in 20% fewer teachers and 10% fewer

C)      in 20% less teachers and 10% less

D)     with 20% fewer teachers and 10% fewer

E)      with 20% less teachers and 10% less

Looking at the answer choices, it becomes fairly clear that the correct answer will hinge primarily on the difference between “fewer” and “less”. If we recall the rules for countable vs. uncountable, anything that we can count must use the adjective “fewer”, while anything that is not countable must use the adjective “less”.

For this example, the first reduction is in the number of teachers. Teachers are human beings (often handsome ones!), and are therefore countable. You can want to spend less time with a specific teacher, but you cannot (correctly) say that you want the school to have less teachers. The request must be for fewer teachers. This already eliminates answer choices C and E because they use the incorrect term.

The second reduction is about classroom time. Time is a wondrous and magical thing (or so young people tell me), but it is not countable. Yes, you can break up time into countable units, such as seconds or minutes, just as you can break up sand into grams or ounces, but holistically time is intangible and therefore uncountable. The plan calls for less time in the classroom, not fewer time. This eliminates answer choices B and D because they use the incorrect term. Only answer A remains and it is indeed the correct answer.

As mentioned earlier, the rules around countable and uncountable nouns are fairly precise, but you are unlikely to be corrected in everyday conversation if you misuse a term. Since the GMAT is testing logic, precision and general attention to detail, it is a perfect type of question to try and trap hurried students who don’t always notice the difference. In daily conversation (and on the radio), you can often get away with imprecision in language. However, if you understand the nuances between countable and uncountable nouns, to paraphrase Ariana Grande, you’ll have one fewer problem on the GMAT.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Calculating Perfect Squares on the GMAT

The major difference between the GMAT and high school exams is that the questions are unpredictable. In high school, we’re taught to memorize certain pieces of information, and then regurgitate them on the final exam. If the question on the exam differed even slightly from the question we’ve committed to memory, we tended to panic, guess and generally fail to see the relationship between what we learned and what we were being asked to solve. As an example, if you know 12^2, you’re already 85.2% of the way to solving 13^2 (you know, roughly…). There is a fairly simple way to go from one perfect square to another, but before we talk about the general case solution, let’s go back to the beginning.

This pattern holds with 0^2, but for simplicity’s sake, let’s starts with 1^2. 1^2 expanded is 1 x 1, and this gives us a product of 1. Let’s look at the next perfect square: 2^2. 2 x 2 = 4. This is an increase of 3 from the first perfect square. The next perfect square is 3^2. 3 x 3 = 9. This represents an increase of 5 from the previous perfect square. Let’s do one more to cement the pattern: 4^2. 4 x 4 = 16. From the previous perfect square, we’ve increased by 7. The next perfect squares are 25, 36 and 49, representing subsequent increases of 9, 11 and 13, respectively. Indeed, each increase between subsequent perfect squares is a positive odd integer, and they’re in sequential order. It turns out that this pattern holds for all perfect squares, allowing us a shortcut to calculate them quickly. Let’s look at why this pattern holds.

From the initial perfect square of 1^2, we increase to 2^2. Consider this in two parts. We start with 1 x 1, and then we go to 1 x 2, and then finally to 2 x 2. What happens at each step? The first step brings up the total by 1, as we are adding another one of the initial element. The second step brings us up by 2, as we are adding another one of the new (n+1) element. This difference is what makes the perfect square 2^2 increase by (1+2=) 3 from the previous perfect square 1^2. Similarly, going from 2^2 to 3^2 can stop by the intermediary step of 2 x 3, and then 3 x 3. The first increase is of 2, and the second is of 3, giving a total of 5. For the general case, we can see that n^2 becomes (n+1) ^2 if we simply take n^2 and increase it by n and then increase it by n+1.

While this level of mathematics is not required on the GMAT, it certainly makes certain calculations much faster. Let’s return to our initial example of 12^2. Most (non-GMAT aficionado) people don’t know 13^2 offhand, but since elementary school has indoctrinated us with the multiplication table up to 12, the majority of people can easily recall that 12^2 is 144. Using this shortcut, we can see that 13^2 is 144 + 12 + 13. Adding these together, we get 169, the correct answer. 14^2 will similarly be 169 + 13 + 14, or 196, and so on.

I don’t consider this strategy a trick in any way, but rather a result of deeply understanding mathematical properties. This is the type of skill that’s rewarded on the GMAT, and it’s often rewarded by solving questions like this in under 2 minutes:

225, or 15^2, is the first perfect square that begins with two 2s. What is the sum of the digits of the next perfect square to begin with two 2s.
(A) 7
(B) 9
(C) 13
(D) 16
(E) 21

This is the type of question that could easily take 5 minutes on the GMAT. We have very little information, only that the number we want is a perfect square that begins with two 2s. Also, that it’s not 225, which is one a lot of people might know (especially if you live in a country with 15% sales tax). Even with a calculator, this question isn’t particularly trivial, so we’ll need to devise a strategy before randomly squaring numbers and hoping they begin with 22…

First things first, the next perfect square cannot possibly be 22x. The next perfect square after 15^2 is 16^2, which is 256 (you can get here any way you like). This means that the next perfect square has to be 22xx. This gives us an order of magnitude to shoot for. Until we have a better idea on which numbers to hone in on, let’s use easy numbers to get a sense of where we’re going:
20^2 = 400
30^2 = 900
40^2 = 1,600
50^2 = 2,500

Okay, so the number must be somewhere between 40 and 50. From here, it may be obvious that we need to be closer to 50, since 22xx is more than halfway between 1,600 and 2,500. As such, an astute test taker might try something like 47^2 or 48^2 and see how close they got. However, instead of guessing, let’s use our perfect square strategy to see how quickly we can calculate the correct number.

50^2 is 2,500. This means that if I were to calculate 49^2, I could simply take 2,500 and remove 50, then remove 49. This is the reverse of adding them together to get from 49^2 to 50^2. You can also think of this subtraction as 2,500 – 99, which means that 49^2 must be 2,401. A cursory test of the unit digit reveals that 9 x 9 would yield a unit digit of 1, so we’re on the right track. Similarly, going to 48^2 from 49^2 involves taking 2401 and subtracting 49 then 48. This would be 2,401 – 97, or 2,304. We got close to 22xx, but we’ll need one more step. 47^2 will be 48^2 – 47 – 48. This is equivalent to 2,304 – 95, leaving us with 2,209.

The number we need is a perfect square that begins with 22, so 2,209 is the correct term. From here, we need to add together the digits and get the total of 13, which is answer choice C.

While there is no direct method to answer questions such as these, it’s important to not use blind guessing, as this can waste a lot of time and won’t help you solve a similar question next time. Back solving is useless in a situation like this as well, so our options are somewhat limited. A simple strategy such as calculating signpost perfect squares like 30^2 and 40^2 is helpful, and in a case such as this can negate much of the difficulty of the problem. Since this exam is a test of how you think, don’t forget that any perfect square is just a hop, skip and a jump from the next perfect square.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Warning: Don’t Fall Into the C Trap on Data Sufficiency Questions

Studying for the GMAT can take over your life. I’m sure many of you are nodding your heads as you read this. If you’re not, you probably haven’t gotten there yet. I sincerely hope that you never do, but it is an almost unavoidable part of studying for this test. Eventually, you start correcting artists in songs (I got one less problem without you… more like one fewer problem) and wondering if your table number is a prime number (how about table 51… oops that’s divisible by 3). The first time you catch yourself using a GMAT specific term, you know you’re really deep in studying for this exam.

Most of the terms you hear are just general math and verbal times that you’ve seen before, but likely not in many years (“gerunds” and “isosceles” come to mind immediately). However, some expressions exist only on the GMAT. As an example, have you come across the term “The C trap” yet? This idiom is used to describe the erroneous assumption that answer choice C is disproportionately chosen on Data Sufficiency questions. As a quick reminder, this choice indicates “both statements taken together are sufficient to answer the question, but neither statement alone is sufficient”. (If you knew it verbatim by heart, congratulations, you’re in GMAT mode).

Why do people select this choice on roughly 30-40% of their data sufficiency questions? The answer is that, since you have two independent statements to evaluate, choosing to use both typically gives you the maximum amount of information. Of course, that doesn’t mean that using both statements is what will provide sufficient information to answer the question. It also doesn’t mean that you can’t get the same information from only one of the two statements. Despite this, test takers consistently feel most comfortable picking answer choice C than any other choice on questions where they’re unsure how to proceed. It seems as if answer choice C makes them feel safe. Unfortunately, time and time again, it’s a trap.

Let’s look at question that highlights this issue:

An animal shelter began the day Tuesday with a ratio of 5 cats for every 11 dogs. If no new animals arrived at the shelter, and the only animals that left the shelter were those that were adopted, what was the ratio of cats to dogs at the end of the day Tuesday?

(1) No cats were adopted on Tuesday.

(2) 4 dogs were adopted on Tuesday.

(A)   Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

(B)   Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

(C)   Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

(E)    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

Let’s begin by taking stock of what we know. This question is asking about ratios. At a certain shelter, the ratio started off as 5:11 for cats : dogs. During the course of the day, some animals were potentially adopted. The question asks about the ratio at the end of the day. The most important thing to note here is that we being with a ratio but not absolute numbers, which means if we get ratios (i.e. half the cats got adopted) we might know the end ratio. If we get absolute numbers, we have almost no chance of having sufficient data. The stimulus gives us no further information, so we need to start looking at the statements.

For simplicity’s sake, let’s start with statement (1). Remember that you can always start with statement (2) if you prefer (or if it seems easier) as both statements are independent. The first statement tells us that no cats were adopted. However, we don’t know anything about the dogs (other that they’re four legged mammals). This statement alone will clearly be insufficient. We can eliminate answer choices A and D.

Looking now at statement 2, we know that exactly four dogs were adopted over the course of the day. This statement will suffer from the same problem as statement 1: we have no information about the cats. This statement will be insufficient on its own, and answer choice B can be eliminated as well.

Looking now to combine the statements, we can consider that the number of dogs dropped by four while the number of cats remained the same. Since we know about both animals, many people believe that the two statements together are sufficient. This would be true if we knew the actual number of each animal at the beginning of the day. Regrettably, we only know the ratio of one to the other, meaning that a change in absolute number is meaningless.

To use concrete numbers, there could have been 5 cats and 11 dogs at the beginning of the day, and the loss of four dogs would change the ratio to 5:7.  Just as likely, we had 50 cats and 110 dogs at the beginning of the day, and the new ratio would be 50:106 (which we could simplify to 25:53 for completeness’ sake).  Since either of these scenarios (and a dozen more) is possible, the answer must be answer choice E. The statements together do not provide enough information.

There is one caveat worth mentioning with ratios. Since the ratio does not tell us about absolute numbers, adding 10 or subtracting 15 is meaningless because we don’t know the original numbers. There is, however, one interesting exception: If you added 5 cats and 11 dogs, then the ratio would naturally remain unchanged. Indeed, as long as the change was in the ratio of 5:11, the ratio would be known: still 5:11. If the ratio deviates in any way, this does not hold. Interestingly, for subtraction, this problem does not occur because removing 5 cats and 11 dogs introduces the non-negligible possibility that there are now 0 cats and 0 dogs left at the shelter. In general, absolute number data is meaningless on ratios. Keep the one exception (adding by the exact same ratio) in mind when considering these types of problems.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# How to Use Your Time Wisely on Reading Comprehension GMAT Questions

On the verbal section of the GMAT, students invariably spend more time on Reading Comprehension questions than on either Sentence Correction or Critical Reasoning problems. In fact, I’ve seen score reports where people spent more time on Reading Comprehension than on the other two question types combined! Students spend a lot of time on these passages because they are consistently packed with pointless information, run-on sentences and dense technical jargon. Attempting to untangle these passages can lead to a lot of frustration for test takers (Fortunately, there’s an app for that).

One reason people spend a lot of time on these questions is that they try to read the entire passage thoroughly. This is normal because this is how most reading is done, be it in newspapers or periodicals or novels. However, on the GMAT, speed is the name of the game. If I were doing a book report on Shakespeare’s works, then I would read the text multiple times, looking for nuance and symbolism. The goal on the GMAT is quite different: you have roughly eight minutes to read a passage and then answer four questions about it. That isn’t much time, but it can work if you’re question-focused.

Specific questions deal with (drum roll please) specific elements of the passage. At first glance, you wouldn’t necessarily recall such minute details, but if you know where to go back in the text, it becomes a trivial case of rereading until you find it. As an example, you might not remember what Luke Skywalker was wearing on Tatooine when he first meets Obi-Wan Kenobi, but you could just rewatch the first act of Star Wars and see for yourself. There is no need to memorize every minor detail, as long as you know where to find the answer, you can just look it up.

Let’s look at a GMAT passage and answer a question that deals with a specific element of the passage (note: this is the same passage I used in October for a function question).

Nearly all the workers of the Lowell textile mills of Massachusetts were unmarried daughters from farm families. Some of the workers were as young as ten. Since many people in the 1820s were disturbed by the idea of working females, the company provided well-kept dormitories and boarding-houses. The meals were decent and church attendance was mandatory. Compared to other factories of the time, the Lowell mills were clean and safe, and there was even a journal, The Lowell Offering, which contained poems and other material written by the workers, and which became known beyond New England. Ironically, it was at the Lowell Mills that dissatisfaction with working conditions brought about the first organization of working women.

The mills were highly mechanized, and were in fact considered a model of efficiency by others in the textile industry. The work was difficult, however, and the high level of standardization made it tedious. When wages were cut, the workers organized the Factory Girls Association. 15,000 women decided to “turn out”, or walk off the job. The Offering, meant as a pleasant creative outlet, gave the women a voice that could be heard by sympathetic people elsewhere in the country, and even in Europe. However, the ability of the women to demand changes was severely circumscribed by an inability to go for long without wages with which to support themselves and help support their families. The same limitation hampered the effectiveness of the Lowell Female Labor Reform Association (LFLRA), organized in 1844.

No specific reform can be directly attributed to the Lowell workers, but their legacy is unquestionable. The LFLRA’s founder, Sarah Bagley, became a national figure, testifying before the Massachusetts House of Representatives. When the New England Labor Reform League was formed, three of the eight board members were women. Other mill workers took note of the Lowell strikes, and were successful in getting better pay, shorter hours, and safer working conditions. Even some existing child labor laws can be traced back to efforts first set in motion by the Lowell Mill Women.

According to the passage, which of the following contributed to the inability of the workers at Lowell to have their demands met?
(A) The very young age of some of the workers made political organization impractical.
(B) Social attitudes of the time pressured women into not making demands.
(C) The Lowell Female Labor Reform Association was not organized until 1844.
(D) Their families depended on the workers to send some of their wages home.
(E) The people who were most sympathetic to the workers lived outside of New England.

If you’ve been following the Veritas technique on Reading Comprehension, then you should have spent about two minutes reading through the passage and summarizing each paragraph in a couple of words. If you didn’t do this, feel free to go back and do it now. Once completed, your summaries of each paragraph should be something like:
1) Lowell Mills and context
2) Labor strife and consequences
3) Legacy of Lowell Mills

Your exact wording may vary, but you want to keep it at about 3-5 words or so. This should give enough of a framework so you know where to go in every question. If we look at the question at hand, it asks why were the workers at Lowell unable to have their demands met. This has to be in the second paragraph, as that was the part that dealt with the actual worker strife.

Rereading this paragraph, we go through a description of what prompted the strike and then how many people participated. Directly following this is the line: “However, the ability of the women to demand changes was severely circumscribed by an inability to go for long without wages with which to support themselves and help support their families”. This was their downfall: they needed money to support themselves and their loved ones (unsurprisingly the downfall of most strikes). The wording used may be somewhat obtuse, but the context makes it quite clear that the issue was money. Going through the answer choices, D is the only option that is remotely close to what we want, and is therefore the correct answer.

On Reading Comprehension questions, it’s very easy to experience information overload (TL;DR for the new generation). A lot of information is contained in each passage, and this is not an accident. The test is designed to try and waste your time with frivolous sentences, so your goal is to read for overarching intent and know that you’ll have to revisit the text on most questions. Specific questions tend to ask about something minor, or possibly tangential, and therefore usually require you to reread the passage. Practice Reading Comprehension timing and you will find that you can answer these specific questions faster.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# Why Does the GMAT Test Geometry?

One topic that always makes me think on the GMAT is geometry. It’s not that geometry is particularly hard, or even particularly easy, but rather that it’s particularly irrelevant! Having done an MBA in the past few years, I can virtually guarantee you that you will never have to calculate the area of a rhombus or the volume of a cone during your graduate studies. It’s possible that you have to calculate various geometric shapes in your career after graduating (say you run an ice cream shop!), but during your education the entire discipline seems somewhat superfluous.

So if geometry isn’t useful in your studies, why would the GMAT regularly contain 4-6 questions that deal specifically with geometry? The answer is: the people making the exam want to know how you think. That’s all. The GMAT is a test designed to measure your critical thinking skills and your ability to reason out conclusions. The fact that geometry is being used as a vehicle to accomplish these goals is only because geometry is a key part of the high school curriculum. Similar questions could easily be formulated about linear algebra, calculus or other mathematical disciplines (please no one tell the GMAC about manifolds). However, the fact that not everyone has seen these disciplines before would give some people an unfair advantage. The GMAT may be many things, but unfair is not usually one of the qualities mentioned (cruel comes up a lot, though).

The other issue about geometry is it seems that it’s a subject that requires a lot of memorization. While it’s true that many formulae (or formulas) need to be committed to memory before taking the test, most questions revolve around how to use that information. On occasion, it may seem that there’s a different formula for every situation, the majority of questions will require you to apply a simple concept or formula in an unfamiliar situation.

Let’s look at an example of a geometry question that doesn’t require any special formula, but stumps a lot of students:

If the radius of a circle that centers at the origin is 5, how many points on the circle have integer coordinates?
(A) 4
(B) 8
(C) 12
(D) 15
(E) 20

There is a necessity to understand some of the verbiage in this question in order to be able to answer it properly. Firstly, a circle that is centered at the origin is centered at point {0,0}. The radius is 5, which means we know the diameter (2*r), the circumference (2*π*r) and the area (π * r^2). However, none of that information really helps us to answer this question. We are interested in how many points on the circle have integer coordinates. Quite simply, a circle has an infinite number of discrete points, so it’s easier to answer this question in the reverse: For each integer coordinate, is that point on the circle?

Let’s start with the obvious ones. The point {5,0} has to necessarily be on the circle. If the origin is {0,0} and the radius is 5, then not only must point {5,0} be on the circle, but so must point {-5,0}. The circle extends in all four directions, so we cannot forget the negative values. Similarly, the points {0,5} and {0,-5} will also be on the points, effectively covering the four cardinal points from the original circle. The circle could look something like this:

After solving for these four points, we must evaluate whether other integer coordinates could be on the circle. One thing should be clear: if the radius is 5, then any integer point above 5 will necessarily not be on the circle, as it is beyond the reach of our radius. We’ve already covered zero, so the only options we have left are one, two, three and four. Of course all of these numbers have negatives and can be considered on either the x or y axis, but still we have a finite number of possibilities to consider.

Another important thing that might not be as obvious is that the answer to this question will necessarily be a multiple of four. Given that a circle extends in all directions by the same distance, it is impossible for point {x, y} to be on the circle and for points {x,-y}, {-x,y} and {-x,-y} to not also be on the circle. This is an important property of all circles and one of the reasons they’re so common in everything from architecture to cooking (and to alien crop circles, if you believe in that). This rule also guarantees that any answer choice that’s not a multiple of four can be eliminated. We can thus eliminate answer choice D (15).

How do we go about finding other points on the circle? (Why am I asking rhetorical questions?) By using the Pythagorean Theorem, of course! Any point on the circle naturally forms a right angle triangle with the radius as the hypotenuse, and the radius is always five. Therefore, if the two other sides can be formed out of integers, we have a point on the circle with integer coordinates. The graph below will highlight this principle:

Since the Pythagorean Theorem states that the squares of the sides will be equal to the square of the hypotenuse, we only need to look for numbers that satisfy the equation a^2 +b^2 = r^2. And given that r is 5, r^2 must always be 25. So if we plug in a as one, we find that 1 + b^2 = 25. This gives us b^2 = 24, or b = √24, which is not an integer. We only have to plug this in three more times, so there’s no reason not to try all the possibilities. If a = 2, then we get 4 + b^2 = 25. The value of b would be √21, which again is not an integer value.

If a = 3, however, we quickly recognize the vaunted 3-4-5 triangle, as 9 + b^2 = 25, meaning b^2 is 16 and therefore b is 4. This means that the points {3,4}, {-3,4}, {3,-4} and {-3,-4} are all on the circle. We’ve brought the total up to 8, but we’re not done. The final value is when a equals four, which will again work and bring in the converse of the last iteration: {4,3}, {-4,3}, {4,-3} and {-4,-3}. These values are distinct from the previous ones, so we now have a total of 12 points. We’ve already checked five, so we can stop here. The answer to this question is answer choice C. There will be 12 distinct values with integer coordinates, as crudely demonstrated below (or on any analog clock).

In geometry, even if it feels like you have to constantly commit more rules to memory, remember that the rules are not nearly as important as knowing how to apply them. This problem can be solved with just the Pythagorean Theorem and a little elbow grease (or a graphing calculator). The GMAT is very much a test of how you think, not of what you know. If you think about geometry problems as cases that must be solved, or obstacles to be overcome, you’ll be in good shape to solve them.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# A Closer Look at Parallel Structure on GMAT Sentence Correction Questions

The holiday season is upon us in North America, as many families unite for Thanksgiving, some decadent shopping, and the imminent Christmas season. While Thanksgiving and Christmas are independently two of the biggest holidays of the year, the fact that they always come together and are so habitually linked makes me think of the GMAT (yes a lot of things make me think of the GMAT, it’s what I do). Just as the thought of Christmas makes a lot of people think of Black Friday deals and line ups at their local stores, some elements on the GMAT are as inextricably linked together.

The most common constructs that come in pairs are idioms, which are accepted turns of phrase, and elements requiring parallel structure. Both of these concepts can come up in sentence correction questions, and both play into whether a sentence has been properly constructed. Idioms often come up in pairs because one part of a sentence necessitates a parallel structure down the road. Similarly, parallel structure needs to have consistent elements or the sentence loses efficacy and becomes hard to read (like reading the word efficacy in a non-GMAT context).

A common example of the duality of idioms is the “Not only… but also…” idiom, whereby something will be described as “not only this… but also that”. If you don’t have the second part of the idiom, the first part doesn’t make much sense. You can say: “Ron is eating turkey”, but if you say “Not only is Ron eating turkey.” There must be some logical conclusion to that sentence, or you’re committing a sentence construction error. As an example: “Not only is Ron eating turkey, but he’s also eating yams.” Now the sentence is complete, as the idiom requires a second portion to complete the entire thought.

A common example of the importance of parallel structure is when making lists (and checking them twice). As an example, consider: “Ron likes eating turkey, watching football and to spend time with family”. The parallel structure is not maintained in this sentence because the first two are participial verbs and the third is an infinitive. You could rewrite this example as “Ron likes eating turkey, watching football and spending time with family” and it would be fine. However, that is not the only option. You could also rewrite this as “Ron likes to eat turkey, to watch football and to spend time with family”, or even “Ron likes to eat turkey, watch football and spend time with family”. Any of these constructions would be acceptable, because they all maintain the consistency required in parallel structures.

Now that we’ve seen how important it is to stick together, let’s look at an example that highlights these concepts in sentence correction:

In a plan to stop the erosion of East Coast beaches, the Army Corps of Engineers proposed building parallel to shore a breakwater of rocks that would rise six feet above the waterline and act as a buffer, so that it absorbs the energy of crashing waves and protecting the beaches.

(A) act as a buffer, so that it absorbs
(B) act like a buffer, so as to absorb
(C) act as a buffer, absorbing
(D) acting as a buffer, absorbing
(E) acting like a buffer, absorb

One ongoing difficulty in sentence correction is that a problem is rarely about only one concept. Frequently multiple issues must be addressed, such as agreement, awkwardness and antecedents of pronouns (and that’s just the letter A!) As such, it’s paramount to identify the decision points and see which types of errors could potentially occur in this sentence. It may not be as obvious on test day as it is now to note that this sentence has some issues with parallelism, but the fact that some verbs are underlined while others are not can help guide your approach here.

There is a verb (rise) before the underlined portion, and another verb (protecting) after the underlined portion. (Rise and protect make me think this sentence is about Batman). The correct answer choice will have to work with both verbs effortlessly, so let’s evaluate them one at a time. The first decision point we have in the underlined portion is deciding between “act” and “acting”, and this verb must match up with the previous verb “rise” as both are being commanded by the wall of rocks that is their shared subject. Since “rise” is an infinitive, and it is not underlined, the correct match must be with “act”. This parallel structure eliminates answer choices D and E, as both have the verb in its participle form. As an aside, please note that you don’t need to know the grammatical terms; they’re listed primarily for clarity.

The second decision point is the other verb, which comes in three different forms (absorbs, absorb, absorbing) in the three answer choices. Since the verb at the end of the sentence is in its participle (protecting), the parallel structure dictates that the answer choice must be answer choice C, as it is the only remaining choice with “absorbing”. We have thus eliminated four answer choices using only parallel structure. While answer choice C is indeed the correct answer, we can also note the idiom “act as a buffer”, which is used correctly, as opposed to “act like a buffer” in answer choice B. This decision point could be sufficient on its own, but you can often knock out a single incorrect answer choice for multiple reasons. Answer choice C is the only choice that does not contain any sentence construction errors.

Often, I compare the concept of parallelism to the banal notion of wearing socks. Any two socks are acceptable as long as they match, but wearing unmatched socks is a sure-fire way to get mocked (by me). Similarly, parallel structure only requires that you remain consistent within the same sentence, not that lists must be constructed exclusively in a certain way. Parallelism is very important in sentence correction, as it’s often the only reason to eliminate an answer choice that otherwise makes grammatical sense.

If you’re studying for the GMAT during the holidays this year, I wish you the best of luck, and remember that studying well and succeeding on the GMAT go hand in hand.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# How to Manage Unmanageable Numbers on the GMAT

When going through the quantitative section of the GMAT, you will often be confronted by numbers that are, shall we say, unwieldy (some people refer to them as “insane”). It is common on the exam to see numbers like 11!, 15^8, or even 230,050,672. Regardless of the form of the number, the common mistake that many novice test takers make is the same: They try to actually solve the number.

Now, some numbers are spelled out down to the decimals, but other numbers, such as 11!, seem unnecessarily abstract. 11 factorial is a big number, but wouldn’t it be simpler if I had a concrete number in front of me instead of a shorthand notation for 10 multiplications. The answer is: not really. If you wanted to expand 11! To get a longhand answer, you’ll end up with a large concrete number that is no easier to manipulate than the shorthand you had before. For example, 11! is actually 39,916,800. Does that make it any easier to use? Again, the answer is: not really.

In essence, every time you see a big number like this, the GMAT is baiting you into performing tedious calculations that don’t help you in any way. Having a cumbersome number is the GMAT’s way of saying “Don’t try and solve this with brute force, there’s a concept here you should recognize”. While it’s uncommon for the GMAT to actually speak, given that it’s an admissions exam, it actually is telling you loud and clear that concentrating on the number is a trap. There will always be some element that will help highlight the underlying issue without performing tedious math.

There are many concepts that may come into play, and it’s hard to approach these questions with a single standard approach, but some elements repeat more frequently than others. One of the first things to look for is the units digit. The units digit gives away many properties of a number. As an example, 39,916,800 ends with a 0, indicating that it is even, and that it is divisible by 10. Different units digits can yield different number properties, so you can learn a lot from one simple digit. The factors of the number in question can often unlock clues as to which numbers to look for among the answer choices. Finally the order of magnitude can also play a pivotal role in determining how to approach a question.

Since we don’t have one definitive strategy, let’s test our mental agility on an actual GMAT question:

For integers x, y and z, if ((2^x)^(y))^(z) = 131,072, which of the following must be true:
(A) The product xyz is even
(B) The product xyz is odd
(C) The product xy is even
(D) The product yz is prime
(E) The product yz is positive

This question is significantly easier if you recognize which power of two 131,072 is off the bat (I knew that Computer Science degree would be good for something). However, let’s approach this knowing that 131,072 is a multiple of two, but that calculating which one would require more time than the two minutes we have earmarked for this question. Furthermore, simply knowing that 131,072 is a power of 2 gives us all the information we really need to solve this question.

We know x, y and z will combine to form some integer, but we’re not sure which. Let’s call it integer R (as in Ron) for simplicity’s sake. Moreover, the way the equation is set up, the powers will all be multiplied by one another, meaning that their exact order won’t matter. As such, the commutative law of mathematics confirms that if ((2^5)^(3))^(2) is the exact same thing as ((2^3)^(2))^(5). If the order doesn’t matter, then there are a lot of potential situations that could occur. So R will equal x + y + z, but the order won’t change anything. Let’s look at the answer choices, and start from the end because they’re easier to eliminate.

Answer choice E asks us whether y*z must be positive. If y*z gives us some positive number, then x would just be whatever is left over to form R. It doesn’t matter is y*z is positive or negative, as x can just come and make up the difference. Let’s say y*z = 4, then x would just be R – 4. If, instead, y*z = -4, then x would just be R – 12 and there would be no difference. In other words, as long as one variable is unrestricted, it will always be able to make up for the restriction on the other two. If you recognize this, you can eliminate C, D and E for the same reason. Two out of three ain’t bad, but in this case, it ain’t enough.

This brings us down to answer choices A and B, which are complimentary. Either the product of the three numbers is even, or it is odd. One of these, logically, must be true. Unfortunately, the best way to verify this appears to be doing the calculation longhand (like the petals of a flower: she loves me, she loves me not). Herein lays a potential shortcut: the units digit. Since the number is a power of two, we can simply follow the pattern of multiples of two and see what we get. Considering primarily the units digit (underlined for emphasis):

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
2^9 = 512

You probably don’t have to go this far to notice the pattern, but it doesn’t hurt to confirm if you’re not sure after 2^5. Essentially, the unit digit oscillates in a fixed pattern: 2, 4, 8, 6, and then repeats. This is helpful, because the number in question ends with a 2, and every power of two that ends with a 2 is either 2^1, 2^5, 2^9, etc. All of these numbers are odd powers of 2, repeating every fourth element. With this pattern clearly laid out, it becomes apparent that the answer must be that the product of these three variables must be odd. As such, answer choice B is correct here. We can also probably deduce from order of magnitude that 131,072 is 2^17.

When it comes to large numbers on the GMAT, you should never try to use brute force to solve the problem. The numbers are arbitrarily large to dissuade you from trying to actually calculate the numbers, and they can be made arbitrarily larger on the next question to waste even more of your time. The GMAT is a test of how you think, so thinking in terms of constantly calculating the same numbers over and over limits you to being an ineffective calculator. Your smart phone currently has at least 100 times your computational power (but not the ability to use it independently… yet…). Brute force may break some doors down, but mental agility is a skeleton key.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# 10 of Your Pressing GMAT Questions Answered by a Veritas Prep Expert

The following interview comes from Top GMAT Prep Courses. Top GMAT Prep Courses recently had the opportunity to conduct a Q&A session with Chris Kane, one of Veritas Prep’s most seasoned GMAT instructors, to inquire about the GMAT and get his take on 10 great questions that many MBA candidates would like to ask with regards to GMAT prep courses and useful tips on how to be successful at achieving their desired GMAT score.

What motivates you to be a GMAT instructor?

“I have been teaching the GMAT for 10 years because I absolutely love what the test is designed to assess and how it makes you learn and think.  This is not a content regurgitation test, but rather it is one that assesses who is good at taking basic content and using that to solve very difficult problems and reasoning puzzles.  I believe that the skills and thinking processes the GMAT assesses are invaluable not only in business but in all walks of life.  I really enjoy unlocking this way of thinking for students and teaching them to love a test that they may have at first despised!”

If you could give three pieces of advice to future GMAT test takers, what would they be?

“1) Do not waste 3 months preparing on your own, receive a low score, and THEN sign up for a high quality GMAT prep course.  Take our full GMAT course before you even open a book or read about the GMAT.  It will save you so much time, energy, and frustration.

Is there a common misconception of the GMAT or of what is a realistic GMAT score?

“I think there are many important misconceptions about the test as a whole and the scoring system in particular.  As I have intimated earlier, the biggest misconception about the GMAT is that it is a content test in which memorizing all the rules and the underlying content will allow you to do well.  This is certainly not the case and it is why so many students get frustrated when they prepare on their own.  The GMAT is so different from the tests that you were able to ace in college with memorization ‘all-nighters.’  Also, I think people underestimate how competitive and difficult the GMAT really is.  Remember that you are competing against a highly selective group of college graduates from around the world who are very hungry to attend a top US business school.  This test is no joke and requires an intensive preparation geared toward success in higher order thinking and problem solving.”

Read the rest of the interview here!

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

# Choosing from 2 Answer Choices in GMAT Critical Reasoning

In life, you are often given binary choices. This is true even if the word binary isn’t something you recognize right away. Binary comes from the Latin “bini”, which means two together, and is used to regroup decisions in which you have exactly two choices. On forms, you might see categories such as “smoker” or “non-smoker”, and you are prompted to answer exactly one of the options. At a restaurant, you might get asked “Soup or salad?” (super salad??), and you are expected to make a decision as to which appetizer you want. Very frequently, these two choices cover the entirety of your options. There is no third option to select.

Now, at a restaurant, you may be particularly hungry and decide to order both the soup and the salad (and the frog legs while we’re at it). Similarly, on forms, someone who selects both options is being confusing. Perhaps you’ve smoked once and didn’t like it. Perhaps you smoke only on long weekends when the Philadelphia Eagles have a winning record. Sometimes people decide they don’t want to pick between the two choices given. However, if the question were changed to “have you ever smoked a cigarette?” and then given yes or no options, the decision becomes much easier. You have to be in one camp or the other, there is no sitting on the fence (like Humpty Dumpty).

For questions that set up this kind of duality, the entire spectrum of possibilities is essentially covered in these two options. There is no third option; there is no “It’s Complicated” selection. There isn’t even a section for you to explain yourself in the comments below. On these questions, you have to either be on one side or the other, you cannot be in both. Equally, you cannot be in the “neither” camp either. Necessarily, to this point in your life, you have either smoked a cigarette or you have not. Since one of them must be true, this certainty offers some insight on inference questions in critical reasoning.

As you probably recall, inference questions require that an answer choice must be true at all times. This isn’t always easy to see as many answer choices seem likely, but simply are not guaranteed. Sometimes, on inference questions, you get two answer choices that are compliments of one another. You get two choices that say something to the effect of “Ron is always awesome” and “Ron is not always awesome”. Even I would go for the latter here, but clearly one of these must be correct. They cannot both be correct, but they also cannot both be false. Having two answer choices like this guarantees that one of them must be the correct answer, and makes your task considerably easier.

Let’s look at an example:

A few people who are bad writers simply cannot improve their writing, whether or not they receive instruction. Still, most bad writers can at least be taught to improve their writing enough so that they are no longer bad writers. However, no one can become a great writer simply by being taught how to be a better writer, since great writers must have not only skill but also talent.

Which one of the following can be properly inferred from the passage above?
(A) All bad writers can become better writers
(B) All great writers had to be taught to become better writers.
(C) Some bad writers can never become great writers.
(D) Some bad writers can become great writers.
(E) Some great writers can be taught to be even better writers.

Since this is an inference question, we must read through the answer choices because there are many possible answers that could be inferred from this passage. When reading through the passage, you probably note that answers C and D are somewhat complimentary. Either the bad writers can become great writers, or they can’t. However, some people might be miffed by the fact that “some writers” is vague and could mean different people in different contexts. However, while the term “some writers” is undoubtedly abstract, it can refer to any subset of writers one or greater (and up to the entire group). Any group of bad writers is thus conceivable in this passage, but the answer choice must be true at all times, so the groups comprised of “some writers” can mean anyone, and these two groups can be considered equivalent.

If you recognize that either answer choice C or answer choice D must be the answer, then you can easily skip over the other three choices. For completeness’ sake, let’s run through them quickly here. Answer choice A directly contradicts the first sentence of this passage: Some bad writers simply cannot improve their writing. Answer choice B contradicts the major point of this passage, which is that great writers have a combination of skill and talent, and you cannot teach talent. Answer choice E makes sense as an option, but it doesn’t necessarily have to be true. This is a classic example of something that’s likely true in the real world, but not necessarily guaranteed by this particular passage.

This leaves us with two options to consider. Can bad writers become great writers, or can they never become great writers? As mentioned above, great writers are born with some level of talent that cannot be mimicked by practice alone. The passage explicitly states “no one can one can become a great writer simply by being taught how to be a better writer”. Even though some bad writers can improve their writing with some help (perhaps even writing a Twilight Saga), some cannot improve their writing at all. If these bad writers cannot improve their writing, they necessarily will never become great writers. Answer choice C must be true based on the passage.

Looking at answer choice D in contrast, it states: “some bad writers can become great writers”. Perhaps some can, but this cannot be guaranteed in any way from the passage. It’s possible that all the writers are terrible even after year of practice. In fact, since we know that some will never improve (the opposite), this conclusion is certainly is not guaranteed. Answer choice C is supported by the passage, answer choice D seems conceivable in the real world, but it is certainly not assured.

On the GMAT, as in life, when confronted with two complimentary choices, you have to end up making a choice. In this instance, because you typically have five choices to consider, whittling the competition down to two choices already saves you time and gives you confidence. Recognizing which option must always be true is all that’s left to do, and that often comes down to playing Devil’s Advocate. When you’re tackling a decision such as this, consider what has to be true, and you’ll make the right choice.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

# 1 Simple Way to Solve Puzzling GMAT Questions

If you’ve ever built a puzzle, you probably know that you can’t expect to start at a certain point and build the entire puzzle without moving around. You may find two or three pieces that fit together nicely, but then you find three pieces that fit together nicely somewhere else, and then work to connect these disparate sections.

A common strategy in puzzles is to build the outsides or the corners first, as these pieces are more easily identifiable than a typical piece, and then try and connect them wherever possible. Indeed, you are unlikely to have ever solved a puzzle without needing to jump around (except for puzzles with 4 pieces or so).

Similarly, you are often faced with GMAT questions that seem like intricate puzzles, and this same strategy of jumping around can be applied. If you start at the beginning of a question and make some strides, you may find your progress has been jammed somewhere along the way and you must devise a new strategy to overcome this roadblock. Jumping around to another part of the problem is a good strategy to get your creative juices flowing.

Let’s say a math question is asking you about the sum of a certain series. A simplistic approach (possibly one used by a Turing machine) would sequentially count each item and keep a running tally. However, a more strategic approach might involve jumping to the end of the series, investigating how the series is constructed, and finding the average. This average can then be multiplied by the number of terms to correctly find the sum of a series in a couple of steps, whereas the brute force approach would take much longer. Since the GMAT is an exam of how you think, the questions asked will often reward your use of logical thinking and your understanding of the underlying math concepts.

Let’s look at a sequence and see how thinking out of order can actually get our thinking straight:

In the sequence a1, a2, a3, an, an is determined for all values n > 2 by taking the average of all terms a1 through an-1. If a1 = 1 and a3 = 5, then what is the value of a20?
(A) 1
(B) 4.5
(C) 5
(D) 6
(E) 9

This question is designed to make you waste time trying to decipher it. A certain pattern is established for this sequence, and then the twentieth term is being asked of us. If the sequence has a pattern for all numbers greater than two, and it gave you the first two numbers, then you could deduce the subsequent terms to infinity (and beyond!). However, only the first and third terms are given, so there is at least an extra element of determining the value of the second term. After that, we may need to calculate 16 intermittent items before getting to the 20th value, so it seems like it might be a time consuming affair. As is often the case on the GMAT, once we get going this may be easier than it initially appears.

If a1 is 1 and a3 is 5, we actually have enough information to solve a2. The third term of the sequence is defined as the average of the first two terms, thus a3 = (a1 + a2) / 2. This one equation has three variables, but two of them are given in the premise of the question, leading to 5 = (1 + a2) /2. Multiplying both sides by 2, we get 10 = 1 + a2, and thus a2 has to be 9. The first three terms of this sequence are therefore {1, 9, 5}. Now that we have the first three terms and the general case, we should be able to solve a4, a5 and beyond until the requisite a20.

The fourth term, a4 is defined as the average of the first three terms. Since the first three terms are {1, 9, 5}, the fourth term will be a4 = (1 + 9 + 5) / 3. This gives us 15/3, which simplifies to 5. A4 is thus equal to 5. Let’s now solve for a5. The same equation must hold for all an, so a5 = (1 + 9 + 5 + 5) /4, which is 20/4, or again, 5. The third, fourth and fifth terms of this sequence are all 5. Perhaps we can decode a pattern without having to calculate the next fourteen numbers (hint: yes you can!).

A3 is 5 because that is the average of 1 and 9. Once we found a3, we set off to find subsequent elements, but all of these elements will follow the same pattern. We take the elements 1 and 9, and then find the average of these two numbers, and then average out all three terms. Since a3 was already the average of a1 and a2, adding it to the equation and finding the average will change nothing. A4 will similarly be 5, and adding it into the equation and taking the average will again change nothing. Indeed all of the terms from A3 to A∞ will be equal to exactly 5, and they will have no effect on the average of the sequence.

You may have noticed this pattern earlier than element a5, but it can nonetheless be beneficial to find a few concrete terms in order to cement your hypothesis. You can stop whenever you feel comfortable that you’ve cracked the code (there are no style points for calculating all twenty elements). Indeed, it doesn’t matter how many terms you actually calculate before you discover the pattern. The important part is that you look through the answer choices and understand that term a20, like any other term bigger than a3, must necessarily be 5, answer choice C.

While understanding the exact relationship between each term on test day is not necessary, it’s important to try and see a few pattern questions during your test prep and understand the concepts being applied. You may not be able to recognize all the common GMAT traps, but if you recognize a few you can save yourself valuable time on questions. If you find yourself faced with a confusing or convoluted question, remember that you don’t have to tackle the problem in a linear fashion. If you’re stuck, try to establish what the key items are, or determine the end and go backwards. When in doubt, don’t be afraid to skip around (figuratively, literal skipping is frowned upon at the test center).

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you weekly advice for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.