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)?*

*3 ∆ 2 > 3**3 ∆ 1 = 3*

* A) **Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
*

D)

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.*

**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*

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!

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

Radio: 7x

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.

*GMATPrep questions courtesy of the Graduate Management Admissions Council.

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

**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*

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 a _{n} is called a cusp of a sequence if a_{n} is an integer but _{an+1} is not an integer. If a_{5} is a cusp of the sequence a_{1}, a_{2},…,a_{n},… in which a_{1} = k and a_{n} = -2(a_{n-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 a_{3}, you should be able to find a_{4}. But if you have a_{4}, it’s a lot harder to identify a_{3}. 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 a_{n} = -2/3 a_{n-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, a_{3}, 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 a_{3} was not an integer, and thus a_{2} 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.

A_{1} = 162

A_{2} = -2/3 (162) = -108

A_{3} = -2/3 (-108) = 72

A_{4} = -2/3 (72) = -48

A_{5} = -2/3 (-48) = 32

A_{6} = -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 A_{4}, not A_{5}. 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 A_{6}, 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).

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.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

*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…

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*By Brian Galvin*

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 l*aws 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, “Man*y 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.

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.

*Official Guide question courtesy of the Graduate Management Admissions Council.