There is an anecdote about a primary school teacher who wanted to keep a misbehaved child busy for a period, so she asked him to sum up all the numbers from 1 to 100. To her dismay, the child answered the question in a matter of seconds, and the answer was correct. The child explained to his teacher that, instead of simply adding 1+2+3…, you could create a pairwise addition that would always yield the same number. If you added 1 to 100, you would get 101. If you added 2 to 99, you would still get 101. If you added 3 to 98, you’d still get 101, and so on. Thus the addition of 100 different numbers could be turned into a multiplication of two simple numbers: 101 x 50. The student in question was mathematical prodigy Carl Friedrich Gauss.

Now such brilliance is hard to see the first time, but easy to transform into a formula once it has been discovered.  Why did this shortcut method work? Quite simply, because the numbers are in arithmetic progression, which is to say, the spacing between each number is a constant. This allows the mean to be equal to the median, and the median is a very easy number to calculate. In an odd numbered set, it is the middle term. In an even numbered set, it is the average of the two middle terms. Thus, from 1 to 100, the median is the average of 50 and 51, or 50.5. Multiplying this number by the number of terms gives us 50.5 x 100, or 5,050. Had we asked for the sum of all numbers from 0 to 100, we’d have a median (and average) of exactly 50, and 101 terms. This is the same equation that Gauss used, and obviously yields the same result as 1 to 100 since we’re only adding the term 0.

In general, the formula is going to be the Mean x Number of terms. There are two possible caveats with this formula, the first is in calculating the number of terms quickly, and the second is in taking into account calculations where the frequency might come into play. Let’s demonstrate this with a (real life) GMAT question:

What is the sum of all even integers from 650 to 750, inclusive?

3,500

35,000

35,700

70,000

70,700

This question can appear daunting if you don’t know how to approach such problems, so let’s delve into the mathematics of how to solve it (without taking a wild Gauss).

First, let’s consider what would happen if we dropped the word “even” from the question. We’d want all the integers from 650 to 750. In this arithmetic progression, the median would be 700, and thus so would the mean. The number of terms is easiest to consider as (Biggest – Smallest) + 1. This is because we have to account for both end points. Consider the number of terms from 50 to 60. We’d have 11 terms (you may want to count using fingers and toes). The total would thus be Mean (700) x number of terms (101), which would equal 70,700. This is the trap answer E because we discounted the word “even”, and clearly 70,000 is the same trap but without the +1 extra term (650 to 749, in effect). It thus has to be either A, B or C, but which one?

The issue of missing terms is addressed by simply dividing by the frequency. In this case, even numbers account for ½ of the total numbers, so we’ll have to divide by 2. The only other issue is to determine where the endpoints must lie. 650 is even, and so is 750, so we don’t need to change anything except the frequency, which becomes: Mean (700) x number of terms ((100/2) + 1). The extra term always needs to be added back in, so in effect we have 700 x 51, or 35,700.

The correct answer is C. 

B is the trap answer in case we overlooked the +1 at the end.

For completion’s sake, let’s examine what would happen had the question asked us for only the odd numbers. The same average would still exist, but the number of terms would now be (biggest-smallest/2) +1, which is ((749-651)/2) +1 = (98/2) +1 = 49+1, or exactly 50. Thus the sum of all the odd numbers from 650 to 750 is 35,000. This jives with our calculations of the even numbers summing to 35,700 and the total of all numbers being 70,700.

Given an infinite amount of time and a calculator (or abacus), you could easily find the answers to these questions without a general case formula. However, since you have about 2 minutes to read the question, accomplish all required calculations and lock in an answer choice, you are best served to have the formulae memorized or a strong notion of how to calculate the answer using the information provided. The GMAT is an exam about how you think more than what you know, but you don’t have to be Gauss if you’re well prepared for questions you expect to see.

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 occasional tips and tricks 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 reason the math is easier on these problems is because the problem is made hard in other ways.  Word problems are considered hard because you have to convert a word problem into a math question.  This involves good reading skills and good critical reasoning skills.

Keep some of the following word problem translations in mind as you navigate some of the toughest word problems.

“Is” means “equal to”

“Is” is “=.”  If you see the word “is” in a word problem, have no fear.  It simply means “equals.”

The number of brown hats is 5% of the total number of hats.  Take “is” and make it “=” and get started! Now you have the number of brown hats = 5% of the total number of hats.

“Of” means “multiplied by”

In a question with fractions, you want to substitute the words “multiplied by” for the “of.”

What is 3/5 of 20?  To solve this problem, take the fraction and multiply it by the other number. So, what is 3/5 x 20?

“Per” means “divided by”

If you see a problem discussing rates, or using the word “per” be prepared to switch into fraction or division mode.  Per is another way of saying “divided by.”

A car travels 50 miles per hour.  The per is literally the line in a fraction.  50 miles/hour.

Note: Sometimes instead of “per” you will see the words “for every.”  For every boy, there are two girls.  So that means 1 boy divided by 2 girls.

Don’t fear word problems.  There are a limited number of word problem types.  Learn the basic approach for most of these, and work on your reading and logic when navigating the answer choices.  Once you have this vocabulary nailed down, and you study reading and logic, you will have a new perspective to word problems and be able to solve them without difficulty.

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

Steve Odabashian received his BA in Economics from the University of Virginia and then went on to receive his JD at Villanova. He has worked in Tokyo as a foreign attorney, done pro bono work for the Committee of Seventy in several Philadelphia elections, and he is a well known pianist and comic entertainer in Philadelphia. Steve has been teaching for Veritas Prep since 2004.

Descriptive items need to be next to or as close as possible to what they are intending to modify.   The following rules govern adjectival phrases and clauses:

The following is a grammar exercise from one of GMAC’s practice tests:

Introduced by Italian merchants resident in London during the sixteenth century, in England life insurance remained until the end of the seventeenth century a specialized contract between individual underwriters and their clients, typically being ship owners, overseas merchants, or professional moneylenders.

The sentence is rambling and awkward.   However, it is not as difficult to decipher what the correct response is if you keep in mind the idea of correct modification.   Notice the beginning phrase:  Introduced by Italian merchants resident in London during the sixteenth century.  It is descriptive and therefore needs to modify the word that immediately follows the comma.

Now look at the opening words of the answer choices:

(A) in England life insurance remained until the end of the seventeenth century a specialized contract between individual underwriters and their clients, typically being

(B) in England life insurance had remained until the end of the seventeenth century a specialized contract between individual underwriters and their clients, who typically were

(C) until the end of the seventeenth century life insurance in England had remained a specialized contract between individual underwriters and their clients, typically

(D) life insurance remained in England until the end of the seventeenth century a specialized contract between individual underwriters and their clients, typically

(E) life insurance remained until the end of the seventeenth century in England a specialized contract between individual underwriters with their clients, who typically were

The first three answer choices can be eliminated:  in England and until the end of the seventeenth century were not introduced by Italian merchants.    It was life insurance that was introduced by Italian merchants.   Thus, only the final two are possible responses.

Of these two, GMAC is additionally testing the idiomatic construction: between…and.   For instance, one would say:  I cannot choose between the veal chop and the rack of lamb.   One would NOT say:  I cannot choose between the veal chop with the rack of lamb.   Thus, (E) can be eliminated.

The correct answer is (D). 

Let us look at another example from the makers of the GMAT:

Currently 26 billion barrels a year, world consumption of oil is rising at a rate of 2 percent annually.

Again, be alert to the opening descriptive phrase:  Currently 26 billion barrels a year, which needs to modify what follows the comma.   Here are the answer choices with the introductory words bolded:

(A) world consumption of oil is rising at a rate of

(B) the world is consuming oil at an increasing rate of

(C) the world’s oil is being consumed at the increasing rate of

(D) the rise in the rate of the world’s oil consumption is

(E) oil is consumed by the world at an increasing rate of

What is currently 26 billion barrels a year?  Certainly it is not the world, the world’s oil, the rise or oil.   It is the world consumption of oil.

The correct answer is (A). 

Modification is important.  It adds clarity, sensibility and specificity to ideas that a writer is attempting to convey.     When modifiers are incorrectly positioned, they create ambiguity for the reader.    Open your eyes and pay closer attention to all modifiers in a sentence to see whether they are properly placed.   With greater attentiveness and a bit of practice, you will hone your ability to recognize these types of errors.   And in return, you will see your GMAT score in the grammar improve.

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

John Chismody is a Veritas Prep GMAT instructor based in Pittsburgh, PA. After receiving his BS in Engineering from the University of Pittsburgh, he went onto Duquesne University to receive his Masters. He moved to the Big Apple for a while, then down to South Beach, but has returned to his native home of Pittsburgh and continues to teach for Veritas Prep. 

How can I tell if I’m looking at a “Parallel Reasoning” question? The question-stem will contain an argument, and the question itself will contain phrases like “method of reasoning,” “parallel reasoning,” “most similar,” “similar reasoning,” or “most closely parallel.” You’ll also see that each answer choice is its own argument, as opposed to an assumption, inference, or flaw.

Let’s look at a simply example!

Argument #1: If someone has blonde hair, then they have blue eyes. My father has blonde hair, therefore my father has blue eyes.

The reasoning here is presented as a conditional A -> B, “blonde hair” means “blue eyes.” This reasoning is then used to make a conclusion, using the exact same pattern: A -> B. Here’s an example of a simple argument that uses parallel reasoning to Argument #1:

Argument #2: The best internet cafes have free wifi. All cafes with free wifi serve unlimited coffee. Therefore, the best internet cafes serve unlimited coffee.

It’s the same reasoning because the logic moves in the same direction from A -> B , going from “wifi” to “coffee,” then “best cafes” to “wifi.” Don’t worry that this argument  is not arranged in exactly the same order as Argument #1, it’s the method of reasoning that must be similar. A correct answer choice can be a little bit different from the question-stem. It’s the LOGIC that counts!

Watch out for…

•  Answer choices that merely mimic the topic of the argument. The correct answer’s argument usually focuses on an entirely different topic. It’s not what is being discussed that matters, but how the reasoning is laid out.
• Answer choices that have the same structure as the question-stem argument, but do not have the same logic! Just because an answer choice contains similar keywords, or has a similar number of sentences, doesn’t mean its logic matches! The premises and conclusion can be rearranged, but the logic of an argument doesn’t change.
• Pacing! These question-types typically take longer than strengthen or weaken CR, because you have 6 arguments to break down, as opposed to 1 (whew!). Practice untimed at first, but as you gain more confident with this question-type, set a timer and try to do them in under 3 minutes, then under 2 minutes.

Look out for Part 2 of this series, where we’ll look at what strategies we can use to break down Parallel Reasoning questions quickly and effectively, and get them correct every time.

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!

Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT. 

1. Strengthening the conclusion
2. Weakening the conclusion
3. Inferring based on the conclusion
4. Method of reasoning used

As you can easily tell from the categories above, the conclusion usually plays a pivotal role in correctly answering the question at hand. Thus, identifying the author’s point is a necessary step that cannot be circumvented. In particular, let’s focus in on strengthening the argument or weakening the argument, two sides of the same coin that can often be solved the exact same way (you may need to insert the word “not” somewhere)

Within the context of a strengthening or weakening question, the three steps to correctly solving the question are always the same (and very similar to casing a joint for a heist)

1. Identify the conclusion
2. Evaluate the premise(s)
3. Find the gap between the conclusion and the premise.

Again, the conclusion is the key to everything. If you correctly identify the conclusion, you’re on the right path to success. If you misidentify the conclusion, you will likely fall into a clever trap laid out for you. Let’s look at an example:

Nate: Recently a craze has developed for home juicers, $300 machines that separate the pulp of the fruits and vegetables from the juice they contain. Outrageous claims are being made about the benefits of these devices: Drinking the juice they produce is said to help one lose weight or acquire a clear complexion, to aid in digestion, and even to prevent cancer. But there is no indication that juice separated from the pulp of the fruit or vegetable has any properties that it does not have when unseparated. Save your money, if you want carrot juice, eat a carrot.

Which of the following, if true, most calls into question Nate’s argument?

(A)  Most people find it much easier to consume a given quantity of nutrients in liquid form than to eat solid foods containing the same quantity of the same nutrients.

(B)  Drinking juice from home juicers is less healthy than is eating fruits and vegetables because such juice does not contain the fiber that is eaten if one consumes the entire fruit or vegetable.

(C)  To most people who would be tempted to buy a home juicer, $300 would not be a major expense.

(D)  Nate was a member of a panel that extensively evaluated early prototypes of home juicers

(E)  Vitamin pills that supposedly contain nutrients available elsewhere only in fruits and vegetables often contain a form of those compounds that cannot be as easily metabolized as the varieties found in fruit and vegetables.

After quickly identifying the type of question (calls into question = weaken), the next step on the road to success is to identify the conclusion. Looking over Nate’s soliloquy, the majority of it is context as to how the juicing craze came about, the positive aspects of juicers (the unexpected plot twist when the juicer was betrayed by Cobra) and the negative aspects of juicers. The conclusion, summed up in a succinct manner at the end is simply “Save your money, if you want carrot juice, eat a carrot.”

The trap that many people fall for here is that Nate’s argument is based primarily on monetary issues. Yes the juicer separates the juice from the pulp, but it’s not worth the money! (C’mon you could take that money and buy ¾ of an Apple share). If you focus in on the money aspect, you probably want to pick answer choice C, because it indicates that the money won’t be a big concern for prospective clients. However, this is a trap based on the phrasing of the conclusion.

The conclusion could have just as easily read “Don’t be a fool, if you want carrot juice, eat a carrot”. This conveys the exact same message, but answer choice C would now have to be something akin to “Most people who would buy this juicer have IQs above 114½”. The call for saving your money is simply used for emphasis; it has little bearing on the actual issue, which is that you get the same nutrients from solid foods as you would from consuming only the juice.

For strengthening/weakening questions, the third step of minding the gap between the premise and the conclusion is necessary to determine which answer choice to select. In this question, the premise is talking about the nutrients of one form versus the other, and the conclusion states that there’s no reason to ever want the juice instead of the solid. What’s the gap? Maybe there’s another reason we would want the juice! Perhaps it tastes better, or your teeth aren’t as solid as they used to be and juice is preferable to trying to bite into an apple (or perhaps you’re trying to cross a border and fruits are illegal but the juice is fine).

Upon rereading the answer choices, A is exactly what you want. The others all fall down in various ways.

(A)  Most people find it much easier to consume a given quantity of nutrients in liquid form than to eat solid foods containing the same quantity of the same nutrients.

Perfect. This gives us a valid reason to want to drink the juice.

(B)  Drinking juice from home juicers is less healthy than is eating fruits and vegetables because such juice does not contain the fiber that is eaten if one consumes the entire fruit or vegetable.

Tempting, but this strengthens the argument instead of weakening it. 180 °.

(C)  To most people who would be tempted to buy a home juicer, $300 would not be a major expense.

Trap answer based on financial considerations.

(D)  Nate was a member of a panel that extensively evaluated early prototypes of home juicers

Again, wouldn’t this make Nate an expert on the subject? Strengthener and 180 °.

(E)  Vitamin pills that supposedly contain nutrients available elsewhere only in fruits and vegetables often contain a form of those compounds that cannot be as easily metabolized as the varieties found in fruit and vegetables.

New topic. Why are we introducing vitamin pills here? Out of scope.

The correct answer is (A). 

On these types of critical reasoning questions, correctly identifying the conclusion is paramount to correctly answering the question. Hijacking the conclusion will result in an answer choice that seems correct, but doesn’t address the underlying point the author is making. And since strengthening and weakening questions make up the majority of Critical Reasoning questions on the GMAT, the only conclusion you should come to is to practice these questions regularly.

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 occasional tips and tricks 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. Don’t study where you sleep.
   We’re all guilty of studying in bed, cross-legged, furiously typing away at a last-minute Quant practice section, but studies have shown that our bodies becomes conditioned with routines. If you consistently use your bed as your office-space, it will be harder for you to mentally “switch off” once you climb under the covers. If possible, do most of your computer-work at a desk or kitchen table, away from your bedroom (or at least a few feet away from your bed).
2. Exercise, even in small bursts.
   We all KNOW we should exercise, but it can be tough to find even 30-60 minutes a day to go for a jog or take a yoga class when you’re in a 3-month GMAT study zone. Even if you have no time to get a true workout in, make yourself take at least three five minute stretch and meditation breaks – one in the morning, one in the afternoon, and one before bedtime. For each break, set your phone alarm for five minutes and quickly stretch out on the floor. Stretch out your spine and listen to yourself breathe. This allows your muscles (especially those around your head and shoulders) to relax into the floor, and remove any tension you may be subconsciously “holding” in your body.
3. Fight insomnia with a total black-out.
   Noise, light, and cold are three of the most common things that can prevent us from drifting off. If you have street lights or a neighbor’s lamp shining in through your bedroom window, consider covering them up with a large blanket before you hit the hay. Try to make your bedroom as pitch-black as possible.  Buy some ear plugs, even if you don’t have noisy roommates. With them in, you’ll be able to listen to your heartbeat, which will lull you to sleep more quickly after a stressful day. Take the plugs to the library to get a more focused study-session in as well!
4. Find some inspirational quotes.
   It may sound silly, but putting up some inspirational quotes or mantras on your wall above your desk such as, “what you seek is seeking you,” or “thoroughness characterizes all great men” or even something as simple as, “I am going to ROCK my GMAT!” can create a less stressful study atmosphere.

Remember: You’ve come this far, and you know you’re going to get your MBA somewhere – all you’ve got to do is stay positive for just a few more months! Good luck!

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!

Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT. 

Basic Properties

A quadrilateral, by definition, is a polygon with four sides created by four straight lines. Some common quadrilaterals are: a square, a rectangle, a parallelogram, and a trapezoid.

Need-to-know fact: The sum of the interior angles of any quadrilateral is 360.

Remember that every time you add a side to a figure, you add 180 degrees to the sum of its interior angles. That is why a triangle’s sum is 180, and any quadrilateral’s sum is 360.  Keep in mind that definition-wise, quadrilaterals are inclusive. This means that a square is ALSO a rectangle, so be aware that just because a question states that a shape is a “rectangle” doesn’t necessarily mean it can’t have four equivalent sides!

Perimeter

The perimeter of a quadrilateral is the sum of its four sides. For a rectangle, the formula is P = l + l + w + w, or P = 2l + 2w. For a square, this becomes P = 4s. For other quadrilaterals, you need to know the length of each side in order to find the perimeter, unless you are given more information about the comparative lengths of the sides. For example, for a parallelogram we know that the opposite sides are equal in value, so knowing two adjacent sides would be sufficient to find the perimeter.

Area

The area of a quadrilateral is the measurement contained within its four sides. There is no one area formula for all quadrilaterals. Instead, each one has a unique equation that must be memorized.

• To find the area of a square, we use the formula A = s², where s = side of the square.
• To find the area of a rectangle, we use the formula A = lw, where l = length and w = width.  T
• To find the area of a parallelogram, we use the formula A = bh, where b = base and h = height. We do NOT simply multiply the two side lengths. Remember the base and the height must be perpendicular.
• To find the area of a trapezoid, we use the formula A = h(b1 + b2) / 2. We essentially take the average of the two bases, and multiply it by the height. Again, the height is perpendicular to each base.

Remember to analyze your incorrect questions from Veritas Prep’s question bank. Use this data to understand your strengths and weaknesses and focus your GMAT prep on the area that need it most!

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!

Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT. 

“I wouldn’t ask too much of her,” Nick says “You can’t repeat the past.” “Can’t repeat the past?” Gatsby cries out. “Why, of course you can!”

So what does this have to do with studying for the GMAT, and getting into business school?

Most GMAT studiers tend to fall into two camps: those who look back on the books they’ve completed, the scores from their practice tests, the number of questions they’ve answered and those who look forward to the concepts they still haven’t covered, the sections of the Official Guide left to complete, and the ever-dwindling weeks left before the Big Test. So which way is better? Should we study for the GMAT like Nick Carraway or like Jay Gatsby?

The answer is a little bit of both! Here’s how looking to the past AND looking to the future can help you achieve higher scores in your prep!

The Past

• Don’t worry too much if your practice test scores are inconsistent, especially if you’re using different companies’ tests. Are you finishing the sections in time? What types of questions are you getting wrong? Use your practice tests as a diagnostic tool to tell you where to go next.
• Don’t ever waste time beating yourself up over the results of one study session. Everyone gets tired, and has days where they just can’t seem to get any questions right! Jay Gatsby might not have been able to let things go, but you certainly can (and should!).
• Look for your own “blind spots” – any particular concepts you’ve been avoiding, even unconsciously?

The Future

• Make sure you’re keeping a realistic study-plan – are you piling too much on, or facing burn out? Try to study in shorter blocks, and take breaks.
• Are your goals realistic? If you’re looking for a 200 point gain in two weeks, you might need to re-consider. It’s not that miracles can’t happen, but a 700+ score rarely happens after a few weeks of cramming.
• Study with purpose. If you can pinpoint via your practice tests exactly what types of questions you’re getting wrong, then you can sit down and try to tackle them in focused 2-hour sessions. Study smarter, not harder!

While Jay Gatsby’s determined clinging to the past might not be the best model for a GMAT test-taker, he is the quintessential “self-made” man, who through his own hard work and discipline became the wealthiest man on Long Island, and typifies the American Dream. So if you can take a well-deserved break from your GMAT studying today, I’d highly suggest a ticket to Gatsby before getting back to your books.

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!

Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT. 

The “” symbol is called the “radical” symbol. You may know the square root, but how comfortable are you with cube roots? For instance:

The “3″ in the above is the “index” of the radical; to simplify radicals, use your knowledge of factors:

64 = 2 x 2 x 2 x 2 x 2 x 2

There are six 2’s in 64. Since the index is 3, we know we need three of the same number to pull it out from underneath the radical. Exponents and radicals appear most frequently on the GMAT in data sufficiency questions dealing with number properties:

If z < 0, then what is ?

If z is negative, let’s say -2 then –z = -(-2) = 2. Looking at the absolute value, the absolute value of z = -2 will be positive 2. Underneath the radical we would be left with 2 x 2 = 4. The square root of 4 is 2, which is the opposite of our original z = -2. No matter what negative value we plug in for z, the correct answer will always be -z.

When multiplying radicals, we can multiply the elements underneath the radicals:

√3 x √2 = √6

When dividing radicals, we can divide the elements underneath the radicals:

√6 / √2 = √3

When adding or subtracting similar radicals, treat the radicals like variables and combine like terms:

2√3 + 4√3 – √2 + 7√2 = 6√3 + 6√2

On the GMAT, you will never be required to know a decimal equivalent of a radical. If you see a complicated-looking radical, try to “ballpark” it. For example, it is enough to recognize that √110 is going to be slightly larger than 10, since √100 = 10. Let’s look at a question involving exponents:

Is x² > x ?

(1) x² > 4

(2) x > -2

Because you know your exponent rules, you know that whether x² > x is true is dependent on what kind of number x is.

From Statement (1), x > 2 or x < -2. For all numbers greater than 2 and less than -2, the answer to this yes/no question is “yes.” Sufficient

From Statement (2), let’s choose two values to try to get two different answers. If x = 0, then the answer to the questions would be “no,” however if x = 4 then the answer would be “yes.” A statement that allows us to answer a yes/no question with both a yes and a no cannot be sufficient.

The rules don’t change because powers and roots are combined with a secondary concept, such as inequalities here, so don’t let a combination of ideas throw you as you practice!

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!

Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT. 

The four most common strategies to get to the right answer are: algebra, conceptual thinking, picking numbers, and backsolving. Backsolving involves plugging in answer choices into the question to see whether it works. Picking numbers helps concretize abstract concepts with multiple variables (remember you can pick your friends and you can pick your nose but you can’t pick your friends’ nose). However the topic I’d like to focus on today is conceptual thinking.

The four strategies I mentioned above are not used arbitrarily in a vacuum; you can mix and match them to suit the problem at hand. Backsolving is often a good choice once you’ve done some algebra, or number picking can get you the right answer if you manipulate the equations provided. However, the strategy that will give you the greatest return is usually to start off with conceptual thinking. Look at the problem and think about what is being asked of you, as well as what information is provided that may guide your understanding. This tends to put you on the right path more often than not.

I often compare the GMAT to a game of Cranium (awesome board game). In Cranium, you must answer a question on a node, and then either take the fast track or the scenic path to the next node. As you can imagine, you can win the game even if you take the scenic path once or twice, but if you take it every time, you will assuredly run out of time. Similarly, on the GMAT, if you don’t know the best way to solve a question, it may take you 3 minutes to get a question right. This is fine if every second or third question is difficult, but if every question takes 3 minutes you’re only going to answer 25 questions out of 37.

Let’s look at a particularly challenging work/rate problem that is made much simpler by understanding what is going on:

Machine A takes 10 hours to complete a certain job and starts that job at 9AM. After one hour of working alone, machine A is joined by machine B and together they complete the job at 5PM. How long would it have taken machine B to complete the job if it had worked alone for the entire job?

(A)   15 hours

(B)   18 hours

(C)   20 hours

(D)   24 hours

(E)    35 hours

Using only algebra and the (hopefully) memorized formulae for Work problems (Work = Rate x Time or Rate = Work/Time), we can break this problem into 3 parts: Machine A alone from 9 AM to 10 AM (like a bad episode of 24), Machines A and B from 10 AM to 5 PM, and then the hypothetical Machine B alone. Let’s set up these three steps to see how we can solve this on the scenic path (ooh look to your left: a 3D dinosaur!).

Machine A takes 10 hours to do the job, so each hour it works finishes 1/10^th of the total job. From 9 AM to 10 AM, Machine A works alone, so at 10 AM, machine B kicks in and 1/10^th of the job is done. Ergo, 9/10^th of the job is left to complete for both machines.

From 10 AM to 5 PM, 7 hours pass, during which 9/10^th of the job gets completed. Thus we can calculate the rate of the machines working together: 9/10 = Rate_A+B x 7 hours. Rate_A+B = 9/70.

Since we know that Rate_A + Rate_B = Rate_A+B (i.e. rates are additive), we can leverage the fact that we know 2 of these 3 rates to find the third using basic fraction addition. 1/10 + Rate_B = 9/70. Putting them all on a common denominator: 7/70 + Rate_B = 9/70, so Rate_B = 2/70, or 1/35.

Now that we have B’s rate of 1/35, we can easily tell that it would take 35 hours to complete the entire job.

The correct answer is (E).

The algebraic solution works fine and gets you the right answer, but there are many moving parts to keep track of and many opportunities for mistakes. Can we get to the same answer but faster (aka the Max Power way) using conceptual understanding and avoid the scenic route (and the pack of velociraptors) entirely?

If machine A does 1/10^th of the work in an hour, and it works from 9 to 5 (what a way to make a living), then it works for 8 hours and accomplishes 80% of the job on its own. This means that machine B only accomplishes 20% of the job, and it does so in 7 hours (10 AM to 5 PM). If the machine does 1/5 of the job in 7 hours, it will take (7×5) 35 hours to complete 5/5 of the job. Answer choice E, using almost no math whatsoever, but rather by exploiting the logic of the question.

In general, if you see how to solve a problem via algebra and are confident you can solve it in 3 minutes or less, then by all means go for it. However, you can save some time if you really understand how questions are set up and what they are testing. It may not be possible to come up with a handy shortcut on test day because of nerves and stress, but during your preparation take a look at how problems are solved and see if you can find a more elegant solution. All roads lead to Rome, and the more routes you know, the less likely you are to get stuck in unfamiliar territory.

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Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you occasional tips and tricks 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.