Counter-intuition on the GMAT

By: Manhattan GMAT Staff

We begin a new series on counter-intuition on the GMAT. Intuition is no doubt a skill that any seasoned businessperson would rank in his/her top-five list of "success makers." Why then do we speak of counter-intuition on the GMAT? Let's clarify first and recognize that there are different kinds of intuition. There is the intuition that tells the experienced do-er: "This situation is similar to one that I've seen in the past, and therefore this is what is going to happen." There is another type of intuition that is more akin to a "sixth sense," like a mother's inexplicable knowledge of what is right for her child. But the type of intuition that we will be talking about is that which delivers the test-taker into the hands of the GMAT test-writers. We will call it test-taker's intuition. Test-taker's intuition is not the intuition of having done 1000 questions of a certain type and recognizing past patterns (a very favorable thing). It is the intuition that guides you to an answer choice because it feels or sounds right or because it looks like a good answer. Unfortunately, this kind of intuition can get you into a lot of trouble on the GMAT.

Problem Solving

What exactly constitutes intuition in Problem Solving? The answer to this question will vary quite a bit, depending on the topic matter that is being tested. Intuition on probability questions will mean one thing, whereas intuition on geometry questions with a diagram will mean something else altogether. However, as we saw in earlier editions of this discussion, we will define the intuition that we are speaking of as that which causes the test-taker to hastily decide upon a certain answer choice because it seems to look right. Put differently, this intuition may be thought of as the mechanism that prevents the test-taker from delving into the deepest layer of the question and uncovering the mathematical principles that are being tested. One area where students commonly fall prey to the whims of this type of intuition is in percent problems. Let's take a look at the following example:

If we express the price of the stock after the first week as a percent, it equals 83 1/3% of the original price. Likewise the price of the stock after the second week equals 66 2/3% of the original price. A hasty glance at these two numbers reveals a decrease in the percent from week one to week two of 83 1/3 - 66 2/3 or 16 2/3. What's our mistake here? In our hastiness, we have glossed over the concept that is being tested here - percent change. Percent change deals with the change between two values and how that change relates to the original value.

The formula for percent change is: Percent change = (valuenew - valueold)/valueold.

The fact that the values given in the problem are percents themselves makes it easy to overlook that we are dealing with percent change. When we simply subtract the two values we come up with a percent, so it is easy to think that this difference equals the percent change!

The actual percent change should have been calculated in this way, where x equals the original price of the stock:

Notice that we kept the values here in fractions because fractions are typically easier to deal with than percents on the GMAT. As an alternative to using a variable to represent the original price of the stock here, we could have substituted in a value for the original price, making the problem a little less abstract. A good value to use here would have been $6, since taking 5/6 and 2/3 of 6 would leave us with integers:

What is important to notice in this example is that this question is designed to prey on the intuition of the unwary test taker. If the question had merely spoken about the percent change between two stock values given in dollars, it would have been much less effective in stymieing its audience. Most GMAT test takers know the percent change formula. What is out of the ordinary here is the use of the percent change formula to show a change in values that are themselves expressed as percents.

How then can the conscientious test taker prevent herself from falling for this ruse? The best thing to do is to stay alert and always be suspicious. If you find yourself finishing a Problem Solving question with a simple addition, subtraction, or multiplication of the given values, chances are you have jumped the gun. Take a step back and re-evaluate the concept that is being tested in the problem. Every Problem Solving question on the GMAT tests one or more mathematical concepts that must be mastered. If you identify the concept that is relevant for that particular question and apply sound principles to solve, you will adeptly steer clear of the perils of intuition on Problem Solving.

Data Sufficiency

More so than any other question type, Data Sufficiency epitomizes the tricky nature of the GMAT. One might think that Data Sufficiency questions should be easier than Problem Solving; after all you don't actually need to come up with an answer to the question - you simply need to decide if you have enough information to solve the question! However, the path to "deciding if you have enough information" is laden with many a trap. Let's focus our discussion of counter-intuition in Data Sufficiency on one such snare.

You may recall from your high school Algebra class the golden rule for solving multiple equations with multiple unknowns: to solve, the number of equations must be equal to the number of unknowns. If you have two unknowns, you need two equations to solve, if you have three unknowns, three equations, etc. In fact, many of you know this rule so well that we could consider it to be part of the fabric of your mathematical intuition. How then can the GMAT capitalize on this prejudice of yours? Let's examine a GMAT-like data sufficiency question to find out:

The question presents an equation with three variables. If we apply the high school algebra rule, three equations should be needed to solve. Three equations implies that we need two additional equations. Which answer choice would provide us with the required extra two equations? C of course - C would give us the equation from statement (1) and the equation from statement (2) to solve for p.

Another way to look at this is to realize that in the question, p's value is dependent on both r and q. If you knew r and q, you could easily solve for p. When you look at the statements, you see that neither one gives you r and q, but statement (1) gives you r, and if you plug that into statement (2) you can get q. Your intuition here could easily lead you to answer choice C.

Unfortunately, though, your intuition led you astray; C is the wrong answer. It's the trap around which the GMAT writers designed this question. Let's try and simplify the question first to see why.

We can begin the process of simplifying the question by eliminating all of the "little denominators" within the larger fraction. With denominators of q, r and 2q, the least common denominator of these fractions is 2qr. Multiply the fraction by a special form of the number one: 2qr/2qr. When we do this all of the "little denominators" cancel out:

With p = 6q/7r, we can rephrase the question here slightly differently. In order to solve for the value p, we do not need individual values for q and r; instead, we simply need the ratio of q to r, or q/r. Statement (2) provides us with that information so the answer here is B: q = 3r so q/r = 3.

Questions involving multiple equations with multiple unknowns often times have a built-in trap. The GMAT takes advantage of the test taker's preconceived notions. Algebraic intuition backfires, and the unexpected emerges as the correct answer. Learn to be suspicious of data sufficiency questions of this sort and not to rely too heavily on your intuition.

Critical Reasoning

What characterizes this type of Critical Reasoning argument on the GMAT is the fact that the argument contains no conclusion. It is merely a list of premises, stated pieces of information that can be used to form some kind of conclusion. The task of the test-taker is to find that conclusion.

Notice that when we read the premises in the above argument, the information naturally leads us to start thinking about possible conclusions. From the first two sentences, we begin to see a possible correlation between a reduction in sales of triple blade razors and a reduction in the amount of money spent on marketing the razors. The third sentence further bolsters this idea by stating that the leading manufacturer of razors used a higher percentage of its marketing budget to promote its razors than Company A did, finally adding that the smallest competitor, Company C, used the smallest percentage. The thrust of the passage seems to be pushing us to draw some kind of conclusion about the amount of money spent on marketing the razors and sales.

When we look at the answer choices, indeed answer choice A seems to capture the very essence of this correlation. However, it is the wrong answer! When crafting a correct answer choice to a Draw a Conclusion question, the GMAT authors have the onus of coming up with a conclusion that is indisputable - they don't want to have angry test-takers coming back and arguing with them! It is worth noting that this differs from the conclusions seen in other types of Critical reasoning arguments; these conclusions are riddled with assumptions and often quite disputable. When the tides are turned and the test-taker is responsible for coming up with the conclusion, the GMAT must make the correct answer a statement that is readily apparent, i.e. obvious from the given premises. This often times equates to a conclusion which is merely a restatement of one or two of the premises in the argument! This is our first example of counter-intuition on the GMAT because an educated test-taker's intuition would lead her to think about a conclusion that actually attempts to draw a correlation and conclude something, not one that merely restates the obvious!

Let's look at some of the other reasons why answer choices A through D are wrong. Answer choice A, while capturing the essence of the implied correlation as described above, makes a huge leap in claiming that a direct relationship exists. Furthermore, answer choice A references "the amount of money that a company spends." The passage doesn't address specifically the amount of money that any of the companies spent; it speaks about the percentage of marketing budget that is used to promote a product. Answer choice B makes this same mistake.

Answer choice C belongs to a common type of answer choice on the GMAT, one in which a trend or pattern is hypothetically extrapolated into the future, into an unknown set of circumstances. The future is hard to predict in the real world, but on the GMAT it's impossible. Answer choice D makes a huge assumption that is not verified anywhere in the passage, namely that the two largest manufacturers of triple blade razors hold more than 2/3 of the market share.

Answer choice E is the correct answer here because it makes no attempt at lofty conclusions. It simply restates a couple of facts that were stated quite plainly in the passage. If Company C increased the percentage of its marketing budget that it dedicated to its razors to 25% during the six year period from 1980 to 1986, then the percentage of its marketing budget that it allocated to its razors was consistently less than that of Compnay A during that period.

Intuitively, most people would pick A on this question. Go against your gut and pick the obvious on a Drawing the Conclusion question!

Sentence Correction

Let's first define intuition as it relates to Sentence Correction. When asked to give an explanation of why they have chosen a certain answer in Sentence Correction, most people will undoubtedly respond "it just sounds right." In fact "good intuition" on Sentence Correction can probably best be likened to having a good ear. Is Sentence Correction then simply designed to test how adept the test taker's ear is in perceiving a properly constructed sentence? As tempting as it is to rely almost exclusively on one's ear, the path to complete mastery of Sentence Correction is a bit more complex than that. In fact, Sentence Correction is designed, first and foremost, to assess the test taker's knowledge of specific grammatical principles: subject-verb agreement, verb tenses, pronoun usage, parallelism, etc. While it is often true that the for the more seasoned test taker, the grammatically sound answer choice will also sound the best, the GMAT test writers have once again found a way to trick test takers on this point. There are numerous examples of Sentence Correction questions in which the answer that our intuition guides us to as "sounding right" is in fact the wrong answer.

One topic area that seems to be a breeding ground for this issue is idioms. Idioms are expressions in the English language that have unique forms. Some idioms are easy to "spot" in their correct form, while others are decidedly foreign to even the most well-trained ear. What makes these more difficult idioms an interesting target for GMAT test writers is the fact that they usually have an un-idiomatic counterpart (i.e. a phrase that is used to convey the same meaning), which sounds more appealing to most people's ears. Let's take a look at the following example:

The question above tests one of the most commonly misused idioms in the English language: "to consider x y" (where x is a noun and y is either a noun or an adjective). If you surveyed 10 educated people, however, chances are more than half of them would say that the correct idiom is "consider x to be y". Why the discrepancy? It's hard to say really, but remember that idioms have a mind of their own - there is no rhyme or reason to describe their behavior. Leave it to the GMAT to capitalize on this fact.

Most people's intuition of what sounds right here would lead them to choose answer choice (A). The correct idiom, "to consider x y" leads us to either (C) or (E). The subject of the sentence, most, is one of those tricky pronouns that can be either singular or plural. In the context of "most of the … opponents," however, most would be plural; in the context of "most of the pie," most would be singular. For a plural subject, the verb must be consider, and the correct answer here is (C).

It is important to note that your intuition (i.e. your ear) should not be categorically ignored in Sentence Correction. In fact, your ear can often time be a valuable tool for eliminating one or two patently awkward answer choices. The danger arises when you use your ear to unilaterally arrive at the correct answer choice, neglecting the grammatical principles that form the backbone of good sentence correction technique.

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