In this article, part two of a three-part series, we will examine how an unreliable type of test-taker's intuition can disrupt your ability to answer Data Sufficiency and Sentence Correction questions.In part one, we covered the Draw a Conclusion question.
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:
What is the value of p if
(1) r = 4
(2) q = 3r
(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient
(E) Statements (1) and (2) TOGETHER are NOT sufficient
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.
This week we continue our discussion of counter-intuition on the GMAT with a look at 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:
Most of the Prime Minister's opponents consider his foreign policy to be a mockery of the country's long-held isolationist tenants.
(A) consider his foreign policy to be a mockery of the country's long-held isolationist tenants.
(B) consider his foreign policy as a mockery of the country's long-held isolationist tenants.
(C) consider his foreign policy a mockery of the country's long-held isolationist tenants.
(D) considers his foreign policy to be a mockery of the country's long-held isolationist tenants.
(E) considers his foreign policy a mockery of the country's long-held isolationist tenants.
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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Related: Counter-Intuition on the GMAT, Part 1: Draw a Conclusion