The Interplay of Quant and Verbal Sections

Introduction

At some point in the test preparation process, most GMAT test-takers will find themselves asking one of the following existential questions: "What exactly does the GMAT test?", "Why do business schools want me to take this exam?", or "How will this help prepare me for business school?"

While some would no doubt anticipate the answer to these questions to speak to the "futility of standardized tests," the real answer may lie elsewhere. In fact, one could argue that the GMAT is designed to test the very skills that one needs to excel in business school. What skills are those? Quite simply put - analytical quantitative and verbal skills. But what are analytical quantitative skills? What are analytical verbal skills? And how do the two relate? In this month's strategy series we will address the interplay of quantitative and verbal skills on the GMAT.

Analytical quantitative skills on the GMAT go beyond the ability to grasp and apply basic mathematical concepts. Doing math on the GMAT is not about regurgitating formulae or algebraic methodologies. YES, one must know all of the relevant mathematical skills inherent in a problem, but perhaps more importantly one must learn to carefully connect the pieces of information and to do so with a critical eye. It is of paramount importance to always keep the big picture in mind and to not fall prey to the many traps the test-writers set-up on the way. A large portion of these traps have to do with the wording of the question.

What is the key then to steering clear of these potholes in the road? Interestingly, one of the chief requirements for doing well on the quantitative portion of the exam is to have sharp verbal skills. READ CAREFULLY. GMAT math questions are notorious for their cryptic verbiage. In word problems, for example, seemingly benign prepositions or qualifiers are slipped in, drastically changing the meaning of the question. Let's take a look at the following illustrative example:

At his 10th birthday party, a child received 30 candies. He was then forced by his parents to give away at least 30% of those candies to his playmates, one to each playmate. If more than a third of the playmates ate the candies that he gave them while the rest gave them back to the child, what is the greatest number of candies that the child could have ended up with?

(A) 23
(B) 24
(C) 26
(D) 27
(E) 29

Reading carefully on word problems involves paying special attention to potentially tricky phrases. In our example above we have three such important phrases: at least, more than, and greatest. Let's start with the latter - "greatest." The word "greatest" here provides us with the framework for the whole question. It signifies that the question is asking us to maximize the number of candies that the child ends up with.

What about the phrase "at least?" We are told that the child was forced to give away at least 30% of his candies. 30% of his candies would be exactly 9 candies, but since it says "at least," he could have given away more! Should we consider more though? In this case the answer is no because remember we are trying to maximize the number of candies he has at the end. The fewer candies he gives away, the more he will have for himself - ask any child!

The final phrase we have to deal with is "more than." The question says that more than a third of the children ate the candy or candies that the child gave them and the rest gave the candies back. A third of the 9 is 3. Here is where we have to be careful. The question says more than a third ate the candies so at the very least 4 of the 9 ate their candy. The greatest number of candies that the child could have received back from his friends is 9 - 4 = 5. Therefore, the greatest number of candies that the child could have ended up with is 30 - 9 + 5 = 26, and the correct answer is C.

The math in this question is not difficult at all. What makes this question a GMAT question is the wording. By reading carefully and paying special attention to qualifying words like more than, at least, and greatest, we can carefully steer clear of the web that the test-writers have set-up for us in a question such as this.

Join is next week as we continue to examine the integration of quantitative and verbal skills on the GMAT.

How Math Finds its Way into the Verbal Section

Let's take a look at a sample Critical Reasoning question in which the numbers play a crucial role:

A fledgling manufacturing company has recently developed a new titanium alloy anti-ballistic vest with an estimated life-span of nearly twice that of the standard Kevlar vest. Due to the high cost of titanium, however, the titanium vest costs three times more than the Kevlar vest to produce. The company announced the release of the new vest to potential retailers, claiming that the titanium vest will be more profitable than the Kevlar counterpart. To promote the introduction of its product into the marketplace, the company has assured potential retailers that the new titanium vest will be their most profitable item.

Which of the following, if true, would offer the most support to the company's claim?

(A) The manufacturing process for the Kevlar vests has been perfected, leaving no room for further reduction in the cost of the Kevlar vests.
(B) A new source of titanium has just been discovered, a fact that will almost certainly cause the market price of titanium to drop by fifty percent, along with the cost of the new vests.
(C) A promising market for anti-ballistic clothing has just opened up in East Asia.
(D) The U.S. military, a major buyer of antiballistic vestments, is willing to spend top dollar on more a more durable vest.
(E) The plastics industry has recently developed a new polymer that has demonstrated amazing force resistance in preliminary tests.

This question falls under the category of a strengthen/weaken the conclusion question. The conclusion in this passage is the company's claim that their new titanium alloy vest will be the most profitable item among retailers.

Because we are always identifying the best answer choice in a Critical Reasoning question, we must always analyze every answer choice before making a selection. When looking at each answer choice, let's keep in mind the conclusion that we are trying to strengthen.

Answer choice A is fairly unrelated to the company's claim of the increased profitability of the titanium vest. Not being able to reduce the cost of the competing Kevlar vest does not insure saleability of a more expensive replacement.

Answer choice B seems to strengthen the conclusion. If the price of titanium goes down and that savings is passed on to the retailers, the titanium vests will become more profitable, especially since they seem to have an innate added appeal because of their durability.

Answer choice C supports the idea that the overall market for ballistic vests may grow in the near future, however, we have no way of knowing to what degree that growth will affect sales of the titanium vest over the standard Kevlar.

Answer choice D strengthens the conclusion because it establishes the US military's preference for a more durable antiballistic vest and expresses their willingness to pay top dollar for the vests.

Answer choice E weakens the conclusion by introducing a new potential competitor for the new titanium vest.

This analysis leaves us with two favorable answer choices: B and D. Now let's use a more mathematical approach to settle the debate between B and D. Profitability has two elements to it, revenue and cost (P = R - C). To increase profit, we can either increase revenue or decrease cost. But are the two elements of the profitability equation really equal? The obvious answer is no. A lower cost helps the profitability equation, but without revenue, you have nothing. Answer choices B supports the idea of high profitability by addressing the issue of lowering the cost. Answer choice D, on the other hand, supports the idea of high profitability by addressing the issue of raising the revenue.

There is one blow to answer choice B that really demonstrates the use of math on some Critical Reasoning passages. The passage speaks about a 300% cost on the titanium vests, compared to the Kevlar standard. Answer choice B intimates that the discovery of a new titanium source will decrease the cost of titanium by 50%. A 50% reduction to the 300% cost still leaves us at 150% cost. Not only have we not guaranteed a source of revenue, but the cost itself still exceeds that of the Kevlar standard.

Not all Critical Reasoning passages provide numerical values, however those that do are good examples of the interplay of the verbal and quantitative sections on the GMAT.

Another Look at the Quantitative Section

Most newcomers to the GMAT approach the quantitative section from an exclusively mathematical framework. After all most math exams are all about the math! Sometimes on the GMAT, though, it's not as much about the math, as it is about the subtleties implicit in the wording of the question. One of the best places for GMAT test writers to capitalize on this is in Data Sufficiency.

Let's start by taking a look at sample data sufficiency question:

Bobby went to the candy store and bought only gumballs and lollipops. If the gumballs cost 25 cents each and the lollipops cost 35 cents each, how many lollipops did Bobby purchase?

(1) Bobby purchased exactly 6 pieces of candy.
(2) Bobby spent exactly $1.80 on the candy.

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

On the surface, this question looks like a typical algebra word problem, testing one's ability to solve two equations with two unknowns (i.e. a system of equations).

The question establishes the need for two unknowns:
g = number of gumballs and l = number of lollipops

The question also establishes the price per candy:
25 cents per gumball
35 cents per lollipop

From statement 1, we can form the equation: g + l = 6. This is one equation with two unknowns, so we cannot solve. The statement is therefore insufficient.

From statement 2, we can form the equation: 25g + 35l = 180, which can be simplified to 5g + 7l = 36. Again this is one equation with two unknowns, so we have the impression that it is insufficient. In fact most first-time GMAT test-takers would jump to C for a question like this. With the two statements, we have two equations with two unknowns and can therefore solve:

g + l = 6     (multiply this equation by -5)
-5g - 5l = -30
5g + 7l = 36
_____________
2l = 6
l = 3

But the answer here is not C! It turns out that statement 2 is sufficient to solve. The secret lies in realizing that this word problem cannot be dryly translated into two equations with two unknowns. There is another piece of information that we must keep in mind when considering the question along with statement 2. The question tells us that Bobby bought only lollipops and gumballs and he spent exactly 180 cents on a fixed number of each candy. What the savvy GMAT test-taker must be able to glean from this setup is that the number of gumballs and the number of lollipops must both be integers. The question makes it quite clear that Bobby couldn't have bough 2.5 gumballs and 3.5 lollipops, for example.

Now that we have used what one could call reading comprehension skills to accurately assess the situation in this problem, we return to our set of quantitative skills. How do we determine whether there is more than one pair of potential integer values for g and l that satisfy the equation 25g + 35l = 180 (i.e. 5g + 7l = 36)? Let's set up a table of integer values for g and l, along with corresponding values for 5g and 7l. We can then see if there is more than one set of 5g and 7l that add up to 36.

g	5g	l	7l
1	5	1	7
2	10	2	14
3	15	3	21
4	20	4	28
5	25	5	35
6	30
7	35

We can quite easily see now that only with g = 3 and l = 3 will the equation 5g + 7l = 36 hold. None of the other values from the 5g column can be added to values from the 7l column to sum to 36. This makes the second statement sufficient, and the answer to this question B, statement (2) ALONE is sufficient, but statement (1) is not sufficient.

The cautious GMAT test-taker will attack a word problem on the math section with great caution. There is likely something in the problem beyond the basic math skills that are needed to solve. The words and the topic matter (in this case whole lollipops and gumballs) set the stage for other strategies that must be employed to solve.

Sentence Correction

Those who prefer the quantitative section of the GMAT, usually do so because of its systematic, rule-laden nature. For this reason, it is also sometimes easier to prepare for the quantitative section. Perhaps more than any other question type in the verbal section, Sentence Correction most resembles the quantitative section in this sense.

To succeed in Sentence Correction, one needs to first master a set of hard, fast grammatical rules. In addition, one also needs to hone a systematic technique of analyzing the answer choices based on meaningful differences. It is these two aspects that most closely tie Sentence Correction to the quantitative section. To see how this plays out, let's take a look at a sample Sentence Correction question:

According to a recent study, much of the concerns that people have expressed about the instability of this country's economic infrastructure are unfounded; the economic stability of this country is not in peril.

(A) much of the concern that people have expressed about the instability of this country's economic infrastructure are unfounded; the economic stability
(B) much of the concern that people have expressed about the instability of this country's economic infrastructure is unfounded, the economic stability
(C) many of the concerns that people have expressed about the instability of this country's economic infrastructure are unfounded, the economic stability
(D) many of the concerns that people have expressed about the instability of this country's economic infrastructure is unfounded; the economic stability
(E) many of the concerns that people have expressed about the instability of this country's economic infrastructure are unfounded; the economic stability

The first meaningful difference among answer choices that we can focus on is the word much versus many. This difference allows us to "split" the answer choices into two groups AB and CDE. If we can determine which of these phrases is correct, we can eliminate one of the groups.

Much is a word that is used to quantify things that are uncountable, e.g. much water, much love. Many, on the other hand, is a word that is used to quantify countable nouns, e.g. many people, many opportunities. In this example, the word that is being quantified is concern. Can concern be quantified? On the one hand, concerns can definitely be quantified, e.g. "I have two concerns regarding your plan to…" However, is it wrong to say "much of the concern?" Concern as a feeling, can also be considered unquantifiable, e.g. "there is much concern over the president's recent decision…" Unfortunately, this first difference results in a stale mate. In this example, the much/many split is a red herring.

The next point of difference, or split, that we can go after is the verb split IS/ARE (BD/ACE). The subject of the verbs is/are is actually the pronoun much or many. Since many is always used to quantify a plural, countable noun, many must go with the verb are. For this reason we can eliminate answer choice D: many - is. Since much is always used to quantify singular, uncountable nouns, much must go with the verb is. For this reason we can eliminate answer choice A: much - are.

The last split that we can use to analyze the answer choices is in the choice of punctuation before the final clause - namely the semicolon (ADE) versus the comma (BC). A semicolon is used to separate independent clauses. An independent clause is a complete idea that stands alone; it has both a subject and a verb. A comma cannot be used to separate two independent clauses unless a conjunction like "and" is used after the comma. The clause "the economic stability of this country is not in peril" is in fact an independent clause so the semicolon is the proper punctuation here. Since A and D have already been eliminated, the correct answer is E.

This same systematic approach of comparing differences among answer choices and applying immutable grammatical rules can be applied to every Sentence Correction question. In this way, Sentence Correction takes on a more formulaic, almost "math-like" stature.

This concludes our discussion of the interplay of the quantitative and verbal sections of the GMAT.

Copyright 2005 , MG Prep, Inc.; May not be reprinted without permission.