secrets from the vault-quantitative comparisons

7/27/2019 Secrets From the Vault-Quantitative Comparisons

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SECRETS FROM THE VAULT

The GRE®: Strategies for

Quantitative Comparison

Questions



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About the author, Ben Leff:

Ben is a GRE Instructor and Faculty Manager for Kaplan Test Prep. He began teaching

for Kaplan in 2007, after completing a BA and MA in History from Brown University. His

Kaplan background includes managing and training faculty members (2009 Midwest

Trainer of the Year) as well as contributing to several course revisions, including Kaplan’s

new curriculum for the Revised GRE. Still, teaching is his favorite part of the job. He

looks forward to teaching the New GRE course for years to come, but he mourns the

loss of analogies, his favorite verbal question type. According to Ben’s students, he is a

“compassionate” instructor “with a unique enthusiastic and energetic approach to

teaching” and he “truly cared and was interested in the subject he taught.” When not

working for Kaplan, Ben enjoys watching and playing sports—though every passing year

brings more watching and less playing.




SECRETS FROM THE VAULT

The New GRE®: Strategies for Quantitative

Comparison Questions

How do you get a top score on the Quantitative Section of the GRE? Most people think

you improve your score by familiarizing yourself with math content. True, you’ll have to

memorize some formulas, review some rules, and brush off your algebra skills.However, that will only take you so far. Kaplan test takers know how to employ

strategic approaches on the GRE that allow them to use the format of the test to their

advantage. This is especially true for Quantitative Comparisons, which reward test

takers who use strategies to help them get to the answer while doing as little work as

possible.

An Introduction to Quantitative Comparisons On Test Day, you’ll see 7-8 Quantitative Comparisons on each quantitative

section, and they’ll be grouped together at the beginning of each math session.

Here’s how they work: you are asked to compare two quantities, and sometimes

there is centered information that applies to both quantities. The four answer

choices are always the same. If Quantity A is always greater than Quantity B,

then the answer is (A). If Quantity B is always greater than Quantity A, then the

answer is (B). If the quantities are equal, the answer is (C). And if the

relationship cannot be determined—if the relationship between the quantities

changes depending on the situation—then the answer is (D).

Quantitative Comparison Answer Choices




Quantitative Comparison questions test geometry, algebra, arithmetic, numberproperties, statistics, among other topics you learned in high school. While

these aren’t advanced topics, you probably haven’t touched them in years.

Therefore, you’ll need to study to learn the rules and formulas you’ll need to

succeed on Test Day.

But Kaplan teaches you that there is more to succeeding on Quantitative

Comparison questions than mere memorization. Quantitative Comparisons test

our ability to determine the relationships between quantities, so we often don’t

have to solve for the exact value of each column. Therefore, strategic

approaches that just focus on determining the relationship between the

quantities rather than their precise values provide the most efficient path to

many correct answers. Here, we’ll discuss three Kaplan strategies for

determining the relationship between quantities.

o Compare Don’t Calculate

o Make the Quantities Look Alike

o Do the Same Thing to Both Quantities

Compare, Don’t Calculate

The great news about Quantitative Comparisons is that you don’t always have to

calculate the exact value of each column. Because this question type only asks for the

relationship between the two quantities, Kaplan students can get to the right answer

while doing less work than their competition. The GRE will reward test takers who

recognize that we can often get to the right answer by Comparing the two quantities

rather than Calculating their exact value.

EXAMPLE:

Steven drives from Town A to Town B at an average speed of 70 miles per hour and

returns, without stopping, to Town A via the same route at an average speed of 60 miles

per hour.

Quantity A Quantity B

Steven’s average speed, in miles per hour,for his round trip journey between Towns

A and B.

This average speed question provides a classic opportunity to Compare rather than

Calculate. We could solve for the exact value for the car’s average speed by setting up

several equations and solving. Indeed, a Problem Solving question might ask you to do




just this. However, on a Quantitative Comparison, we can get to the right answer much

more efficiently.

First, we must avoid the temptation to say “70 mph one way, 60 mph on the return trip,so the average speed must be half way in between, or 65.” This is not true! We can

only average the speeds to get the total average speed if an equal amount of time was

spent on each leg. Instead, we must remember that the part of the trip that took longer

will have more “pull” on the average. So, for example, if the car spent a longer time

travelling at 60 mph than at 70 mph, the average speed will be closer to 60 than 70.

So we need to ask ourselves, which part of the trip took longer? Well, as anyone who

drives knows, it takes longer to get somewhere when you go slower. That’s why we are

tempted to speed! So the car travelled at 60 mph longer than it travelled at 70 mph. As

such, the average speed isn’t 65, but rather, a little less than 65. Therefore, the correct

answer is (B).

Even though we never figured out the exact value of the average speed (it’s about 64.6,

but we don’t care!), we were still able to solve by Comparing rather than Calculating.




Make the Quantities Look AlikeIt’s a lot easier to compare two quantities when they are in somewhat similar form. For

example, it is hard to tell at first glance whether 5/8 or .615 is larger. However, if werewrite 5/8 in decimal form as .625, it is much easier to see that 5/8 is larger than .615.

That’s the idea behind Making the Quantities Look Alike. We manipulate or simplify

one or both of the quantities so that our two quantities are in a similar form. Once we

do that, the relationship between the quantities will often emerge. Let’s see how this

works with a few examples.

EXAMPLE:


The form of the two quantities is similar, but there are some small differences that

indicate that we should try to Make the Quantities Look Alike. Both quantities are

fractions, but they have different denominators. It will be easier to compare the

fractions once the denominators look alike, so let’s make that happen. Since all of the

coefficients in Quantity A are divisible by 3, we can reduce and thereby rewrite this

quantity as Similarly, the coefficients in Quantity B are all divisible by 2, so

Quantity B can be rewritten as .


Thus, the quantities are actually equal, and Making the Quantities Look Alike made that

much easier to see. The correct answer is (C).

EXAMPLE:


When we see exponents this large, we should immediately suspect that we need not

calculate the exact value of each column. Rather, we should find a way to put the

quantities in similar form so we are able to compare them effectively. Quantity B has

factored out, so let’s see if we can manipulate Quantity A in a similar manner. By

factoring out , we can make Quantity A look like Quantity B:





Therefore, by Making the Quantities Look Alike, we are able to see that the quantities

aren’t quite identical. Since Quantity A is and Quantity B is , the

correct answer is (A).

Thus, we can see that Making the Quantities Look Alike is a great strategy when we have

slightly different formats. This strategy helps us solve questions the way that the GRE

wants us to: efficiently and without unnecessary calculation.

Do the Same Thing to Both Quantities The golden rule of algebra is that you can isolate variables by doing the same thing to

both sides of an equation. This principle is also quite useful when we attack

Quantitative Comparisons. By Doing the Same Thing to Both Quantities, we can

simplify each column and Make the Quantities Look Alike. All we care about is the

relationship between quantities, and Doing the Same Thing to Both Quantities lets us

focus on what matters: the differences between the quantities.

Some rules of engagement here: you can add or subtract any number from bothquantities. You can also multiply or divide both quantities by any positive number. You

cannot multiply or divide both quantities by a negative number, or else you will change

the relationship between the quantities. For this reason, be very careful about

variables! Only multiply or divide both sides by an expression containing a variable

when you know that the expression is positive.

EXAMPLE:


(y+2)(6y+5) (2y+3)(3y+4)




We’ll actually start this question by Making the Quantities Look Alike. They are already

in a similar form, but not a very useful one—it’s hard to tell which column is larger. So

our first step is to FOIL and express both quantities as expanded quadratics:Quantity A Quantity B

(y+2)(6y+5) (2y+3)(3y+4)

6y^2 +5y+12y+10 6y^2 +8y+9y+12

6y^2 +17y+10 6y^2 +17y+12

Notice that the two quantities look very similar now. We can simplify by subtracting the

same thing from both quantities. We can subtract 6y2

from both sides, as well as

subtract 17y from both sides. We are left with a very simple comparison: 10 vs. 12.


6y^2 +17y+10-6y

2

-17y 6y^2 +17y+12-6y

2

-17y6y^2 +17y+10-6y2-17y 6y^2 +17y+12-6y

2-17y

10 12

Quantity B is greater, so Choice B is correct. By Making the Quantities Look Alike and

Doing the Same Thing to Both Quantities, we neutralized an ugly mess of variables.

EXAMPLE

0<a<b<1


a+b-ab A

Once again, we can Do the Same Thing to Both Quantities to simplify a seemingly

complex comparison. We start by subtracting a from both quantities to get the

following comparison.


b-ab 0

Then we can add ab to both quantities to make it clearer what we are comparing:


b ab




Now, we notice that both quantities have a common factor of b. We should be careful

about dividing by a variable, but the centered information told us that b is positive, so it

is ok. When we divide by b, the remaining comparison is


1

This has become a much easier comparison. The centered information flatly states that

a is less than 1, so (A) is the correct answer.

EXAMPLE


-5x + 20 -5(x+4)

This quantitative comparison can also be solved by Doing the Same Thing to Both

Quantities, but we must be careful. Remember that we CANNOT multiply or divide by a

negative number because that flips the relationship between the quantities. Therefore,

you must resist the temptation to multiply both sides by -1. If you do that, you will get

to the wrong answer!

Instead, we can start by Making the Quantities Look Alike. If we distribute the -5

through the expression in Column B, we can rewrite that column as


-5x + 20 -5x-20

Then we can add 5x to both sides to create a very simple comparison


-5x +5x + 20 -5x + 5x – 20

20 -20

Quantity A is greater, so the correct answer is (A). Once again, Making the Quantities

Look Alike and Doing the Same Thing to both quantities made our lives much simpler.




Practice QuestionsIn summary, there’s more to mastering Quantitative Comparisons than memorizing

formulas and math rules. Kaplan test takers learn to use strategic approaches that turn

messy, complex-looking questions into simple comparisons. We’ve learned three

valuable Kaplan strategies for efficiently attacking Quantitative Comparison questions.

Now put them into action on these challenging practice questions.

QUESTION 1


4(

QUESTION 2


-1

QUESTION 3


QUESTION 4

cd <0





EXPLANATIONS

1) C

When we see that both quantities are easily divisible by a common factor, we will know

that we should do the Same Thing to Both Quantities. Here we can divide bothquantities by 4 to get


(

Next, we have to make the quantities look alike. Whenever we see an expanded

quadratic in the numerator of a fraction, we should ask ourselves: would I be able to

cancel anything out if I factored? Here, y2-z

2is a classic quadratic that shows up

repeatedly on the GRE. It equals (y+z)(y-z). As such, we can cancel out the (y+z) from

the numerator and denominator to get y-z.Quantity A Quantity B

(

So after Doing the Same Things to Both Quantities and Making the Quantities Look

Alike, we see that the two quantities are identical. The answer is (C).

2) B

The exponent in this question is astronomical—a good indicator that we should

Compare rather than Calculate. There is no way that the GRE wants us to calculate the231

stroot of a number. Instead, our job will be to use what we know about the

properties of exponents to compare the value of x with -1. First, we can infer from the

centered information that x is a negative number, since only negative numbers would

“stay negative” when raised to an odd power. Based on this knowledge, we know that x

is negative, but is it less than -1?

Let’s think about what would happen if x were between 0 and -1. If that were the case,

and we raised it to a big power, the value would just get closer to closer to zero. In

order for x^231 to equal -4000, x must be more negative than -1. Therefore, even

though we can’t calculate the value of x , we can compare it to -1 and know that

Quantity A is less than Quantity B. The correct answer is (B).

3) C

The techniques of Making the Quantities Look Alike and Doing the Same Thing to Both

Quantities will help us solve this messy-looking Quantitative Comparison. First, we

notice that quantities are under radicals. Since GRE convention holds that radicals refer




to the positive square root, we can legally square both quantities to get:


Next, we can Make the Quantities Look Alike by using FOIL to expand Quantity B.


After we have used our Kaplan strategies, we have found that the two quantities are

identical. The correct answer is (C).

4) D

Our first instinct may be to test different numbers on this Quantitative Comparison, butwe will be best served by doing some critical thinking before we start testing. First, the

centered information tells us that cd <0, which means that either c or d , but not both, is

negative. Next, let’s try to manipulate each quantity to Make the Quantities Look Alike.

If we split each quantity into two separate fractions, we get:


Then we subtract 1 from both quantities to make a simple comparison.


Now testing numbers is much simpler than it was before we Made the Quantities Look

Alike. If c=2 and d =-3, then Quantity A is = - and Quantity B is . Quantity B

is greater. But what if c=3 and d=-2? Then Quantity A would be = - and Quantity B

would be = - . Now Quantity A is greater. Since the relationship changes based on

the numbers we pick, the correct answer is (D).

secrets from the vault-quantitative comparisons

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