secrets from the vault-quantitative comparisons
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7/27/2019 Secrets From the Vault-Quantitative Comparisons
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GRE® is a registered trademark of the Educational Testing Service. Kaplan materials do not contain actual
GRE items and are neither endorsed by nor affiliated in any way with the ETS.
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.
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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
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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
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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.
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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:
Quantity A Quantity B
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 .
Quantity A Quantity B
Thus, the quantities are actually equal, and Making the Quantities Look Alike made that
much easier to see. The correct answer is (C).
EXAMPLE:
Quantity A Quantity B
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:
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Quantity A 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:
Quantity A Quantity B
(y+2)(6y+5) (2y+3)(3y+4)
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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.
Quantity A Quantity B
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
Quantity A Quantity B
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.
Quantity A Quantity B
b-ab 0
Then we can add ab to both quantities to make it clearer what we are comparing:
Quantity A Quantity B
b ab
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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
Quantity A Quantity B
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
Quantity A Quantity B
-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
Quantity A Quantity B
-5x + 20 -5x-20
Then we can add 5x to both sides to create a very simple comparison
Quantity A Quantity B
-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.
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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
Quantity A Quantity B
4(
QUESTION 2
Quantity A Quantity B
-1
QUESTION 3
Quantity A Quantity B
QUESTION 4
cd <0
Quantity A Quantity B
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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
Quantity A Quantity B
(
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
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to the positive square root, we can legally square both quantities to get:
Quantity A Quantity B
Next, we can Make the Quantities Look Alike by using FOIL to expand Quantity B.
Quantity A 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:
Quantity A Quantity B
Then we subtract 1 from both quantities to make a simple comparison.
Quantity A Quantity B
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).
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