the ultimate guide to solving gre quantitative comparison questions
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http://www.BarronsTestPrep.com/gre
The Ultimate Guide to Solving GRE
Quantitative Comparison Questions
Barron’s Guide for Quantitative
Comparison Questions
http://www.BarronsTestPrep.com/gre
Quantitative Comparison questions ask you to
compare two quantities – Quantity A and Quantity B – and choose one of the four possible answers that relate the two quantities.
Example:
Q. 1 < 𝑎 < 𝑏 < 𝑐 < 𝑑
Quantity A Quantity B
𝑎3𝑏5 𝑐7𝑑9
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
The quantity in Column A is greater
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Introduction
Despite their convoluted appearance,
Quantitative Comparisons are some of
the easiest questions on the Math
section of the GRE. This is due to three
things:
A. Limited answer choices (only 4);
B. Students’ ability to use Elimination to
solve;
However the most important reason is…
As a student you are probably accustomed to finding the exact solution of a
problem that you are given. This is NOT the case with Quantitative
Comparisons, and in fact should be avoided whenever possible! If you can
figure out which column is larger WITHOUT performing any calculations, then
you have solved the question and saved yourself valuable time.
In this eBook, we will share with you some important tips and strategies to
ace the GRE Quantitative Comparison questions.
You Don’t Have to Find Actual Values to Solve Them.
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Some Problems Can ONLY
Be Solved By Comparing,
Not Calculating!
The problem at the beginning of this list illustrates this
principle perfectly. Unless you are an algebra
connoisseur, you may not know the obscure rule that
proves the correct answer here. But try comparing:
You know c and d are greater than a and b, so c7 and
d9 must both be greater than a3 and b5:
1 < 𝑎 < 𝑏 < 𝑐 < 𝑑
Example:
Quantity A Quantity B
𝑎3𝑏5 𝑐7𝑑9
Two positive numbers multiplied Two LARGER positive numbers multiplied
This fact irrefutably makes B the correct answer.
If you can’t immediately calculate, don’t freak
out! Try comparing. After all, these are
Quantitative Comparisons.
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“
They Can Be
Solved Analytically
It may seem hard to believe (or too good to be true, depending
on your disposition) that there is a straightforward way to solve
this cumbersome question format. But it’s true! Many
Quantitative Comparison questions can be solved using the
following workflow strategy, called “Could They Be Equal,
Must They Be Equal.
.
“
” The Analytical Approach:
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Example:
Q.
Quantity A Quantity B
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
The quantity in Column A is greater
Solution:
Start off by asking “Could they be equal?”
The easiest way to answer this question is to assume certain values for the
variables e.g. when 𝒙 = 𝒚 = 𝟎, the two columns are equal
Quantity A Quantity B
0 0 = 0 0 0 = 0
The answer to the first question is No and we can immediately eliminate
Answer Choice A and B.
Next ask yourself “Must they be equal?”
Once again the easiest way to answer this question is to assume certain
values for the variables e.g. when 𝒙 = 0,𝒚 = 1, we see that column B is
larger:
Quantity A Quantity B
0 1 = 1 0 1 = 1
The answer to the second question is also No and we can also eliminate
Answer Choice C.
D is the Correct Answer.
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Don’t Ever Choose D If There Are Fixed Values in Columns A and B.
If the values in columns A and B are fixed values, then there
is no way that the comparison is indeterminate. Even if you
can’t figure out which is larger, don’t guess D
Example:
Q.
Quantity A Quantity B
95 94 94
The answer to the above question cannot be D. The question can be solved easily using Math:
95 94 = 94 9 94 = 94 9 1 = 94 8
Since 94 8 > 94, Quantity A is greater than Quantity B
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“D” is NOT for
Difficult
The relationship cannot be
determined is often a tempting
solution when you can’t figure
out how to solve a tough
problem. However, on difficult
questions, more often than not,
the solution will simply be hiding
from you. If you can verify the
reason why a question can NOT
be solved, then and only then
should you choose D. If you
have to guess on a very difficult
problem that you can’t solve,
don’t guess D.
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They’re Similar to
Equalities/Inequalities
Despite their seemingly abstract structure, there are
actually a number of concrete tools that you can use to
navigate through this problem type. First and foremost,
many of the techniques that you use to solve equalities
and inequalities may be used to modify the Quantities in
Quantitative Comparison problems:
You can add the same number to quantities A
and B or subtract the same number from
quantities A and B.
You can multiply or divide Quantity A and
Quantity B by the same positive non-zero
number.
You can square both Quantity A and Quantity
B.
Knowing exactly what tools you have available is a vital
part of solving these problems! Don’t underestimate these
simple techniques.
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Example:
Q. =
Quantity A Quantity B
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
The quantity in Column A is greater
Solution:
Add: 𝑦 on both sides:
The easiest way to answer this question is to assume certain values
for the variables e.g. when 𝒙 = 𝒚 = 𝟎, the two columns are equal
Quantity A Quantity B
𝑥 𝑦 𝑧 𝑦
Simplify: We know: 𝑥 𝑦 = 𝑧 𝑦 , next subtract 𝑧 𝑦
from both sides:
Quantity A Quantity B
𝑧 𝑦 𝑧 𝑦
𝑧 𝑦 𝑧 𝑦 𝑧 𝑦 𝑧 𝑦
7 3
Since 7 > 3, Quantity in Column A is larger.
A is the Correct Answer.
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Common Sense
is Key
Avoid doing more than you have to on these problems;
your intuition can give you keen insights that may allow
you to skip entire problems! Take a look at this example:
Example:
Q. Kyle scored 75 on each of her first three math tests and scored 80 on her 4th and 5th tests.
Quantity A Quantity B
Kyle’s average after 4 tests Kyle’s average after 5 tests
Solution:
Can you solve this problem using intuition alone?
In this case, column B is greater, because the scores on tests 4 and 5 are higher than
those of 1, 2, and 3. On the test, being able to solve a problem like this quickly and
definitively will give you more time and energy to expend on tougher questions.
Want to learn more about how to actually solve these problems? Check out our lecture
titled “Solving Quantitative Comparison Problems” to get the inside scoop on these
esoteric questions.
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
The quantity in Column A is greater
http://www.BarronsTestPrep.com/gre
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