the ultimate guide to solving gre quantitative comparison questions

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The Ultimate Guide to Solving GRE

Quantitative Comparison Questions

Barron’s Guide for Quantitative

Comparison Questions


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


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.


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:


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.


“

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:


Example:

Q.






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


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:


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.


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.


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


“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.


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.


Example:

Q. =






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


𝑥 𝑦 𝑧 𝑦

Simplify: We know: 𝑥 𝑦 = 𝑧 𝑦 , next subtract 𝑧 𝑦

from both sides:


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.


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.


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.






Barron’s GRE Course for Online GRE Prep:

Personalized Prep based on Adaptive Learning

60+ Hours of Video Instruction

75+ Lessons

4 Full Length Tests with Projected Scores

1 Diagnostic Test with Projected Scores

1000+ practice Questions

The Revised General Test

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the ultimate guide to solving gre quantitative comparison questions

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