Given that m and n are both larger than p and… | GMAT Sprint

Free Practice Question

PS · Problem Solving

605-655

Absolute Values/Modules

Given that m and n are both larger than p and q, which of the following statements is necessarily true?

I. m + n > p + q
II. mn > pq
III. |m| + |n| > |p| + |q|

Answer Choices

Correct answer marked below

I only

Correct

II only

I and II

I and III

I, II and III

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Explanation

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Official Explanation

Official

Given that

m

and

n

are both larger than

p

and

q

, we analyze the statements:

Statement I:

m + n > p + q

Since

m > p

and

n > q

, adding these inequalities gives

m + n > p + q

.

Conclusion: Statement I is necessarily true.

Statement II:

mn > pq

This is not always true. For example, if

m = -1

n = -2

p = -3

, and

q = -4

, then

mn = 2

and

pq = 12

, so

mn > pq

is false.…

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Comments

GuluJan 4, 2025

Great!

JayaJul 20, 2024

thanks!

SerenaFeb 26, 2024

thanks!

What this question tests

What it tests

Your ability to solve absolute-value equations and inequalities by considering both cases.

Common trap

Dropping the absolute value bars entirely or missing that |x| = k has two solutions when k > 0.

Given that m and n are both larger than p and q, which of the following statements is necessarily true? I. m + n > p + q II. mn > pq III. |m| + |n| > |p| + |q|