Given that |a| = |b| and ab < 0, which of the… | GMAT Sprint

Free Practice Question

PS · Problem Solving

sub-505

Absolute Values/Modules

Given that $|a| = |b|$ and $ab < 0$ , which of the following statements must be true?

Correct answer marked below

ab^2 > 0

b a^2 > 0

a + b = 0

Correct

a/b + 1 = 3

1/a + 1/b = 1/3

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Explanation

Preview

Official Explanation

Official

In this scenario, we know that the absolute values of a and b are equal, meaning

|a| = |b|

. Additionally, since

ab < 0

, one of the variables must be negative while the other is positive. For example, let

a = 2[m] and [m]b = -2

, or

a = -2

and

b = 2

. We can evaluate the options:…

Comments

NelseeMar 14, 2025

finally understood this

JustinJul 15, 2024

thank you taking time to upload it!

What this question tests

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

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