Given that a |b| II. a/b > 1 III. a^b < 0

Given that a < b < 0, which of the following… | GMAT Sprint

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555-605

Absolute Values/Modules

Given that a < b < 0, which of the following statements must be true?
I. |a| > |b|
II. a/b > 1
III. a^b < 0

Answer Choices

Correct answer marked below

I only

II only

III only

I and II only

Correct

I and III only

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Explanation

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Official Explanation

Official

When a < b < 0, both a and b are negative numbers. For instance, consider a = -4 and b = -3 or a = -1/3 and b = -1/2. The absolute value of a will be greater than that of b, indicating that a is 'more negative' than b. Therefore, |a| > |b| holds true. Since both a and b are negative, the ratio a/b will be positive, leading to a/b > 1. However, the statement a^b may not hold true for all cases, such as when a = -4 and b…

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Comments

MishalOct 26, 2024

Great!

AmberMar 22, 2025

Thank for sharing!

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 a < b < 0, which of the following statements must be true? I. |a| > |b| II. a/b > 1 III. a^b < 0