Given that |x+3|3>4 and x<0, which of the fol… | GMAT Sprint

Free Practice Question

PS · Problem Solving

505-555

Absolute Values/Modules

Given that $\frac{|x+3|}{3}>4$ and $x<0$ , which of the following values could x take?

I. -5
II. -12
III. -16

Answer Choices

Correct answer marked below

I only

II only

III only

Correct

II and III only

I, II, and III

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Explanation

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Official Explanation

Official

To solve

\frac{|x+3|}{3}>4

, we first multiply both sides by 3, yielding

|x+3| > 12

. This implies that

x+3 > 12

x+3 < -12

.

Solving these gives

x > 9

x < -15

. Since we also have the condition

x<0

, we focus on

x < -15

. Now we evaluate the options:…

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Comments

SanjanaJun 10, 2024

Thank you very much!

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 ∣x+3∣3>4\frac{|x+3|}{3}>43∣x+3∣​>4 and x<0x<0x<0, which of the following values could x take? I. -5 II. -12 III. -16