Given that |x+y|-z 0 II. w > 0 whenever z 0

Given that |x+y|-z < w, which of the followin… | GMAT Sprint

Practice Questions Blog Pricing

Free Practice Question

PS · Problem Solving

655-705

Inequalities

Given that $|x+y|-z < w$ , which of the following statements must hold true?
I. $x+y > 0$
II. $w > 0$ whenever $z < 0$
III. $w+z > 0$

Answer Choices

Correct answer marked below

I only

II only

III only

II and III only

Correct

I, II, and III

See the full step-by-step explanation

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

Track your performance and improve

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

Start for free Sign in

Explanation

Preview

Official Explanation

Official

|x+y|-z < w

, we can rewrite it as

|x+y| < z + w

, which implies

z + w > 0

. Now, let's analyze the statements: I.

x+y > 0

This is not necessarily true. II.

w > 0

whenever [m]z <…

Read the full explanation

Create free account Sign in

Comments

ShantanuJan 3, 2024

Good question

What this question tests

What it tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Common trap

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.

Given that ∣x+y∣−z<w|x+y|-z < w∣x+y∣−z<w, which of the following statements must hold true? I. x+y>0x+y > 0x+y>0 II. w>0w > 0w>0 whenever z<0z < 0z<0 III. w+z>0w+z > 0w+z>0