Is $zw$ positive?

(1) $z + w^3 = 20$
(2) $z$ is positive

Answer Choices

Correct answer marked below

Statement (1) ALONE is sufficient

Statement (2) ALONE is sufficient

BOTH statements TOGETHER are sufficient

EACH statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient

Correct

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

Unlock the full explanation

Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.

Create free account Sign in

Comments

MoshaiJun 26

wait why isnt it C? if z is positive and z + w^3 = 20 then w^3 has to be less than 20... but w could still be negative right?

JwarkJul 8

yeah exactly, w^3 could be negative and z just gets bigger to make 20. so zw ends up negative.

UmangJun 29

the trap here is thinking a positive z plus something equals 20 means the something is positive. nope, w^3 can be negative and z just compensates. classic sign trap.

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

Is zwzwzw positive?(1) z+w3=20z + w^3 = 20z+w3=20(2) zzz is positive