If AB ≠ 0 and A^3B = AB^3, then which of the… | GMAT Sprint

Free Practice Question

PS · Problem Solving

555-605

Algebra

If $AB ≠ 0$ and $A^3B = AB^3$ , then which of the following must be true?
I) $|A| = -|B|$
II) $|A| = |B|$
III) $A = B = 2$

Answer Choices

Correct answer marked below

None

II only

Correct

III only

I and II only

I, II, and III

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Explanation

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Official Explanation

Official

To solve the equation

A^3B = AB^3

, we can divide both sides by

AB

(since

AB ≠ 0

), leading to

A^2 = B^2

. This implies that

|A| = |B|

. Therefore, statement II is true. However, statement I,

|A| = -|B|

,…

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Comments

NiyaFeb 12, 2025

Can someone explain it other way?

ChiamakaMar 14, 2025

thanks a lot

EnnioJan 30, 2025

thanks a lot

MdFeb 8, 2025

thank you very much!

chungSep 5, 2024

this pattern comes up frequently

AmoghFeb 7, 2025

Thank you very much!

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.

If AB≠0AB ≠ 0AB=0 and A3B=AB3A^3B = AB^3A3B=AB3, then which of the following must be true? I) ∣A∣=−∣B∣|A| = -|B|∣A∣=−∣B∣ II) ∣A∣=∣B∣|A| = |B|∣A∣=∣B∣ III) A=B=2A = B = 2A=B=2