If xy

Question

If xy < 0, which of the following must be true?

I. x + y = 0

II. 2y - 2x < 0

III. x^2 + y^2 > 0

A. I only
B. III only
C. I and III
D. II and III

pratikshanaik · Answer

I think the Answer is III only

GMATinsight · Answer

xy < 0 
 i.e. signs of x and y are opposite and both are non zero numbers

Question asks  "MUST be true"

I. x + y = 0 Not necessarily true as we do NOT know whether absolute values of x and y are equal or not

II. 2y - 2x < 0 i.e. y < x Not necessarily true as we do NOT know whether y is negative or x. we know one of them is negative and other is positi

III. x^2 + y^2 > 0 Has to be true as they are both non zero and their squares must be positive

Answer: Option B

Niha01 · Answer

B. III only. Since x or y can both be positive or negative, but always opposite signs at a time.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If xy < 0, which of the following must be true?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If xy < 0, which of the following must be true?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards