For integers x and y, x2y0 . Which of the following must be true?

Question

For integers x and y,  x^2y > 0 . Which of the following must be true?

I. xy > 0
II. x > 0
III. y > 0

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

PraveenChahal · Answer

X can be positive or negative but y must always be positive so answer is C

Sent from my Moto G (4) using  GMAT Club Forum mobile app

KSBGC · Answer

1. x is an integer
2. x^2y>0

from points 2 we can deduce that x could be negative or could be positive. As  x^2  will always be positive , y has to be positive all time. Thus, only iii is correct. The correct answer is C.

BrentGMATPrepNow · Answer

APPROACH #1 : Apply inequality property: 
Given:  x²y > 0 
Since we know x² is POSITIVE, we can safely divide both sides by x² to get:  y > 0 
So, statement III is certainly true.

As you can see, applying the inequality property only gets us so far. From here, I'd start testing values...

APPROACH #2 : Test values
Let's test some x and y values that satisfy the given condition that x²y > 0

For example  x = -1  and  y = 1  satisfies the inequality x²y > 0

Now let's use these values to check our 3 statements: 
I. xy > 0. Plug in our values to get: ( -1 )( 1 ) = -1. This means xy is NOT greater than 1. The question asks, "Which of the following   must   be true?" 
So statement I is NEED NOT be true. 
This means we can ELIMINATE answer choices A and E

II. x > 0. Plug in x-value to get:  -1  > 0
This is NOT true. 
This means we can ELIMINATE answer choices B and D

This leaves us with answer choice C only, which means statement III MUST be true

Answer: C

RELATED VIDEO
 https://www.youtube.com/watch?v=S_fjYmCtvy0

Mo2men · Answer

x^2y > 0

It means that 2 number with same sign; either both positive or both negative. But  x^2  is always positive, so y MUST be positive and. However, x can take negative or positive sign. Therefore: Mus be answer is only y > 0

Answer: C

AkshdeepS · Answer

As we know, x can be positive or negative, the only required condition to satisfy the inequality is that y > 0.

Hence (C)

ScottTargetTestPrep · Answer

Since x^2 is always positive, y must be positive as well. So III is true. However, x could be either positive or negative. If x is negative, neither I nor II would be true.

Answer: C

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.

For integers x and y, x2y>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

For integers x and y, x2y>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