For integers x and y, x²y>>0. Which of the following must be true?

[BTGModeratorVI]

For integers x and y, x²y>>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

Answer: C
Source: Veritas Prep

[swerve]

For integers x and y, x²y>>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

Answer: C
Source: Veritas Prep

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

Hence, C

[Brent@GMATPrepNow]

For integers x and y, x²y>>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

Answer: C
Source: Veritas Prep

One approach is to 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

Cheers,
Brent

[Scott@TargetTestPrep]

For integers x and y, x²y>>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

Answer: C
Source: Veritas Prep

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