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

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

by swerve » Fri Apr 03, 2020 2:31 pm
BTGModeratorVI wrote: ↑
Fri Apr 03, 2020 9:40 am
 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
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Re: For integers x and y, x²y>>0. Which of the following must be true?

by Brent@GMATPrepNow » Sat Apr 04, 2020 5:38 am
BTGModeratorVI wrote: ↑
Fri Apr 03, 2020 9:40 am
 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

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

by Scott@TargetTestPrep » Mon Apr 27, 2020 3:46 am
BTGModeratorVI wrote: ↑
Fri Apr 03, 2020 9:40 am
 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

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