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For integers x and y, [m]x^2y > 0[/m]. Which of the followin
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05 Jan 2021, 07:37
05 Jan 2021, 07:37
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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
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
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Posts: 6218
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Re: For integers x and y, [m]x^2y > 0[/m]. Which of the followin
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05 Jan 2021, 09:37
05 Jan 2021, 09:37
1
Carcass wrote:
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
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
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
Re: For integers x and y, [m]x^2y > 0[/m]. Which of the followin
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23 Apr 2022, 17:49
23 Apr 2022, 17:49
For x^2y > 0, y must be positive because no matter the sign that X has, x^2 must be positive.
Point III is a must have, thus we can cross out option A and B.
X can be negative or positive because every squared value equals to a positive number, thus Point II is not a must have. Thus, we can cross out option D and E.
Option C is the correct answer.
Point III is a must have, thus we can cross out option A and B.
X can be negative or positive because every squared value equals to a positive number, thus Point II is not a must have. Thus, we can cross out option D and E.
Option C is the correct answer.
