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If x is negative and y is positive, which of the following m
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06 Jan 2021, 09:48
06 Jan 2021, 09:48
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If x is negative and y is positive, which of the following must be positive?
A. x/y
B. xy
C. 2y + x
D. (x + y)^2 + 1
E. 3x/y
Kudos for the right answer and explanation
A. x/y
B. xy
C. 2y + x
D. (x + y)^2 + 1
E. 3x/y
Kudos for the right answer and explanation
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Joined: 10 Apr 2015
Posts: 6218
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If x is negative and y is positive, which of the following m
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06 Jan 2021, 10:25
06 Jan 2021, 10:25
1
Carcass wrote:
If x is negative and y is positive, which of the following must be positive?
A. x/y
B. xy
C. 2y + x
D. (x + y)² + 1
E. 3x/y
A. x/y
B. xy
C. 2y + x
D. (x + y)² + 1
E. 3x/y
APPROACH #1: Scan the answer choices
Upon scanning the five answer choices, I see that D is always positive.
D. (x + y)² + 1
Since (x + y)² is greater than or equal to 0 for all values of x and y, we can be certain that (x + y)² + 1 must be positive
Answer: D
APPROACH #2: Use counter-examples to eliminate for answer choices
A. x/y
If x = -1 and y = 1, then x/y = (-1)/1 = -1, which is not positive.
Eliminate answer choice A
B. xy
If x = -1 and y = 1, then xy = (-1)(1) = -1, which is not positive.
Eliminate answer choice B
C. 2y + x
If x = -3 and y = 1, then 2y + x = 2(1) + (-3) = -1, which is not positive.
Eliminate answer choice C
E. 3x/y
If x = 1 and y = -1, then 3x/y = (3)(-1)/(1) = -3, which is not positive.
Eliminate answer choice E
By the process of elimination, the correct answer is D
Re: If x is negative and y is positive, which of the following m
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23 Apr 2022, 17:55
23 Apr 2022, 17:55
If x is negative and y is positive, which of the following must be positive?
A. x/y => negative / positive = must be negative
B. xy => negative x positive = must be negative
C. 2y + x => 2 (negative) + positive can be positive if 2y < X
D. (x + y)^2 + 1 => must be positive because every squared values will always be positive, positive + positive = must be positive
E. 3x/y => negative / positive = must be negative
Correct Answer: D
A. x/y => negative / positive = must be negative
B. xy => negative x positive = must be negative
C. 2y + x => 2 (negative) + positive can be positive if 2y < X
D. (x + y)^2 + 1 => must be positive because every squared values will always be positive, positive + positive = must be positive
E. 3x/y => negative / positive = must be negative
Correct Answer: D
