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\(2y - x = 2xy\) and \(x\ne 0.\) If \(x\) and \(y\) are integers, which of the following could equal \(y?\)

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\(2y - x = 2xy\) and \(x\ne 0.\) If \(x\) and \(y\) are integers, which of the following could equal \(y?\)

by Vincen » Wed Sep 30, 2020 6:36 am

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\(2y - x = 2xy\) and \(x\ne 0.\) If \(x\) and \(y\) are integers, which of the following could equal \(y?\)

(A) 2
(B) 1
(C) 0
(D) -1
(E) - 2

Answer: D

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Re: \(2y - x = 2xy\) and \(x\ne 0.\) If \(x\) and \(y\) are integers, which of the following could equal \(y?\)

by Scott@TargetTestPrep » Fri Oct 09, 2020 9:18 am
Vincen wrote: ↑
Wed Sep 30, 2020 6:36 am
 \(2y - x = 2xy\) and \(x\ne 0.\) If \(x\) and \(y\) are integers, which of the following could equal \(y?\)

(A) 2
(B) 1
(C) 0
(D) -1
(E) - 2

Answer: D

Solution:

Rearranging the terms of the equation, we have:

2y - 2xy = x

2y(1 - x) = x

y = x/[2(1 - x)]

We see that if x = 2, we have:

y = 2/(-2) = -1

(Note: We use x = 2 because we are given that x ≠ 0, and we see that x can’t be 1, either, otherwise the denominator 2(1 - x) would be 0. Therefore, the next logical integer value for x is 2, and it happens to yield a value for y that is one of the answer choices. If it hadn’t, we could have used x = 3 or x = -1.)

Answer: D

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