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If (1+x)y = y(x-1), which of the following mus be true?

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by swerve » Thu Jan 04, 2018 7:53 am
If (x + 1)*y = y*(1 - x), which of the following must be true?

A. x = -1 or y = 0
B. y = 0
C. x = 1 or y = 1
D. x = -1 or y = -1
E. x = 0

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I don't understand it. I need your help. Thanks.
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by Brent@GMATPrepNow » Thu Jan 04, 2018 8:12 am
swerve wrote:If (x + 1)*y = y*(1 - x), which of the following must be true?

A. x = -1 or y = 0
B. y = 0
C. x = 1 or y = 1
D. x = -1 or y = -1
E. x = 0
GIVEN: (x + 1)(y) = ( y)(1 - x)
Expand both sides: xy + y = y - xy
Subtract y to get: xy = -xy
Add xy to both sides to get: 2xy = 0
So, EITHER x = 0 OR y = 0

Answer: B & E (hmmmmmmm)

ASIDE: If we plug x = 0 into the equation, we get y = y (works)\
If we plug y = 0 into the equation, we get 0 = 0 (works also)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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