Integer constraints

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2y - x = 2 xy and x is not equal to 0. If x and y are integers, which of the following could equal y?


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

[srcc25anu]

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

if x is positive, NuM will be +ve, DEN will be -ve hence Y cannot be +ve
that eliminates A, B and C

If x is -ve, NUM will be -ve, DEN will 1 - (-ve number) = +ve again Y should be -ve

If x = 2, y = 2 / (2 - 4) => y = -1

Hence Y could equal -1. Answer D