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GRE - Quantitative Reasoning - Algebra

If x =1/y and y =1/(1-x), then y =

If x =1/y and y =1/(1-x), then y =
(A) 2
(B) 1/2
(C) -1/2
(D) -1
(E) -2

Given,

x = 1/y

and y = 1/(1-x)

substituting x in second equation

y = 1 / (1 - 1/y)

y = y/(y - 1)

y2 - y = y

y2 - 2y = 0

y(y - 2) = 0

y = 0 or y = 2

since x = 1/y, y=0 is not possible

thus y = 2