MathRevolution wrote:
[GMAT math practice question]
If \(\frac{1}{x}-\frac{1}{y}=\frac{1}{z}\), what is the value of \(y\), in terms of \(x\) and \(z\)?
\(A. \frac{xz}{(z-x)}\)
\(B. \frac{xz}{(x-z)}\)
\(C. \frac{x}{z(z-x)}\)
\(D. \frac{z}{x(x-z)}\)
\(E. xz(z-x)\)
Let \(x=1\) and \(y=\frac{3}{2}\), with the result that \(\frac{1}{z} = 1 - \frac{2}{3} = \frac{1}{3}\), so \(z=3\).
Since the question stem asks for the value of y, the correct answer must yield \(\frac{3}{2}\) when x=1 and z=3.
Since B and D include x-z and thus will yield a negative result, eliminate B and D.
Since E includes only multiplication and thus cannot yield \(\frac{3}{2}\), eliminate E.
Between A and C, only A yields \(\frac{3}{2}\):
\(\frac{xz}{z-x} = \frac{1*3}{3-1} = \frac{3}{2}\)
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