MrWallSt wrote:
If x / (x+y) = n, and x / (x-y) = m, then x/y=? (|x| does not equal |y|, xy does not equal 0)
A. 3mn/2
B. (3m)/(2n)
C. (n * (m+2))/2
D. 2nm / (m-n)
E. (n^2 - m^2) / nm
You can do it either algebraically or by assuming numbers:
Algebra:
Note that we are happier with (x+y)/x rather than x/(x+y) since in the former case we can make manipulations easily. So let's take the inverse of both n and m
\(\frac{1}{n} = \frac{(x+y)}{x} = 1 + \frac{y}{x}\) ....(I)
\(\frac{1}{m} = \frac{(x-y)}{x} = 1 - \frac{y}{x}\) .....(II)
Since we have both m and n in our answer, lets subtract II from I to get
\(\frac{1}{n} - \frac{1}{m} = \frac{2y}{x}\)
\(\frac{(m-n)}{2mn} = \frac{y}{x}\)
\(\frac{x}{y} = \frac{2mn}{(m-n)}\)
Answer (D)
Or Plug in numbers: x = 2, y = 1
n = x/(x+y) = 2/3
m = x/(x-y) = 2
x/y = 2
Now put n = 2/3 and m = 2 in the options. Only option (D) gives you x/y = 2.
Hence answer (D)
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Karishma
Veritas Prep GMAT Instructor
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