LM wrote:
If m > 0 and n > 0, is \(\frac{m + x}{n + x} > \frac{m}{n}\)?
(1) m < n
(2) x > 0
Note:
If \(\frac{a}{b} > \frac{c}{d}\) and all values are positive, then:
Rephrase 1: \(ad > bc\)
Rephrase 2: \(\frac{a}{c} > \frac{b}{d}\)
Alternate approach:
Statement 2: x > 0Applying rephrase 2 to the question stem, we get:
\(\frac{m+x}{m} > \frac{n+x}{n}\)
\(1 + \frac{x}{m} > 1 > \frac{x}{n}\)
\(\frac{x}{m} > \frac{x}{n}\)
Applying rephrase 1, we get:
\(nx > mx\)
If we divide by positive value x, we arrive at the following rephrase of the question stem:
Is n > m ?No way to determine whether n > m.
INSUFFICIENT.
Statement 1: m < nLet m=1 and n=2.
Plugging these values into the question stem, we get:
\(\frac{1+x}{2+x} > \frac{1}{2}\) ?
If x=1, the answer is YES, since 2/3 > 1/2.
If x=-1, the answer is NO, since 0 < 1/2.
INSUFFICIENT.
Statements combined:Rephrased question stem in Statement 2:
Is n > m ?Statement 1 indicates that the answer to this question is YES.
SUFFICIENT.
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