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# M15-02

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Math Expert
Joined: 02 Sep 2009
Posts: 49543

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16 Sep 2014, 00:54
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Difficulty:

55% (hard)

Question Stats:

63% (02:27) correct 37% (02:17) wrong based on 30 sessions

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If $$M$$ and $$N$$ are positive, is $$\frac{MN}{M + N} \gt 1$$?

(1) $$\frac{1}{M} \gt \frac{1}{N} \gt \frac{1}{2}$$

(2) $$M = N - 1$$

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Math Expert
Joined: 02 Sep 2009
Posts: 49543

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16 Sep 2014, 00:54
1
Official Solution:

Statement (1) by itself is sufficient. Because both $$\frac{1}{M}$$ and $$\frac{1}{N}$$ are larger than $$\frac{1}{2}$$, their sum is larger than 1: $$\frac{1}{M} + \frac{1}{N} = \frac{M + N}{MN} \gt 1$$. Thus, $$\frac{MN}{M + N} \lt 1$$.

Statement (2) by itself is insufficient. Consider $$N = 2$$ (the answer to the question is "no") and $$N = 1000$$ (the answer to the question is "yes").

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Intern
Joined: 02 Jan 2018
Posts: 27
GMAT 1: 730 Q49 V40

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04 Jul 2018, 14:40
So obvious when it's written out - feel like a complete idiot!
Re: M15-02 &nbs [#permalink] 04 Jul 2018, 14:40
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# M15-02

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