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# M15-02

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Math Expert
Joined: 02 Sep 2009
Posts: 55188

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16 Sep 2014, 00:54
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Difficulty:

55% (hard)

Question Stats:

61% (02:31) correct 39% (02:14) wrong based on 46 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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16 Sep 2014, 00:54
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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: 26
Location: United Kingdom
GMAT 1: 740 Q50 V41
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04 Jul 2018, 14:40
So obvious when it's written out - feel like a complete idiot!
Intern
Joined: 27 Jul 2017
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26 Sep 2018, 16:14
why can't M or N be a fraction or a decimal eg .25?
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26 Sep 2018, 20:45
abastie wrote:
why can't M or N be a fraction or a decimal eg .25?

They can be fractions: 1/M > 1/2 means that 0 < M < 2.
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28 Sep 2018, 21:38
meaning why cant M= 1/3 itself so 1/3= 3 wouldnt this make that statement not necessarily bigger than 1?
Math Expert
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29 Sep 2018, 00:07
abastie wrote:
meaning why cant M= 1/3 itself so 1/3= 3 wouldnt this make that statement not necessarily bigger than 1?

The point is, (1) is sufficient because it gives a NO answer to the question for all values of M and N which satisfy 1/M > 1/N > 1/2. Meaning that MN/(M + N) < 1 for all values of M and N (for fractions and integers) which satisfy 1/M > 1/N > 1/2.
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Re: M15-02   [#permalink] 29 Sep 2018, 00:07
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# M15-02

Moderators: chetan2u, Bunuel

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