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M15-02

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M15-02  [#permalink]

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New post 15 Sep 2014, 23:54
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (02:32) correct 38% (01:54) wrong based on 42 sessions

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Re M15-02  [#permalink]

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New post 15 Sep 2014, 23:54
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").


Answer: A
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Re: M15-02  [#permalink]

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New post 04 Jul 2018, 13:40
So obvious when it's written out - feel like a complete idiot!
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M15-02  [#permalink]

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New post 26 Sep 2018, 15:14
why can't M or N be a fraction or a decimal eg .25?
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New post 26 Sep 2018, 19:45
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New post 28 Sep 2018, 20:38
meaning why cant M= 1/3 itself so 1/3= 3 wouldnt this make that statement not necessarily bigger than 1?
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New post 28 Sep 2018, 23:07
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 &nbs [#permalink] 28 Sep 2018, 23:07
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