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If \(m\) and \(n\) are positive integers, then is \(m\) an even integer?

(1) \(\frac{m}{n}\) is an odd integer --> \(m=n*odd\) --> if \(n=odd\) then \(m=odd\) but if \(n=even\) then \(m=even\). Not sufficient.

(2) \(m+n\) is an even integer --> either both are odd or both are even. Not sufficient.

(1)+(2) Still the same two cases are possible: either both are odd (for example \(m=3\) and \(n=1\)) or both are even (for example \(m=2\) and \(n=2\)). Not sufficient.

When you post a question from the GMAT Club Tests the next time, please indicate the Test and question number. For example, this one should have "m25-35" or something similar in the thread title. Thank you for cooperation.

suhasrao wrote:

If M and N are positive integers, then is M an even integer? 1. M/N is an odd integer. 2. M+N is an even integer.

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient

I picked A as the solution, as M and N have to be odd for M/N to be odd.

Please advice if someone has a different solution.

Re: Problem solving question (m25-35) [#permalink]

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15 Sep 2010, 15:13

E.

(1). If M/N = odd, then we have Odd/Odd = Odd (49/7 = 7) or Even/Even = Odd (6/2 = 3). So M and N are Odd/Odd or Even/Even. (2). If M + N = Even, then we have the same information. Odd + Odd = Even (3+5 = 8) and Even + Even = Even (4+6 = 10).

Combine then both together and we still don't know whether M, N are odd or M, N are even. (From above we know if both were true then M would be what N is, so knowing either would answer the question. We know neither.)
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Re: Problem solving question (m25-35) [#permalink]

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22 Mar 2012, 20:46

just place examples into each situation. 1. M/N use 18/2 = 9 odd so M is even or 15/5 = 3 odd so M is odd. Insufficient 2. only odd + odd or even + even can equal even. insufficient.

combined both say the same thing that m and n are both odd or both even but no specific on which one.
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Re: Problem solving question (m25-35) [#permalink]

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20 Sep 2012, 06:38

We need to remember a few scenarios. Every other scenario gives you EVEN.

A) ODD X ODD = ODD (This automatically implies that ODD/ODD = ODD, assuming that the denominator is a factor of numerator) B) ODD +- EVEN = ODD c) EVEN/EVEN = TROUBLE-MAKER (Watch out for this guy, the result is unpredictable ) d) ZERO is considered EVEN. BUT ZERO is neither positive nor negative, its just ZERO
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