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# Problem solving question (m25-35)

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19 Jan 2010, 19:07
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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.
2. $$M + N$$ is an even integer.

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

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

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20 Jan 2010, 04:29
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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.

stmnt1 - M/N is odd

here if N = 1 then M will be odd but if N is 2 then M will be even[ 6,10 etc]. hence insuff

stmnt2 - M+N is even here also M and N can be both odd or even. Hence insuff

taking together we have if N = 1 let M = 5 then M/N is odd and M+N is even

if N =2 and M = 6 then M/N is odd and M+N is even
so M can be both even or odd.

will go with E

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20 Jan 2010, 04:35
1) M and N Could be both odd or both even. Consider following examples: 10/2 = 5; 15/5=3. Therefore we cannot determine whether M is even

2) Same case here: M,N are both odd OR both even. consider following: 10+2=12; 15+5=20. That is a dead-end too

Combining the statements is fruitless. We can't narrow down possibilities.

It's (E)

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20 Jan 2010, 04:53
Hi,

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.

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

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21 Jan 2010, 22:11
I went with E as well by plugging in a few combos of m and n that work for both 1 and 2. (m,n) (6,3);(5,1);(6,2);(9,3);(33,11).

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

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15 Sep 2010, 05:56
E

statement 1 and 2 hold true for M being Even and Odd, for Both.

I used egs - 21/7, 10/5 and 10/2, couldn conclude.

Statement 1 - Odd/Odd = Odd ; Even/Even = Odd/Even; 21/7 and 10/2
Statement 2 - Odd + Odd = Even; Even + Even = Even; 21 + 7 = 28; 10 + 2 = 12.

With Both statements together -
Assuming M/N - Odd (21/7 & 10/2)

M can be even or Odd (10 or 21) and Statement 2 is still TRUE.

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

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15 Sep 2010, 07:59
E

statement 1 and 2 hold true for M being Even and Odd, for Both.

I used - 21/7, 3/3 and 10/2, couldn conclude.

Statement 1 - Odd/Odd = Odd ; Even/Even = Odd/Even; 21/7 and 10/2
Statement 2 - Odd + Odd = Even; Even + Even = Even; 21 + 7 = 28; 10 + 2 = 12.

With Both statements together -
Assuming M/N - Odd (21/7 & 10/2)

M can be even or Odd (10 or 21) and Statement 2 is still TRUE.

Hence "E"

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

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15 Sep 2010, 08:41
E by plugging even & odd numbers.
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Re: Problem solving question (m25-35) [#permalink]

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15 Sep 2010, 09:07
E by using 6,2 and 9,3 values

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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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20 Sep 2011, 18:57

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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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27 Mar 2012, 02:46
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Expert's post
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.

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

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19 Sep 2012, 06:49
I ruled out A and B.

When it came to C, we know M/N = odd

From 1,
M = N * Odd

From 2,
M = Even - N

Combining both, N * Odd = Even - N
N (Odd + 1) = Even
N * (Even) = Even

Since we know N is an integer, E/E = Even or Odd

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

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19 Sep 2012, 12:16
great explanation by Bunuel , Without confusion it can be solved by his way.
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Re: Problem solving question (m25-35) [#permalink]

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19 Sep 2012, 12:17
great explanation by Bunuel , Without confusion it can be solved by his way.Kudos +1 to you.
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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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Re: Problem solving question (m25-35) [#permalink]

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18 Sep 2013, 09:49
Easy one. Plug and check and odd even properties

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Re: Problem solving question (m25-35)   [#permalink] 18 Sep 2013, 09:49
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# Problem solving question (m25-35)

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