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Problem solving question (m2535) [#permalink]
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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. 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. Please advice if someone has a different solution.



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Re: Problem solving question (m2535) [#permalink]
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27 Mar 2012, 02:46



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Re: Problem solving question [#permalink]
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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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Re: Problem solving question [#permalink]
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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 deadend too
Combining the statements is fruitless. We can't narrow down possibilities.
It's (E)



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Re: Problem solving question [#permalink]
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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 "m2535" 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.
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Re: Problem solving question (m2535) [#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 (m2535) [#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 (m2535) [#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 (m2535) [#permalink]
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15 Sep 2010, 08:41
E by plugging even & odd numbers.
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Re: Problem solving question (m2535) [#permalink]
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15 Sep 2010, 09:07
E by using 6,2 and 9,3 values Posted from my mobile device
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Re: Problem solving question (m2535) [#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 (m2535) [#permalink]
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20 Sep 2011, 18:57
easy one..answer is E



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Re: Problem solving question (m2535) [#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 (m2535) [#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
Answer is E.



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Re: Problem solving question (m2535) [#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 (m2535) [#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 (m2535) [#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 = TROUBLEMAKER (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 (m2535) [#permalink]
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18 Sep 2013, 09:49
Easy one. Plug and check and odd even properties




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