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# If M and N are positive integers, then is M an even integer?

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If M and N are positive integers, then is M an even integer? [#permalink]

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09 Feb 2012, 17:57
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Feb 2012, 18:08, edited 1 time in total.
Added the OA
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Re: Integers [#permalink]

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09 Feb 2012, 18:06
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If M and N are positive integers, then is M an even integer?

(1) 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: either both are odd (for example m=3 and n=1) or both are even (for example m=2 and n=2). Not sufficient.

Answer: E.
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Re: Integers [#permalink]

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12 Feb 2014, 12:20
Bunuel wrote:
If M and N are positive integers, then is M an even integer?

(1) 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: either both are odd (for example m=3 and n=1) or both are even (for example m=2 and n=2). Not sufficient.

Answer: E.

Statement 1 says M/N = Odd

Only Odd / Odd can give an odd integer. If M is even then even / even = even or even / odd = not integer.

Statement 1 is sufficient to say that M is not even right?

Can you help with this?
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Re: Integers [#permalink]

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13 Feb 2014, 01:10
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Qoofi wrote:
Bunuel wrote:
If M and N are positive integers, then is M an even integer?

(1) 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: either both are odd (for example m=3 and n=1) or both are even (for example m=2 and n=2). Not sufficient.

Answer: E.

Statement 1 says M/N = Odd

Only Odd / Odd can give an odd integer. If M is even then even / even = even or even / odd = not integer.

Statement 1 is sufficient to say that M is not even right?

Can you help with this?

That's not correct at all! What about 6/2 = even/even = 3 = odd? Also, what about 6/3 = even/odd = 2 = even?
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Re: If M and N are positive integers, then is M an even integer? [#permalink]

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22 Aug 2016, 02:30
Here as we need to get if M is even or not
Statement 1 => M/N = odd => M and N have the same Even / odd nature => not suff
statement 2 => M+N=even => E,E or O,O => Not suff
Clearly combining them is also not suff here
Smash that E

Note => If X/Y=Z for all X,Y,Z are the integers
=> If Z is even => X must be even ; Y can be even or odd
If Z is odd => X and Y must have the same even odd nature
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Re: If M and N are positive integers, then is M an even integer?   [#permalink] 22 Aug 2016, 02:30
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# If M and N are positive integers, then is M an even integer?

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