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

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Manager
Joined: 29 Nov 2011
Posts: 81

Kudos [?]: 381 [0], given: 37

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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Difficulty:

45% (medium)

Question Stats:

65% (00:44) correct 35% (00:57) wrong based on 110 sessions

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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.

Kudos [?]: 381 [0], given: 37

Math Expert
Joined: 02 Sep 2009
Posts: 42322

Kudos [?]: 133091 [1], given: 12408

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09 Feb 2012, 18:06
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Expert's post
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.

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Kudos [?]: 133091 [1], given: 12408

Manager
Joined: 18 Dec 2012
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Kudos [?]: 58 [0], given: 34

Location: India
Concentration: General Management, Strategy
GMAT 1: 660 Q49 V32
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WE: Manufacturing and Production (Manufacturing)

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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.

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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Kudos [?]: 58 [0], given: 34

Math Expert
Joined: 02 Sep 2009
Posts: 42322

Kudos [?]: 133091 [1], given: 12408

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13 Feb 2014, 01:10
1
KUDOS
Expert's post
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.

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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Kudos [?]: 133091 [1], given: 12408

Retired Moderator
Joined: 12 Aug 2015
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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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Kudos [?]: 878 [0], given: 602

Re: If M and N are positive integers, then is M an even integer?   [#permalink] 22 Aug 2016, 02:30
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