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M, N, O, and P are positive integers and M-O+N=even and

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VP
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M, N, O, and P are positive integers and M-O+N=even and [#permalink] New post 20 Apr 2005, 22:15
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M, N, O, and P are positive integers and M-O+N=even and N+P-M=odd, then which of the following must be odd?

1. M+N
2. N+P
3. P+Q
4.O+P
5.P+M

Last edited by MA on 22 Apr 2005, 19:47, edited 2 times in total.
VP
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 [#permalink] New post 20 Apr 2005, 23:01
4...

M-O+N=(M+N)-O=even => (M+N) can be odd or even and O can be odd or even

N+P-M=(N-M)+P=odd => (N-M) can be even or odd and P can be odd or even

O+P is always odd cause when O is odd and (M+N) is odd for (M+N)-O to be even; P must be even for (N-M)+P to be odd...O+P=odd...same reasoning the other way around.
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Senior Manager
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 [#permalink] New post 20 Apr 2005, 23:28
my way to do this is:
M-O+N=even
N+P-M=odd
add 1 and 2
M-O+N+N+P-M=odd+even=odd
so 2N+P-O=odd
since 2N is even
P-O is odd
when P-O is odd
also P+O is odd
Senior Manager
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Joined: 19 Feb 2005
Posts: 492
Location: Milan Italy
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Kudos [?]: 9 [0], given: 0

 [#permalink] New post 22 Apr 2005, 10:11
:wink: :wink:
Logic, not mathematical knowledge, is the key to solve GMAT math; problem is, not always you have the right way to do things...
  [#permalink] 22 Apr 2005, 10:11
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M, N, O, and P are positive integers and M-O+N=even and

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