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If m and n are integers and m+n is odd, which of the f
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17 Aug 2020, 12:44
17 Aug 2020, 12:44
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If m and n are integers and m+n is odd, which of the following must be odd?
A. m
B. mn
C. 2m + n
D. 3m − n
E. mn + m
A. m
B. mn
C. 2m + n
D. 3m − n
E. mn + m
Re: If m and n are integers and m+n is odd, which of the f
[#permalink]
18 Aug 2020, 00:26
18 Aug 2020, 00:26
1
We know that m+n is odd. This means that either m is odd and n is even or n is odd and m is even.
A - m is not necessarily odd, take m=2 and n=3, this satisfy the condition but m will be even --> eliminate A.
B - m+n is odd so we know that one of them has to be even. Say it's m that's even and n is odd. Then mn=even x odd = even. --> eliminate B.
C - Again, it could be, but it must not necessarily be. Take m odd and n even for instance. Then 2m is even and n even, the sum is then even --> eliminate C.
D - Here we check the different cases:
(i) m even and n odd then 3m is even and n is odd. But even - odd = odd
(ii) m odd and n even then 3m is still odd and n is even. Again odd - even = odd.
--> D works
E - Just need to check the case where m is even and n is odd, then mn is even and m is even, so mn+n is even. --> Eliminates E.
A - m is not necessarily odd, take m=2 and n=3, this satisfy the condition but m will be even --> eliminate A.
B - m+n is odd so we know that one of them has to be even. Say it's m that's even and n is odd. Then mn=even x odd = even. --> eliminate B.
C - Again, it could be, but it must not necessarily be. Take m odd and n even for instance. Then 2m is even and n even, the sum is then even --> eliminate C.
D - Here we check the different cases:
(i) m even and n odd then 3m is even and n is odd. But even - odd = odd
(ii) m odd and n even then 3m is still odd and n is even. Again odd - even = odd.
--> D works
E - Just need to check the case where m is even and n is odd, then mn is even and m is even, so mn+n is even. --> Eliminates E.
gmatclubot
Re: If m and n are integers and m+n is odd, which of the f [#permalink]
18 Aug 2020, 00:26
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