NUMBERS

[vaibhav101]

if m and n are integers , is m odd?
1) m+n is odd
2) $$m+n=n^2+5$$

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Hi vaibhav101,

We're told that M and N are integers. We're asked if M is ODD. This is a YES/NO question and can be solved by TESTing VALUES and Number Properties.

1) (M+N) is ODD.

IF....
M=1, N=0 then the answer to the question is YES.
M=0, N=1 then the answer to the question is NO.
Fact 1 is INSUFFICIENT.

2) M + N = N^2 + 5

With the equation in Fact 2, the values of N and N^2 will have the same Number Property (If N = 0, then N^2 = 0, if N=Odd, then N^2 = Odd, if N=Even, then N^2 = Even).

IF....
M=5, N=0 then the answer to the question is YES.
M=5, N=1 then the answer to the question is YES.
M=7, N=2 then the answer to the question is YES.
M=11, N=3 then the answer to the question is YES.
It certainly appears that M will ALWAYS be Odd. We can prove it with a few Number Property equations:

IF.....
N = 0, then M + 0 = 0 + 5.... so M = 5 and the answer to the question is YES.
N=Odd, then M + Odd = Odd + Odd, so M MUST be Odd and the answer to the question is YES.
N=Even, then M + Even = Even + Odd, so M MUST be Odd and the answer to the question is YES.
Thus, M will ALWAYS be Odd and the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer: B

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