Is (m+n)^3 an odd number?
1) m and n are integers
2) mn=15
Source : Math Revolution
Official Answer : B
1) m and n are integers
2) mn=15
Source : Math Revolution
Official Answer : B
Hi ziyuenlau,
This question can be solved with a mix of TESTing VALUES and Number Properties.
We're asked if (M+N)^3 is an ODD number. This is a YES/NO question. Before we deal with the two Facts, here are the Number Properties to note....
IF....
(M+N) = an odd integer, then the answer to the question is YES.
(M+N) = an even integer, then the answer to the question is NO.
(M+N) = a NON-integer, then the answer to the question is NO.
1) M and N are integers
With Fact 1, there's no restriction on whether the sum of M and N is even or odd, so the answer to the question could be YES or NO.
Fact 1 is INSUFFICIENT
2) (M)(N) = 15
With this Fact, there are only two possibilities:
-M and N are both ODD (for example, 3 and 5), so the SUM would be EVEN and the answer to the question is NO.
-M and/or N are non-integers (for example 2 and 7.5), so the SUM would be a NON-INTEGER and the answer to the question is NO.
There is no way for M and N to end in a sum that is odd, so the answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT
Final Answer: B
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