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

GMAT assassins aren't born, they're made,
Rich

ziyuenlau wrote:Is (m+n)^3 an odd number?

1) m and n are integers
2) mn=15

Source : Math Revolution
Official Answer : B

Hi ziyuenlau,

The question is whether (m+n)^3 odd.

Since the exponent 3 is odd, we can write above as (m+n)^(odd).

Any number with an exponent which is odd is odd if the base is odd.

Thus, if (m+n) is odd, the answer is Yes, else No.

Rephrased question: Is (m+n) odd?

Let's take each statement one by one.

S1: m and n are integers

Clearly insufficient. If one of m and n is even and the other is odd, (m+n) is odd; however if m and n both are either odd or both are even, (m+n) is even. No unique answer.

S2: mn=15

We do not know whether m and n are integers. However, we cannot discard this statement on that basis.

Case 1: Since mn = 15 = an odd number, m and n each would be an odd integer, making (m+n) an even number. The answer is NO.

Case 2: Say one of m and n is not an integer. Say m = 1/15 and n = 225, thus, (m+n) is not an odd number. The answer is still NO.

Sufficient.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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