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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