Hi All,
We're told that M and N are POSITIVE INTEGERS. We're asked if (√M)^N is an integer. This is a YES/NO question. We can solve it with a mix of Number Property rules and TESTing VALUES.
1) (√M) is an integer
Fact 1 tells us that M is a 'perfect square' (re: 1, 4, 9, 16, 25, etc.). Since (√M) is a positive integer - and N is a positive integer - then we're raising a positive integer to a positive integer power. That will ALWAYS lead to a positive integer, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
2) (√N) is an integer
Fact 2 tells us that N is a 'perfect square' (re: 1, 4, 9, 16, 25, etc.), but we do NOT know whether (√M) is an integer or not.
IF....
M=1 and N=1, then 1^1 = 1 and the answer to the question is YES.
M=2 and N=1, then √2^1 = √2 and the answer to the question is NO.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
