Hi nikhilgmat31,
This question has an odd 'design' to it - we're told that M and N are DISTINCT PRIME NUMBERS and that A = (M^3)(N^2). By definition that means that A MUST be a positive integer (but the question writer points that out, which is not typical). We're asked if A is divisible by 72. This is a YES/NO question.
Since M and N are both DISTINCT PRIMES, we should focus on the 72 for a moment...
72 = (2^3)(3^2)
Since prime numbers do NOT have other factors (besides themselves and the number 1), for A to be divisible by 72, M MUST be 2, N MUST be 3 and A MUST be 72. In that one circumstance, you'll end up with a YES answer. In any OTHER circumstance, you'll end up with a NO answer.
Fact 1: 25(M)(N) is a multiple of 15
To be divisible by 15, a number MUST include a 3 and a 5 in its prime-factorization. 25 'contains' the 5, so one of the variables MUST be a 3...
IF...
M=2
N=3
25MN = 150 (which is a multiple of 15)
The answer to the question is YES
IF...
M=3
N=5
25MN = 375 (which is a multiple of 15)
The answer to the question is NO
Fact 1 is INSUFFICIENT
Fact 2: 6(M^2) is divisible by 12
To be divisible by 12, a number MUST include a 3 and two 2s in its prime-factorization. 6 'contains' a 3 and one 2, so M MUST be 2...
IF...
M = 2
6(M^2) = 24 (which is divisible by 12)
N = 3
Then the answer to the question is YES
IF...
M = 2
6(M^2) = 24 (which is divisible by 12)
N = 5
Then the answer to the question is NO
Fact 2 is INSUFFICIENT
Combined, we know...
One of the variables MUST be a 3
M MUST be a 2
Since the M is 2, the N MUST be 3 and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
