baru wrote:
If positive integer A =\(m3\)\(n2\), where m and n are distinct prime numbers, is A divisible by 72?
(1) 25mn is a multiple of 15
(2) 6\(m2\) is divisible by 12
baru could you please edit the question so the powers are written properly?
As this is a question dealing with integers and divisibility, it is almost guaranteed to have to do with prime factorization.
Then we'll go the Precise route of prime factorizing 72 to see what we need to do.
72 = 36*2 = 6^2 *2 = (2^3)(3^2)
So the answer to the question is yes only if m= 2 and n = 3.
(1) if 25mn is a multiple of 15 then 5mn is a multiple of 3 so (at least) one of m,n must be 3. This is not enough.
(2) if 6m^2 is divisible by 12 then m^2 is divisible by 2 and therefore m = 2. without knowledge on n, this is not enough.
Combined, we know that m = 2 and n = 3, exactly what we need.
Sufficient.
(C) is our answer.