Data Sufficiency

jainrahul1985 wrote:If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of t*p^2?
(1) m has more than 9 positive factors
(2) m is a multiple of p^3

OA B

Let m = (p^x)*(t^y). Then m has (x + 1)(y + 1) positive factors.

(1) m has more than 9 positive factors implies that (x + 1)(y + 1) > 9
If x = 2, y = 3, then m = p² * t^3 = t * p² * t², which is clearly a multiple of t * p².
If x = 1, y = 4, then m = p * t^4, which is not a multiple of t * p².
No definite answer; NOT sufficient.

(2) m is a multiple of p^3 implies m = k * p^3, which implies k has to be t^a * p^b (where a ≥ 1 and b ≥ 0)
We know that m = p^x * t^y and m = t^x * p^y * p^3) will be a multiple of (p^2)*t; SUFFICIENT.

The correct answer is B.