Data Sufficiency

Hello, Another GMAT prep problem I cannot find the solution for. I would really really appreciate the help with this one.

If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of (p^2)t?

(1) m has more than 9 positive factors.

(2) m is a multiple of p^3

the correct answer is B.

Thank you very much.

question stem: m has only prime factors p and t.

is m multiple of (p^2)*t = p*p*t

so we already know that m is a multiple of p*t and we now must find out whether there is another factor p in m

statement 1:
doesn't tell you if there are 1 p and 8 ts (m would be no multiple of (p^2)*t then)
or if there are 8 ps and 1 t or something in between (m would be a multiple of (p^2)*t then)

INSUFFICIENT

statement 2:
m = multiple of p^3=p*p*p
there are even more than 2 ps. Therefore m is a multiple of (p^2)*t, it is even a multiple of (p^3)*t.
SUFFICIENT

Answer is B

Nermal,


Wonderful explaination. Thank you very much.