Given: The prime numbers 'p' and 't' are the only prime factors of the integer 'm'.
=> m = (p^a)*(t^b) , where a and b are greater than or equal to 1. In simple words, m is composed of one or more p's and one or more t's.

Now one possible case is m = pt. In this case, m is not a multiple of p^2*t. Therefore we need more information.

Statement 1: m has more than 9 positive factors.
=> m is composed of more than one p's and/or more than one t's.

Some possible cases are m = p*t^k , where k is greater than or equal to 4. In these cases m has more than 9 positive factors.

Like for k = 4, m = p*t^4. The factors are 1, p, t, t^2, t^3, t^4, pt, p*t^2, p*t^3 and p*t^4.

But in these cases, m is not a multiple of p^2*t.

Not SUFFICIENT.

Statement 2: m is multiple of p^3.
=> m = (p^3)^a*t^b , where a and b are greater than or equal to 1. In simple words, m is composed of three or more p's and one or more t's.

Thus m always contains p^2*t in it. Because, m is multiple p^3 => m is multiple of p^2 and m has t as a prime factor => m is a multiple of t. Thus, m is multiple of p^2*t.

SUFFICIENT.

The correct answer is B.