GMAT Prep Number Theory question- Experts please reply ASAP

[anks17]

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

1. m has more than 9 positive factors
2. m is a mutiple of p^3

Statement 1 is sufficient
Statement 2 is sufficient
Statement 1 and Statement 2 togethet are sufficient
Either Statement alone is sufficient
Neither Statment is sufficient

Can you please confirm the answer.

[eagleeye]

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

1. m has more than 9 positive factors
2. m is a mutiple of p^3

Can you please confirm the answer.

B is correct.

We are told that m has p and t as the only prime factors. This means that all factors of m (other than 1) are either multiples of p or t. The number of factors will depend on the powers of p and t in m. With this in mind, lets look at the statements.

1. m has more than 9 positive factors
If m = p^5 * t, m will be a multiple of p^2 * t
If m = t^5 * p, m will not be a multiple of p^2 * t
Insufficient.

2. m is a mutiple of p^3
If m is a multiple of p^3, it definitely has p^2 as a factor. Since t is already a factor (from question stem), m is definitely a multiple of p^2 * t. Sufficient.

B is correct.

[anks17]

Thanks a lot eagleeye. Can you please also reply to the other DI question posted by me.