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cubicle_bound_misfit
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If p and t are the only prime factors of m, we know the prime factorization of m is p^a * t^b, where a and b are positive integers. The question asks whether m is divisible by p^2 * t; but, we already know that m is divisible by pt. Really, the question is just asking: is the exponent on p greater than 1 in the prime factorization of m? That is, is a > 1?
From statement 1, we know that m has more than 9 divisors. That doesn't mean that a > 1 necessarily; it may be that b is large and a = 1. (incidentally, if a = 1, then as long as b > 3, m will have at least 10 positive divisors, assuming p and t are different).
From statement 2, we know that p^3 is a divisor of m. That guarantees that a is at least 3, which is even more than we need to know. So sufficient.
I've assumed throughout the above that p and t are different primes, and it's worth considering what might happen if p = t. Statement 1 is certainly insufficient, since it's possible that p is different from t. If p = t, the question becomes: is m divisible by p^3? So statement 2 is certainly sufficient; it says precisely that. So if we allow for the possibility that p=t, it doesn't affect the answer.
