prime numbers

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prime numbers

by fangtray » Sat Sep 17, 2011 4:46 am
If the prime numbers P and T are the only prime factors of integer M, is M a multiple of P^2T?

1) m has more than 9 positive factors
2) m is a multiple of p^3


i'm more curious if there is a trick to quickly do this problem.

thanks

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by cans » Sat Sep 17, 2011 5:12 am
M = P^x * T^y
M = n* P^2 * T???
B) m is multiple of P^3. then it is also multiple of P^2. Sufficient
A) if m is only pt, factors = 1,p,t,m
if m=pt^4, factors: 1,p,t,pt,pt^2,t^2,pt^3,t^3,t^4,m = 10 factors (>9). not multiple
Thus insufficient. if m=p^4 *t, it will have 10 factors but will be multiple of p^2*t
IMO B
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Cans!!

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by fangtray » Mon Sep 19, 2011 5:40 am
the answer is D