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.
GMAT prep, prime factors
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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
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