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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 m^3

2) should be : m is a multiple of \(P^3\)

1) is nsf, suppose m=p*t*t*t*t*t*t*t*t

2) is suf. p, t are the only prime factors, and m is a multiple of p^3, therefore m=n*p*p*p*t, n is an integer

so, m is a multiple of (p^2)*t

Answer is B.

Agree that answer is B. But we do not need to check 9 factors in this way because m=p*t*t*t*t*t*t*t*t will have 18 factors:) I mean the idea is right but we can as well check for m=p*t*t*t*t where number of factors is 10 > 9 and m = p*p*p*t*t where the number of factors is 12 > 9. In the first case p^2*t is not a factor, in the second case it is.

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 m^3

2) should be : m is a multiple of \(P^3\)

1) is nsf, suppose m=p*t*t*t*t*t*t*t*t

2) is suf. p, t are the only prime factors, and m is a multiple of p^3, therefore m=n*p*p*p*t, n is an integer

so, m is a multiple of (p^2)*t

Answer is B.

Agree that answer is B. But we do not need to check 9 factors in this way because m=p*t*t*t*t*t*t*t*t will have 18 factors:) I mean the idea is right but we can as well check for m=p*t*t*t*t where number of factors is 10 > 9 and m = p*p*p*t*t where the number of factors is 12 > 9. In the first case p^2*t is not a factor, in the second case it is.

Bunuel, I don't quite understand how second statement is sufficient. Please explain with a numerical example..
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Re: If the prime numbers p and t are the only prime factors of [#permalink]

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25 Jan 2013, 00:06

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The 2nd statement listed in this problem is incorrect. It should be \(p^3\), not \(n^3\). See attached image for the original problem.

======== 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 INSUFFICIENT: it doesnt tell exponent/powers of prime factors p & t. We dont know whether m is multiple of p^2.

2) m is a multiple of \(p^3\) SUFFICIENT: If m is a multiple of \(p^3\), then m must be multiple of \(p^2\). As 't' is also a prime factor of m, then m must be multiple of \(p^2*t\) e.g. say m=24, p=2, t=3. As 24 is multiple of \(p^3 = 2^3=8\), 24 must be multiple of \(p^2=2^2=4\), and therefore 24 is also multiple of \(p^2*t=2^2*3=6\)

Re: If the prime numbers p and t are the only prime factors of [#permalink]

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25 Jan 2013, 02:49

PraPon wrote:

Attachment:

GMAT Prob.png

The 2nd statement listed in this problem is incorrect. It should be \(p^3\), not \(n^3\). See attached image for the original problem.

======== 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 INSUFFICIENT: it doesnt tell exponent/powers of prime factors p & t. We dont know whether m is multiple of p^2.

2) m is a multiple of \(p^3\) SUFFICIENT: If m is a multiple of \(p^3\), then m must be multiple of \(p^2\). As 't' is also a prime factor of m, then m must be multiple of \(p^2*t\) e.g. say m=24, p=2, t=3. As 24 is multiple of \(p^3 = 2^3=8\), 24 must be multiple of \(p^2=2^2=4\), and therefore 24 is also multiple of \(p^2*t=2^2*3=6\)

Hence choice(C) is the answer.

so say m has r also as a prime factor, then m must be a multiple of p^2*t*r and of p*t*r?
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