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If the prime numbers p and t are the only prime factors of

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Director
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If the prime numbers p and t are the only prime factors of [#permalink] New post 10 Dec 2006, 00:07
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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 p^3.

Please help.
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Re: Data sufficiency [#permalink] New post 10 Dec 2006, 06:08
das_go wrote:
LM wrote:
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.

Please help.


B !


Getting E
Am I missing something here?

OK A is INSUFF

Coming to B

(p^2)*p/m = k where k is an integer-----------(a)

but we are sked if (p^2)*t/m = k1 ( where k1 is an int)-------(b)

since p and t being co primes how can we deduce from (a) and (b) ?
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Re: Data sufficiency [#permalink] New post 10 Dec 2006, 06:48
trivikram wrote:
das_go wrote:
LM wrote:
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.

Please help.


B !


Getting E
Am I missing something here?

OK A is INSUFF

Coming to B

(p^2)*p/m = k where k is an integer-----------(a)

but we are sked if (p^2)*t/m = k1 ( where k1 is an int)-------(b)

since p and t being co primes how can we deduce from (a) and (b) ?


st is inusff
st2 m is multple of P^3 thus m is multiple of p^2 and t is factor of m m is a multiple of t as well
thus m is multiple of p^2*t
so b is suff
VP
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Re: Data sufficiency [#permalink] New post 10 Dec 2006, 08:31
yogeshsheth wrote:
trivikram wrote:
das_go wrote:
LM wrote:
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.

Please help.


B !


Getting E
Am I missing something here?

OK A is INSUFF

Coming to B

(p^2)*p/m = k where k is an integer-----------(a)

but we are sked if (p^2)*t/m = k1 ( where k1 is an int)-------(b)

since p and t being co primes how can we deduce from (a) and (b) ?


st is inusff
st2 m is multple of P^3 thus m is multiple of p^2 and t is factor of m m is a multiple of t as well
thus m is multiple of p^2*t
so b is suff


Thanks Yogesh. I got it

m is having co primes as factors

or m = p*t this is given

now we are aked if m is a factor of (p*t) * p which is YES and B is suff
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 [#permalink] New post 10 Dec 2006, 09:42
1 -> INSUFF
2 -> m is a multiple of p^3. What if m = P^3 ? am I doing something wrong?
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 [#permalink] New post 10 Dec 2006, 09:54
deep wrote:
1 -> INSUFF
2 -> m is a multiple of p^3. What if m = P^3 ? am I doing something wrong?


m cannot be just p^3, since it is given that m has p as well as t as it's prime factors. so, if it is p^3 * X, can may be broken down as t * Y.
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Re: Data sufficiency [#permalink] New post 10 Dec 2006, 11:41
LM wrote:
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.

Please help.


From stem m/pt = integer

1) No useful info given ----> INSUFF

2) Tells us m/p^3 = integer so m/p*p^2 is also integer SUFF
Re: Data sufficiency   [#permalink] 10 Dec 2006, 11:41
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