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

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

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19 Aug 2009, 11:55
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51% (02:01) correct 49% (01:12) wrong based on 157 sessions

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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

OPEN DISCUSSION OF THIS QUESTIONS IS HERE: if-the-prime-numbers-p-and-t-are-the-only-prime-factors-of-85836.html
[Reveal] Spoiler: OA

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Re: Prime Numbers and Divisibility [#permalink]

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19 Aug 2009, 14:15
1
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gulatin2 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 m^3

Can you please confirm this problem?

St. 2 doesn't sound right
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Re: Prime Numbers and Divisibility [#permalink]

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19 Aug 2009, 17:00
2
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gulatin2 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 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

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Re: Prime Numbers and Divisibility [#permalink]

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19 Aug 2009, 18:06
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Correct me if i am wrong..
I Have seen same question in GMATPrep ( m is a multiple of P^3) and Agree with Flyingbunny
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Re: Prime Numbers and Divisibility [#permalink]

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20 Aug 2009, 04:50
flyingbunny wrote:
gulatin2 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 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

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.
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Re: Prime Numbers and Divisibility [#permalink]

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21 Aug 2009, 22:26
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I enjoyed this. Thanks.
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Re: Prime Numbers and Divisibility [#permalink]

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25 Jan 2013, 00:34
Economist wrote:
flyingbunny wrote:
gulatin2 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 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

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

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25 Jan 2013, 01:06
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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 $$p^2*t=2^2*3=6$$

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

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25 Jan 2013, 03:49
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 $$p^2*t=2^2*3=6$$

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

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25 Jan 2013, 05:30
Expert's post
OPEN DISCUSSION OF THIS QUESTIONS IS HERE: if-the-prime-numbers-p-and-t-are-the-only-prime-factors-of-85836.html
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Re: If the prime numbers p and t are the only prime factors of [#permalink]

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25 Jan 2013, 09:42
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Sachin9 wrote:
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?

Yes. That is correct.
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Re: If the prime numbers p and t are the only prime factors of   [#permalink] 25 Jan 2013, 09:42
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