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If the prime numbers p and t are the only prime factors of [#permalink]
 19 Aug 2009, 11:55
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66% (01:21) wrong based on 13 sessions
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
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Re: Prime Numbers and Divisibility [#permalink]
19 Aug 2009, 14:15
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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]
19 Aug 2009, 17:00
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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^31) 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.
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Re: Prime Numbers and Divisibility [#permalink]
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
Answer B
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Re: Prime Numbers and Divisibility [#permalink]
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^31) is nsf, suppose m= p*t*t*t*t*t*t*t*t2) 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.
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Re: Prime Numbers and Divisibility [#permalink]
21 Aug 2009, 22:26
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I enjoyed this. Thanks.
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Re: Prime Numbers and Divisibility [#permalink]
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^31) is nsf, suppose m= p*t*t*t*t*t*t*t*t2) 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..
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Re: If the prime numbers p and t are the only prime factors of [#permalink]
25 Jan 2013, 01:06
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Attachment: 
GMAT Prob.png [ 37.3 KiB | Viewed 770 times ]
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^3SUFFICIENT: 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*te.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=6Hence choice(C) is the answer.
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Re: If the prime numbers p and t are the only prime factors of [#permalink]
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^3SUFFICIENT: 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*te.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=6Hence 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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Re: If the prime numbers p and t are the only prime factors of [#permalink]
25 Jan 2013, 05:30
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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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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
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25 Jan 2013, 09:42
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