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Re: Prime Numbers and Divisibility [#permalink]
20 Aug 2009, 03:50
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
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.
Re: Prime Numbers and Divisibility [#permalink]
24 Jan 2013, 23:34
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
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]
25 Jan 2013, 00:06
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Attachment:
GMAT Prob.png [ 37.3 KiB | Viewed 3639 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 \(p^3\) 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]
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? _________________
hope is a good thing, maybe the best of things. And no good thing ever dies.
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