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GMATPrep2: Multiple of prime factors

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GMATPrep2: Multiple of prime factors [#permalink] New post 03 Sep 2009, 03:36
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33% (04:54) correct 66% (02:35) wrong based on 0 sessions
Don't know how to approach the first statement..

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[Reveal] Spoiler:
B
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Re: GMATPrep2: Multiple of prime factors [#permalink] New post 03 Sep 2009, 07:40
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m can be written as this:
m = p^x*t^y where x and y are positives integers. (this is the decomposition of m as product of primes factors)

The question is asking if x>=2?

1) from this stament we can say that x+y > 9 : not sufficient

2) from this one: x > 3 sufficient
answer B
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Re: GMATPrep2: Multiple of prime factors [#permalink] New post 03 Sep 2009, 07:56
Since p and t are the only primes,
m=p^it^j where j>=1 and i>=1
If m is a multiple of p^2t, i>=2 and j>=1. Since we know that j>=1, we have only to prove that i>=2.

Statement 1

i\times j+1>9(note that generally the formula for the number of primes is (j+1)(i+1) but since we can elimintae all cases with i=0 or j=0, the formula is i\times j+1...1 is added since the case j=0 and i=0 can never eliminted )

Not sufficent
consider the case i=1 and j=9...not a multiple of p^2t

Statemet 2
sufficient since i=3 and m=p^3t^j where j>=1.
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Re: GMATPrep2: Multiple of prime factors [#permalink] New post 03 Sep 2009, 16:02
madeinafrica wrote:
m can be written as this:
m = p^x*t^y where x and y are positives integers. (this is the decomposition of m as product of primes factors)

The question is asking if x>=2?

1) from this stament we can say that x+y > 9 : not sufficient

2) from this one: x > 3 sufficient
answer B


I liked the approach..good one..
Re: GMATPrep2: Multiple of prime factors   [#permalink] 03 Sep 2009, 16:02
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