GMATPrep2: Multiple of prime factors : DS Archive
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# GMATPrep2: Multiple of prime factors

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Manager
Joined: 20 Aug 2009
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GMATPrep2: Multiple of prime factors [#permalink]

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03 Sep 2009, 02:36
00:00

Difficulty:

(N/A)

Question Stats:

33% (04:54) correct 67% (02:35) wrong based on 2 sessions

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Don't know how to approach the first statement..

OA
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Joined: 20 Jul 2009
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Schools: Kellogg; Ross (); Tuck
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Re: GMATPrep2: Multiple of prime factors [#permalink]

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03 Sep 2009, 06:40
1
KUDOS
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
Manager
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Re: GMATPrep2: Multiple of prime factors [#permalink]

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03 Sep 2009, 06:56
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.
Manager
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Re: GMATPrep2: Multiple of prime factors [#permalink]

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03 Sep 2009, 15:02
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

I liked the approach..good one..
Re: GMATPrep2: Multiple of prime factors   [#permalink] 03 Sep 2009, 15:02
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