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# If r and s are positive integers, is r/s an integer? (1)

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If r and s are positive integers, is r/s an integer? (1) [#permalink]  13 Jan 2008, 07:26
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If r and s are positive integers, is r/s an integer?

(1) Every factor of s is also a factor of r.

(2) Every prime factor of s is also a prime factor of r.
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Re: OG 11 - DS 125 [#permalink]  13 Jan 2008, 07:31
lumone wrote:
If r and s are positive integers, is r/s an integer?

(1) Every factor of s is also a factor of r.

(2) Every prime factor of s is also a prime factor of r.

I think each statement is not sufficient alone
I statement cannot be because suppose
8 and 12, they both have 2 as a factor but 8/12 is not integer
8 and 4, they both have 2 as a factor 8/4 is integer
that is why is not sufficient
II statement
we know that 2 is even prime and examples from first statement can be given there and again it is not sufficient
combined together they give nothing more than alone, so I think it is E
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Re: OG 11 - DS 125 [#permalink]  14 Jan 2008, 09:20
Expert's post
A

1. "Every factor of s is also a factor of r.". s is a factor of itself. SUFF.
2. r=2*2, s=2*2*2 or s=2. INSUFF.
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Re: OG 11 - DS 125 [#permalink]  14 Jan 2008, 09:43
lumone wrote:
If r and s are positive integers, is r/s an integer?

(1) Every factor of s is also a factor of r.

(2) Every prime factor of s is also a prime factor of r.

1. if s is 70 then its factors are 2*5*7. r must be a multiple of 70, thus r/s is an integer.suff
2. it could be that s is 2^3 * 3, while r is 2*3. thus, r/s would be 1/4. not suff
Re: OG 11 - DS 125   [#permalink] 14 Jan 2008, 09:43
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