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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]

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23 Apr 2011, 15:34
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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-r-and-s-are-positive-integers-is-r-s-an-integer-128005.html
[Reveal] Spoiler: OA

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Re: If r and s are positive integers, is r/s an integer? 1) [#permalink]

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23 Apr 2011, 16:51
agdimple333 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.

Every integer can be written in terms of its prime factors and total number of factors will depend on the frequency of such prime factors.

Statement 1) says that all the factors of s are also factors of r, so r + K*s where K is an integer and hence r/s is an integer - Sufficient

Statement 2) says that all the prime factors of s are also prime factors of r, but we do not know the frequency of these prime numbers and hence do not know about other factors of r and s and hence cant say if r/s is an integer. If r is greater than s, then r/s is integer whereas if s is greater than r, it is not (lets say two numbers 2*3 and 2*3*3 have same prime factors 2 and 3, but their ratio can be an integer or not depending on which one is in numerator) - Insufficient

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Re: If r and s are positive integers, is r/s an integer? 1) [#permalink]

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23 Apr 2011, 17:06
hmm, this question looks a bit familiar!

Another vote for A.

1) sufficient as pretty much tells you outright that r/s will work out nicely in this case.
2) insufficient
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Re: If r and s are positive integers, is r/s an integer? 1) [#permalink]

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23 Apr 2011, 17:48
1. Sufficient
As this tells us r is a multiple of s. Hence r/s got to be an integer.

2. Not sufficient.

We don't know the frequency of these primary numbers in numerator and denominator.
Eg 10/20 has 2,5 as prime factors in numerator and denominator.but not an integer.

20/10 on the otherhand is an integer.

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Re: If r and s are positive integers, is r/s an integer? 1) [#permalink]

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24 Apr 2011, 21:20
(1)

S is a factor of itself, hence s is a factor of r, r/s is an integer

(1) is sufficient.

(2)

Let r = 10, s = 20

r/s is not an integer, even though 2 and 5, the prime factors of 20 are factors of 10 as well

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Re: If r and s are positive integers, is r/s an integer? 1) [#permalink]

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30 Jan 2016, 01:12
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Re: If r and s are positive integers, is r/s an integer? 1) [#permalink]

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30 Jan 2016, 02:25
agdimple333 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.

If r and s are positive integers, is r/s an integer?

(1) Every factor of s is also a factor of r. If every factor of s is also factor of r, then in fraction r/s, s will just be reduced and we get an integer. Sufficient.

(2) Every prime factor of s is also a prime factor of r. The powers of prime factors of s could be higher than powers of prime factors of r. eg 25/125=1/5 not an integer. Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-r-and-s-are-positive-integers-is-r-s-an-integer-128005.html
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Re: If r and s are positive integers, is r/s an integer? 1)   [#permalink] 30 Jan 2016, 02:25
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