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

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

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New post 19 Jul 2017, 20:50
BANON 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.



This question is relatively straightforward

St 1

Every factor of s in also a factor of r- this means that every factor of s must be a factor of r- so in other words s must be the same size as r -neither can be larger

St 2

2 x3 /3 x 2 x 2 this satisfies the condition but is obviously not an integer so insufficient

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

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New post 16 Mar 2018, 08:53
sTATEMENT 1: It means r is greater than or equal to s. not r is greater than s.


mcelroytutoring wrote:
For condition #1, remember that this is just a fancy way of indicating that r > s.

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

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New post 13 May 2018, 22:52
Bunuel wrote:
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.

Answer: A.

Hope it's clear.


For statement 1, how do we know that we won't run into a similar problem with statement two in which we could have 2^2*3^2/2^3*3^3?
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Re: If r and s are positive integers, is r/s an integer?  [#permalink]

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New post 13 May 2018, 23:26
thinkpad18 wrote:
Bunuel wrote:
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.

Answer: A.

Hope it's clear.


For statement 1, how do we know that we won't run into a similar problem with statement two in which we could have 2^2*3^2/2^3*3^3?


Hello

We CANNOT take your example, where r = 2^2 * 3^2 and s = 2^3 * 3^3, as this will violate the condition in statement 1.

Statement 1 says that every factor of s is also a factor of r. But if s has more powers of 2 and/or 3 than r, then s will have some factors which are not factors of r. Eg, in your example, 2^3, 3^3, 2^3 * 3^2 .. etc.. are factors of s but they are not factors of r.

So if we go by statement 1 condition, if all factors of s have to be factors of r also, then all powers of all prime numbers contained in s, will also be contained in r. Hence r/s has to be an integer.
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Re: If r and s are positive integers, is r/s an integer?  [#permalink]

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New post 23 Aug 2018, 12:11
In 1st case If s=8 and r=12 , then r/s doesn't give an integer. In this case A is not sufficient.
Am I right?
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Re: If r and s are positive integers, is r/s an integer?  [#permalink]

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New post 23 Aug 2018, 20:55
sarvesh93sah wrote:
In 1st case If s=8 and r=12 , then r/s doesn't give an integer. In this case A is not sufficient.
Am I right?


If you were right then the OA would not be A. So, there must be a mistake in your reasoning. s = 8 and r = 12 does not satisfy the first statement which says: EVERY factor of s is also a factor of r. One of the factors of s = 8, is 8 itself (recall that an integer is a factor of itself) and 8 is not a factor of r = 12.
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Re: If r and s are positive integers, is r/s an integer? &nbs [#permalink] 23 Aug 2018, 20:55

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