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

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Manager
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If r and s are positive integers, is (r/s) an integer? [#permalink]  27 Feb 2008, 13:31
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This came up in my review, my answer was incorrect.

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.

Can you provide rationale as well?
Manager
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Re: DS question [#permalink]  27 Feb 2008, 17:04
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RyanDe680 wrote:
This came up in my review, my answer was incorrect.

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.

Can you provide rationale as well?

E - each statement is sufficient. here is my rational:

1 - if each factor of r is also a factor of s then when you break down the numbers into their factors you will cancel each other out and have an integer. actually this will probably yield to one.
2 - each number can be broken down to a set of prime factors. a number is either prime(divisible only by 1 and itself) or can be broken down into prime numbers. so the same thing here as with 1. all prime will cancel each other out and yield an integer.

what is the OA?
Director
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Re: DS question [#permalink]  27 Feb 2008, 19:36
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Should be 'A'.

Stmt1: if every factor of s is a factor of r, r/s will yield an integer.
example: r=6, s =3
r=6, s=6

stmt2: r=6 s=12,
r=6, s=6
Intern
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Re: DS question [#permalink]  27 Feb 2008, 19:49
since s is a factor of itself, based on statement (1), s is a factor of r which means r/s is a integer
Manager
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Re: DS question [#permalink]  28 Feb 2008, 05:22
The OA is A (statement 1 alone is sufficient).
Intern
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Re: DS question [#permalink]  28 Feb 2008, 15:26
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Not sure how the OA can be A...here's why I think it's E:

What is s is 4 and r is 6...what am I missing here?
Manager
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Re: DS question [#permalink]  28 Feb 2008, 15:36
varunk wrote:
Not sure how the OA can be A...here's why I think it's E:

What is s is 4 and r is 6...what am I missing here?

every factor of s is a factor of r.
so the factors calncell each other out and you are left with an integer.
1 is suffic.
but why 2 is not suff.

any CEO here to shed some light?
VP
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Re: DS question [#permalink]  28 Feb 2008, 16:09
(2) Every prime factor of s is also a prime factor of r.

2 is insufficient because consider s=4 r=10

prime factor of S is 2
prime factor of r is 5 and 2

so back to stat 2, every prime factor of S (which 2 is the only prime factor) is also a prime factor of R (which is 10) well 2 is prime factor of 10 as well

however 10/4 is not an integer
Intern
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Re: DS question [#permalink]  28 Feb 2008, 17:36
RyanDe680 wrote:
This came up in my review, my answer was incorrect.

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.

Can you provide rationale as well?

statement 1 - since s is a factor of itself, and every factor of s is a factor of r, statement 1 answers the question directly.

statement 2 - Example 4, 8 - ok. Example 4,6 - not ok. So not sufficient.

Director
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Re: DS question [#permalink]  29 Feb 2008, 13:17
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I get A as well.

Stmt 1: Every factor of s is also a factor of r.

All the factors of s in the denominator cancel with r in the numerator and since they are both positive integers your left with a positive integer.

Stmt 2: Every prime factor of s is also a prime factor of r.

Since we dont know anything about the non prime factors this is insuff.

For example r could be 12 and s could be 11.
Manager
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Re: DS question [#permalink]  01 Mar 2008, 20:33
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First statement sufficient as every factor of s is a factor of r as well so they cancel out to make an integer
Remember we cannot take example of r=6 and s=4 as somebody has taken previously as there are two factors of two in 4 but only one factor of 2 in 6.
Statement 2 insufficient
e.g r=9 and s=6
and r=9 and s=3
Intern
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Re: DS question [#permalink]  25 Sep 2008, 06:30
I'm not a fan of this question. If, for example S = 12, its prime factorization is 2^2 * 3.

According to statement 2, EVERY prime factor of s (I took this to mean 2, 2, and 3 since it has two 2's, which are both prime factors). Basically I thought the trick was that you had to understand that for every integer, there is a prime factorization, and therefore the two statements were basically the same. I guess I misinterpreted (2), but still, how would you KNOW how to interpret that?
VP
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Re: DS question [#permalink]  26 Sep 2008, 12:47
tamg08 wrote:
I'm not a fan of this question. If, for example S = 12, its prime factorization is 2^2 * 3.

According to statement 2, EVERY prime factor of s (I took this to mean 2, 2, and 3 since it has two 2's, which are both prime factors). Basically I thought the trick was that you had to understand that for every integer, there is a prime factorization, and therefore the two statements were basically the same. I guess I misinterpreted (2), but still, how would you KNOW how to interpret that?

What a worst coincidence! I did the same. I was looking for numbers that had the same prime factors. But I guess we are wrong.

Every prime factor of s is also a prime factor of r.

does not mean that every prime factor of s need not be a prime factor of r as many times in s. It can just be a subset of the numbers. as some said 4,8 good 4,6 not good
Re: DS question   [#permalink] 26 Sep 2008, 12:47
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