If r and s are positive integers, is r/s an integer? 1) : DS Archive
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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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10 Aug 2005, 15:26
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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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10 Aug 2005, 15:55
A.

1. if every factor of s is a factor of r, then r/s is definitely an integer. e.g., let s = 2 or 3 for every factor of s to be a factor of r, r must be >=2 or 3. so sufficient

2. Every prime factor of s is also a prime factor of r
if every prime factor of say 4 (which is 2) is a prime factor of r = 14 (which is 2, 7), then for all we know, 14/4 is not an integer. thus insuff
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10 Aug 2005, 17:06
2 questions:

1) We know 6=3x2 and 6 also = 3x2x1. Is 1 a factor of 6?

2) Suppose s=40=2x2x2x5, r=20=2x2x5, can 1) still enough to make it?
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10 Aug 2005, 20:23
I think my question#2 has a loophole, as it does not fit the description of given 2).

40 has a factor of 8 which is not a factor of 20...
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10 Aug 2005, 22:10
1) Every factor of s is also a factor of r

since s is a factor of itself, so we can say r can be divided by s

A
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11 Aug 2005, 09:56
Acc. to me:

E

Would you share your reasoning with us? Thanks!
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11 Aug 2005, 10:10
jinino wrote:
Acc. to me:

E

Would you share your reasoning with us? Thanks!

In fact, in general could people not post answers without reasoning on this board please ? It does not normally help anyone.

It tends to happen after someone has given a detailed correct answer, that someone else then posts another answer without any explanation.
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11 Aug 2005, 10:13
By the way, the official answer is A and the explanation matches the one provided by Folaa3.
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11 Aug 2005, 10:54
qpoo's answer is much better for the first bit.

s is a factor of s, therefore s is a factor of r, so r/s is an integer.
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11 Aug 2005, 13:37
qpoo wrote:
1) Every factor of s is also a factor of r

since s is a factor of itself, so we can say r can be divided by s

A

Very good one!
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12 Aug 2005, 06:28
Sorry guys for not posting my expln!

Now that I figured out that my explanation is wrong, I may as well not post it
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Thanks!

12 Aug 2005, 06:28
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