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Manager
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If r and s are positive integers, is r/s an integer? 1) [#permalink]
 10 Aug 2005, 16:26
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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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VP
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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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Manager
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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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Manager
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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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Senior Manager
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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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Manager
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rchadha wrote: Acc. to me:
E
Would you share your reasoning with us? Thanks!
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Manager
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jinino wrote: rchadha 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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Manager
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By the way, the official answer is A and the explanation matches the one provided by Folaa3.
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Manager
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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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SVP
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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! 
_________________
Keep on asking, and it will be given you;
keep on seeking, and you will find;
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Manager
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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!
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close
