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common factor greater than 1

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common factor greater than 1

by arora007 » Mon Jan 03, 2011 8:19 am
Set S consists of n distinct positive integers, none of which is greater than 12. What is the greatest possible value of n if no two integers in S have a common factor greater than 1?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 11
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Source: — Problem Solving |

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by Whitney Garner » Mon Jan 03, 2011 8:47 am
arora007 wrote:Set S consists of n distinct positive integers, none of which is greater than 12. What is the greatest possible value of n if no two integers in S have a common factor greater than 1?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 11
I believe this is a question from an old OG set (but I would love for the original poster to cite the source/author to verify before I walk through the solution for this specific problem).

To find the largest list of numbers that do not share a common factor greater than 1, we are looking for the number of primes in that list. BUT, we do not want to forget that 1 is also an option.

:)
Whit

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Note to those studying this: if I were you, I would NOT read / study problems that do not have the source cited. There are several very important reasons for this:

1) If you don't know the source, then you don't know whether you are compromising your future practice tests. What if the question is from the practice test you're about to take and now you see a question that you've already seen before? When that happens, it can blow the validity of your whole test! (Not if it happens just once, of course, but what if it happens multiple times?)

2) If you're taking a practice test and do see a question you've seen before, you'll probably answer it more quickly. This will give you a false sense of timing security because you now have a little more time... but that situation will NEVER be replicated on the real test.

3) The source might be bad. Do you want to study from a bad source? I don't!
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by prachich1987 » Mon Jan 03, 2011 9:14 am
arora007 wrote:Set S consists of n distinct positive integers, none of which is greater than 12. What is the greatest possible value of n if no two integers in S have a common factor greater than 1?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 11
IMO : C
Set can contain (1,2,3,5,7,11)
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by arora007 » Mon Jan 03, 2011 11:45 am
Hey Whitney... Dont know the real source... got it from a "Problem solving.pdf" which had some 46 odd sections. this came in section 13.

I found this question interesting...so just wanted others in the forum too to try their skills on such a question..

yeah you are right we should include 1 also...

prachich1987 you got it right!!
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