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DS - Div/Primes: If the integer n is greater than 1, is n =

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DS - Div/Primes: If the integer n is greater than 1, is n =

by II » Sun Aug 10, 2008 9:12 am
If the integer n is greater than 1, is n equal to 2?

(1) n has exactly two positive factors

(2) The difference of any two distinct positive factors of n is odd

I know the answer to this ... but wanted to understand more on statement 2.

Thanks.
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by mals24 » Sun Aug 10, 2008 11:25 am
IMO B

st 1 says n is prime it could be any prime number INSUFF

st 2 says The difference of any two distinct positive factors of n is odd
This st means that if we subtract any two positive factors of n the difference should be odd.
the only number that satisfies this condition is 2
for example take foll numbers:
factors of 3 = 1,3 3-1=odd
factors of 4= 4,1,2 4-1=odd but 4-2even
factors of 10 = 10, 1, 5, 2 10-1=odd; 5-1=even
so on and so forth

i hope the explanation was clear for st 2
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by II » Sun Aug 10, 2008 1:32 pm
sure I got this !
... I think you meant to say "3-1 = even" !
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by mals24 » Mon Aug 11, 2008 5:43 am
woops sorry for the typo
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by jsl » Mon Aug 11, 2008 6:16 am
mals24 wrote:IMO B

st 2 says The difference of any two distinct positive factors of n is odd
This st means that if we subtract any two positive factors of n the difference should be odd.
Is the official answer definitely B? If you pick 6, factors include 1, 2, 3, 6. If you subtract 2 from 3, the remainder is odd...

I thought the answer is C...
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by mals24 » Mon Aug 11, 2008 6:38 am
@jsl
But if you subtract 2 from 6, the answer is even so that eliminates 6 as an option and narrows down the option to 2 hence B is SUFF..

The factors of an odd # are always odd and every time u subtract 2 odd # the answer is even so that eliminates all odd #s

The factors of all even # (except 2) are a combination of more than 2 even n odd # so there will be at least one pair of factors which when you subtract the answer will be even. so that eliminates all even # except 2

I hope its clear
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by lanm03 » Sun Feb 15, 2009 3:16 pm
I think the confusing part of the question is the word "any":

"The difference of any two distinct positive factors of n is odd."

Factors of 10: 1, 2, 5, 10
5-2=3 (odd)

Factors of 6: 1, 2, 3, 6
3-2=1 (odd)

With this reasoning, n could be 10 or 20.

I think by changing the word "any" to "every" makes more sense. Just a thought...

BTW, the answer according to the book is B. I'm just pointing out an observation.
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