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what is the value of x

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gmatmachoman Legendary Member Default Avatar
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what is the value of x

Post Tue Apr 06, 2010 2:36 am
x is a positive integer; what is the value of x?
1) The sum of any two positive factors of x is even
2) x is a prime number and x < 4

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pops Master | Next Rank: 500 Posts Default Avatar
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Post Tue Apr 06, 2010 10:42 pm
gmatmachoman wrote:
x is a positive integer; what is the value of x?
1) The sum of any two positive factors of x is even
2) x is a prime number and x < 4
statement 1:
sum of any two positive factors is even
1 implies => all the factors are either even or all are odd.
if all the factors are even so that if we pick any 2 of them sum will be even (even+even=even).. but since 1 is a factor so all factors are odd will make sense (odd+odd=even)

so only conclusion from statement 1 is x has all odd factors.
insufficient

statement 2: x is a prime number < 4
it can be 2 or 3
insufficient

statement 1 and 2 combined:
factors of 2: 2, 1
factors of 3: 3, 1 (sum = 4 which is even)

hence x=3

C

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eaakbari Master | Next Rank: 500 Posts
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Post Tue Apr 06, 2010 7:57 pm
jerryragland wrote:
@eaakbari -

Thanks for your reply. Can you explain your below logic in detail -

This implies x is odd and therefore does not have any even factors. As even + odd = odd and will always be 1 odd multiple.
I may have phrased that wrong. I meant the number 1 will always be a factor and hence will always cause any number with all even factors to have the sum of factors as odd

8 =2 *2*2*1 ; sum 7

A number with all even factors will be broken down in 2^n and when that is added will give you even result and when its added with 1 , result odd

HTH

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eaakbari Master | Next Rank: 500 Posts
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Post Tue Apr 06, 2010 2:55 am
Statement one

This implies x is odd and therefore does not have any even factors. As even + odd = odd and will always be 1 odd multiple.
But this info is not enough.Hence Insuff

Statement two. The number can be 2 or 3.Insuff

Combined
We know from(1) that number should be odd and from 2 that number is 2 or 3
Hence x = 3

Suff

Answer C

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jerryragland Senior | Next Rank: 100 Posts Default Avatar
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Post Tue Apr 06, 2010 2:04 pm
@eaakbari -

Thanks for your reply. Can you explain your below logic in detail -

This implies x is odd and therefore does not have any even factors. As even + odd = odd and will always be 1 odd multiple.

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el_torero Junior | Next Rank: 30 Posts Default Avatar
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Post Tue Apr 06, 2010 6:53 pm
one huge fact that's useful here is that 1 is NOT prime.

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