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what is the value of x

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gmatmachoman GMAT Titan Default Avatar
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what is the value of x Post Tue Apr 06, 2010 2:36 am
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    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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    eaakbari GMAT Destroyer!
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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

    jerryragland Rising GMAT Star 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.

    el_torero Just gettin' started! 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.

    eaakbari GMAT Destroyer!
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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

    pops Really wants to Beat The GMAT! 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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