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Prime & Square

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joyseychow Really wants to Beat The GMAT! Default Avatar
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Prime & Square Post Thu Aug 06, 2009 7:35 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    Is the positive integer n equal to the square of an integer?
    (1) For every prime number p, if p is a divisor of n, then so is p2.
    (2) sqrt root (n) is an integer.

    I got this correct. But I'm still not sure about Stmt 1. Pls. Explain. Thks!

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    shahdevine Really wants to Beat The GMAT! Default Avatar
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    Post Thu Aug 06, 2009 7:53 am
    joyseychow wrote:
    Is the positive integer n equal to the square of an integer?
    (1) For every prime number p, if p is a divisor of n, then so is p2.
    (2) sqrt root (n) is an integer.

    I got this correct. But I'm still not sure about Stmt 1. Pls. Explain. Thks!
    statement 1)

    restate:

    for every prime number that is a factor of n then p^2 is also a factor of n.

    let's make our prime number(p) = 5. N at least would have to equal 25 in order for p^2 to be a factor of N. So n=p^2. However, n could have additional primes that are not p. For instance n could equal 50, whose factors are 5^2 and 2. If this were the case n does not equal the square of an integer. It equals the square of an integer times another prime number. So insufficient.

    Statement 2)

    sqroot n = an integer
    n = integer squared

    sufficient

    B is answer.

    pls confirm.

    you got this!

    navalpike Really wants to Beat The GMAT! Default Avatar
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    Post Thu Aug 06, 2009 9:16 am
    My answer is D.

    A.) I am translating this to mean that if there is "any" prime number in N, then the p^2 version of that prime is also in N. Meaning - Every prime is squared.

    If this is the correct interpretation, then this is sufficient. A perfect square, when reduced to primes, will have even numbers as exponents of those primes. For Example.

    2*3*5*7 = Not a perfect square

    2^2*3^2*5^2*7^2 = perfect square.

    Sufficient.



    Last edited by navalpike on Fri Aug 07, 2009 10:04 am; edited 1 time in total

    zeenab Just gettin' started! Default Avatar
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    Post Thu Aug 06, 2009 10:18 am
    I think the answer is D as well.

    If a number is a perfect square, all of its prime factors have to occur an even number of times in its factorization. Which means, if the number is divisible by a prime number n, it should be divisble by n^2 as well.
    So if the corollary holds good as well.
    Example -

    Take 100 which is 10^2

    (5*2)^2 - so the number is divisible by 5 and 5^2 and 2 and 2^2.

    OA please?

    shahdevine Really wants to Beat The GMAT! Default Avatar
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    Post Thu Aug 06, 2009 4:54 pm
    zeenab wrote:
    I think the answer is D as well.

    If a number is a perfect square, all of its prime factors have to occur an even number of times in its factorization. Which means, if the number is divisible by a prime number n, it should be divisble by n^2 as well.
    So if the corollary holds good as well.
    Example -

    Take 100 which is 10^2

    (5*2)^2 - so the number is divisible by 5 and 5^2 and 2 and 2^2.

    OA please?
    you may be right. my interpretation is wrong. we need OAs...

    mehravikas GMAT Titan Default Avatar
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    Post Thu Aug 06, 2009 6:55 pm
    Answer shouldn't be D...

    Statement 1 -

    n = 45, p = 3

    p is a divisor of n
    also p^2 is a divisor of n

    but n in this case is not a square of an integer.

    shahdevine wrote:
    zeenab wrote:
    I think the answer is D as well.

    If a number is a perfect square, all of its prime factors have to occur an even number of times in its factorization. Which means, if the number is divisible by a prime number n, it should be divisble by n^2 as well.
    So if the corollary holds good as well.
    Example -

    Take 100 which is 10^2

    (5*2)^2 - so the number is divisible by 5 and 5^2 and 2 and 2^2.

    OA please?
    you may be right. my interpretation is wrong. we need OAs...

    tohellandback GMAT Destroyer! Default Avatar
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    Post Thu Aug 06, 2009 7:15 pm
    joyseychow wrote:
    Is the positive integer n equal to the square of an integer?
    (1) For every prime number p, if p is a divisor of n, then so is p2.
    (2) sqrt root (n) is an integer.

    I got this correct. But I'm still not sure about Stmt 1. Pls. Explain. Thks!
    edited..
    IMO B- look for scoobydooby's example
    1) it says that all the prime factors of n have even powers- i was wrong
    it says that the powers are greater than 2. Can be even. Can be odd
    Not sufficient

    2) Sufficient

    @mehravikas,
    1) says every prime number.
    In your example 45= 3^2*5.
    you haven't considered 5.

    _________________
    The powers of two are bloody impolite!!



    Last edited by tohellandback on Thu Aug 06, 2009 11:57 pm; edited 1 time in total

    scoobydooby GMAT Titan Default Avatar
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    Post Thu Aug 06, 2009 11:50 pm
    would go with B

    stmnt 1 is not sufficient by itself.

    if N=9, divisible by 3 and 3^2 . yes N perfect square
    if N=27, divisble by 3 and 3^2. no N not perfect square

    stmnt 2 sufficient
    all perfect squares have integers as their square roots.

    shahdevine Really wants to Beat The GMAT! Default Avatar
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    Post Sun Aug 09, 2009 7:57 am
    scoobydooby wrote:
    would go with B

    stmnt 1 is not sufficient by itself.

    if N=9, divisible by 3 and 3^2 . yes N perfect square
    if N=27, divisble by 3 and 3^2. no N not perfect square

    stmnt 2 sufficient
    all perfect squares have integers as their square roots.
    cool i'm not crazy...for a minute i was racking my brains. I thought I was from another planet when everyone was getting Ds instead of B.

    arorag GMAT Destroyer! Default Avatar
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    Post Sun Aug 09, 2009 8:07 am
    should be B
    For A lets have n=8, p= 2, p2= 4

    joyseychow Really wants to Beat The GMAT! Default Avatar
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    Post Wed Aug 12, 2009 10:36 pm
    Yes OA is indeed B

    vittalgmat GMAT Destroyer! Default Avatar
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    Post Wed Aug 12, 2009 11:30 pm
    The question is a bit confusing.. esp stmt 1.

    But this is a good discussion.
    I got B with my interpretation.


    thanks everyone.
    -V

    vikram_k51 Really wants to Beat The GMAT! Default Avatar
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    Post Thu Aug 13, 2009 11:14 am
    Is the positive integer n equal to the square of an integer?
    (1) For every prime number p, if p is a divisor of n, then so is p2.
    (2) sqrt root (n) is an integer.

    D

    dikku07 Rising GMAT Star Default Avatar
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    Post Thu Aug 13, 2009 2:18 pm
    in favour of B

    jjk Rising GMAT Star Default Avatar
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    Post Mon Aug 17, 2009 7:47 pm
    B

    You can test statement 1 by setting n equal to 9 or 18 and p equal to 3.

    If n = 9 and p = 3, 9/3 and 9/9 yield integers.

    If n = 18 and p = 3, 18/3 and 18/9 yield integers.

    However, 18 is NOT a square of an integer. Statement 1 is thus insufficient.

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