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Number Properties - Multiples

This topic has 2 expert replies and 1 member reply
singhmaharaj Senior | Next Rank: 100 Posts
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Number Properties - Multiples

Post Tue Apr 29, 2014 6:44 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If x and y are integers greater than 1, is x a multiple of y?

    (a) 3y^2 + 7y = x

    (b) x^2 - x is a multiple of y

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    Post Tue Apr 29, 2014 7:00 am
    Quote:
    If x and y are integers greater than 1, is x a multiple of y?
    (1) 3y² + 7y = x
    (2) x² - x is a multiple of y

    Target question: Is x a multiple of y?
    Asking whether x is a multiple of y is the same as asking whether x = (y)(some integer)
    For example, 12 is a multiple of 3 because 12 = (3)(4)
    So, let's rephrase the question as...
    REPHRASED target question: Does x = (y)(some integer)?

    Statement 1: 3y² + 7y = x
    Factor to get x = y(3y + 7)
    If y is an integer, then (3y + 7) must be an integer
    In other words: x = y(some integer)
    Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

    Statement 2: x² - x is a multiple of y
    There are several values of x and y that satisfy this condition. Here are two:
    Case a: x = 4 and y = 2 (this satisfies statement 2 because x² - x = 12, and 12 is a multiple of 2). In this case, x IS a multiple of y
    Case b: x = 5 and y = 2 (this satisfies statement 2 because x² - x = 20, and 20 is a multiple of 2). In this case, x is NOT a multiple of y
    Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

    Answer = A

    Cheers,
    Brent

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    Amrabdelnaby Master | Next Rank: 500 Posts Default Avatar
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    Post Thu Dec 24, 2015 1:35 pm
    I have a question pertaining to statement 2.

    I actually considered it sufficient without even doing any calculations because I applied the following rule backwards.

    If K is a divisor of M, and K is a divisor of N, then K is a divisor of M+N, M-N, and N-M.

    Now since it appears to be that statement 2 is insufficient, here comes my question:

    If K is a divisor of M-N, it doesn't necessarily entail that K is a divisor of M and a divisor of N? In other words, can we not apply the above mention rule backwards or am I missing something here?

    Please advise.

    Brent@GMATPrepNow wrote:
    Quote:
    If x and y are integers greater than 1, is x a multiple of y?
    (1) 3y² + 7y = x
    (2) x² - x is a multiple of y

    Target question: Is x a multiple of y?
    Asking whether x is a multiple of y is the same as asking whether x = (y)(some integer)
    For example, 12 is a multiple of 3 because 12 = (3)(4)
    So, let's rephrase the question as...
    REPHRASED target question: Does x = (y)(some integer)?

    Statement 1: 3y² + 7y = x
    Factor to get x = y(3y + 7)
    If y is an integer, then (3y + 7) must be an integer
    In other words: x = y(some integer)
    Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

    Statement 2: x² - x is a multiple of y
    There are several values of x and y that satisfy this condition. Here are two:
    Case a: x = 4 and y = 2 (this satisfies statement 2 because x² - x = 12, and 12 is a multiple of 2). In this case, x IS a multiple of y
    Case b: x = 5 and y = 2 (this satisfies statement 2 because x² - x = 20, and 20 is a multiple of 2). In this case, x is NOT a multiple of y
    Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

    Answer = A

    Cheers,
    Brent

    Post Thu Dec 24, 2015 3:43 pm
    Quote:
    If K is a divisor of M-N, it doesn't necessarily entail that K is a divisor of M and a divisor of N? In other words, can we not apply the above mention rule backwards or am I missing something here?
    No. You can see this with simple numbers. Say M = 9 and N = 7. 9 - 7 = 2, so we can set K equal to 2. Clearly, 2 is not a divisor of either 9 or 7. (And a reminder that just because x --> y does not necessarily mean that y --> x.)

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