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divisible by 2, 3, and 15

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sanju09 GMAT Instructor
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divisible by 2, 3, and 15 Post Thu Nov 17, 2011 3:16 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?
    (A) k + 5
    (B) k + 15
    (C) k + 20
    (D) k + 30
    (E) k + 45

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    neelgandham Community Manager
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    Post Thu Nov 17, 2011 3:20 am
    sanju09 wrote:
    If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?
    (A) k + 5
    (B) k + 15
    (C) k + 20
    (D) k + 30
    (E) k + 45
    k is divisible by 2, 3, and 15, so for k + x to be divisible by these numbers x should also be divisible by all these numbers.From the options, only 20 and 30 are divisible by 2, and only 30 is divisible by 3(between 20 and 30), so Option D - k+30

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    Last edited by neelgandham on Thu Nov 17, 2011 3:22 am; edited 1 time in total

    kmittal82 GMAT Destroyer!
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    Post Thu Nov 17, 2011 3:20 am
    I'm sure there's an "algebraic" way of doing this, but its much simpler to test it with k = 30 (which is the lowest k divisible by 2,3 and 15)

    Plugging k = 30, (D) is the only option which is still divisible by 2,3 and 15

    Abhishek009 GMAT Destroyer!
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    Post Thu Nov 17, 2011 6:52 am
    sanju09 wrote:
    If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?
    (A) k + 5
    (B) k + 15
    (C) k + 20
    (D) k + 30
    (E) k + 45
    2 , 3 and 15 are co prime numbers...

    Now to find the least common no which is divisible by 2, 3 and 15 we take the LCM of the numbers which is 30....

    Hence k = 30

    Again we need to find the number , divisible by the no's will be by checking the options individually -

    A. 30 +5 which is not divisible by 2 and 3

    B. 30+15 which is not divisible by 2 and 3

    C. 30+20 which is not divisible by 2 and 3

    D. 30 + 30 which is divisible by 2 and 3 and 15...

    Hence answer will be D..

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