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GmatKiss GMAT Titan Default Avatar
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powers Post Sat May 05, 2012 12:30 pm
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    The product of all the prime numbers less than 20 is closest to which of the following powers of 10?

    A.10^5
    B.10^9
    C.10^7
    D.10^6
    E.10^8

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    Post Sat May 05, 2012 5:44 pm
    Grouping and rounding is the best way to go:


    2*3*5*7=210, round down to 200.

    19*11=209, round down to 200. We now have:

    200*200*13*15*17, or 40,000*13*15*17, or 10^4*13*15*17, or 10^4*(10+3)*(10+5)*(10+7)

    We can see that we'll have a total of 7 10's, so 10^7 is the answer we're looking for.

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    Post Sun May 06, 2012 4:23 am
    GmatKiss wrote:
    The product of all the prime numbers less than 20 is closest to which of the following powers of 10?

    A.10^5
    B.10^9
    C.10^7
    D.10^6
    E.10^8
    Since the answer choices are VERY far apart, we can BALLPARK.
    For every value that we round UP, we should compensate by rounding another value DOWN.

    2*3*5*7    *11*13*17*19
    210 * 10*15 * 15*20
    200*150*300 = 9,000,000.

    The closest power of 10 = 10,000,000 = 10^7.

    The correct answer is C.

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    Last edited by GMATGuruNY on Tue Mar 26, 2013 6:28 am; edited 1 time in total

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    Anurag@Gurome GMAT Instructor
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    Post Tue May 08, 2012 9:11 pm
    GmatKiss wrote:
    The product of all the prime numbers less than 20 is closest to which of the following powers of 10?

    A.10^5
    B.10^9
    C.10^7
    D.10^6
    E.10^8
    We can regroup the numbers, 2, 3, 5, 7, 11, 13, 17, and 19, to multiply them.
    2 * 3 * 5 * 7 * 11 * 13 * 17 * 19
    = (2 * 5) * (3 * 7) * 11 * 13 * 17 * 19
    = 10 * 21 * 11 * 13 * 17 * 19

    Now approximating, we get 10 * 20 * 10 * 10 * 20 * 20 = 8 * 10^6, which is 10^7 appr.

    The correct answer is C.

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