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Product of prime numbers

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Deepthi Subbu Master | Next Rank: 500 Posts Default Avatar
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Product of prime numbers

Post Tue Mar 12, 2013 8:50 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The product of all prime numbers less than 20 is closest to which of following powers of 10 ?

    In OG13, the answer is calculated based on multiplication. Is there a short cut?

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    Post Tue Mar 12, 2013 8:55 am
    Deepthi Subbu wrote:
    The product of all prime numbers less than 20 is closest to which of following powers of 10 ?
    (A) 10^9
    (B) 10^8
    (C) 10^7
    (D) 10^6
    (E) 10^5
    I added the answer choices.
    Since the numbers are very spread apart (each answer choice is 10 times greater than the next answer choice), we can be somewhat aggressive with our estimation.

    We have the product (2)(3)(5)(7)(11)(13)(17)(19)

    Let's see if we can group the numbers to get some approximate powers of 10

    First (2)(5)=10, so we get (2)(3)(5)(7)(11)(13)(17)(19) = (10)(3)(7)(11)(13)(17)(19)

    Next, 11 is close enough to 10, so we get: (10)(3)(7)(11)(13)(17)(19) = (10)(3)(7)(10)(13)(17)(19) [approximately]

    Next, (7)(13)=91, which is pretty close to 100. So we get (10)(3)(7)(10)(13)(17)(19) = (10)(3)(100)(10)(17)(19) [approximately]

    Finally, 3(17)=51, and (51)(19) is very close to (51)(20), which is very close to 1000
    So,(10)(3)(100)(10)(17)(19) = (10)(1000)(100)(10)= 10,000,000 [approximately]

    Since 10,000,000 = 10^7, the best answer is C

    Cheers,

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    Post Tue Mar 12, 2013 1:18 pm
    Quote:
    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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