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Re: The product of all the prime numbers less than 20 is closest [#permalink]

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02 Jul 2012, 03:17

Hi,

Difficulty level: 650

Product of prime numbers less than 20 = 2*3*5*7*11*13*17*19 =(2*5)*3*(7*13)*(11*17)*19 =3*10*91*189*19 ~(30)*(90*19)*190 ~5700*1710 ~5700*1700 ~9690000 \((=10^6)\)

Thus, Answer is (D)

Regards,

Last edited by cyberjadugar on 02 Jul 2012, 03:39, edited 2 times in total.

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The product is \(2*3*5*7*11*13*17*19 = 10 * 21 * 11*(13*17) * 19 \approx10*20*10*15^2*20=900*10^4\approx10^7\).

Therefore, answer C
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Re: The product of all the prime numbers less than 20 is closest [#permalink]

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02 Jul 2012, 12:58

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2*3*5*7*11*13*17*19 = 210*(10+1)(10+3)(10+7)(10+9) 210 ~ 10*10*2 So the original equation will be equivalent to 10*10*2*(10+1)(10+3)(10+7)(10+9) The highest order of the equation will be 10^6, and other part of expression will not make it closer to 10^7. I have solved it mostly on hunch, no sure how correct I am.

Re: The product of all the prime numbers less than 20 is closest [#permalink]

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25 Oct 2013, 04:45

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I have approached in the following way:-

2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 = 10 x 21x 11 x 13 x 17 x 19 = 10 x 10 x 2.1 x 10 x 1.1 x 10 x 1.3 x 10 x 1.7 x 10 x 1.9 = 10^6 x (2.1 x1.1 x 1.3 x 1.7 x 1.9)

The approximation of the (2.1 x 1.7 x 1.9 x 1.3 x 1.1) will be close to 10, so the answer is 10^7

Re: The product of all the prime numbers less than 20 is closest [#permalink]

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05 Mar 2014, 11:48

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Similar to Bunuel's first approach: I thought it was easiest to just do : 2*3*5*7 = 210 11 roughly 10 13 roughly 10 17 roughly 20 19 roughly 20 so 210*10*10*20*20 = 8*10^6 = 10^7

Re: The product of all the prime numbers less than 20 is closest [#permalink]

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11 Apr 2014, 19:07

Can anyone comment on my method's effectiveness/efficiency: Prime numbers < 20 are: 2, 3, 5, 7, 11, 13, 17, 19 (Count = 8) Median = 9 (through (7+11)/2) So product should be approx. close to 9^8 which in turn is closest to 10^7, thus answer is 10^7.

Re: The product of all the prime numbers less than 20 is closest [#permalink]

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01 Aug 2016, 20:48

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The product of all the prime numbers less than 20 is closest [#permalink]

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03 Dec 2016, 19:39

High Quality Question from the Official Set. Its always good to remember the first 10 primes 2 3 5 7 11 13 17 19 23 29

Now the product of all primes <20 => 2*3*5*7*11*13*19 Product => 210*143*323 Approximating => Product =>200*150*300 => 9000000 which is close to 10^7 Hence C _________________

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