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Can this problem be solved quicker?

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Joined: 03 Jun 2011
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Can this problem be solved quicker? [#permalink] New post 03 Jun 2011, 09:43
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

0% (00:00) correct 100% (01:41) wrong based on 7 sessions
"The product of all the prime numbers less than 20 in closest to which of the following powers?
A) 10^9
B) 10^8
C) 10^7
D) 10^6
E) 10^5
The book says to take all the prime numbers less than 20 and multiply them, which is what I originally did, I was just wondering if there is a quicker way to do this. Thanks!
[Reveal] Spoiler: OA
Expert Post
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Concentration: Entrepreneurship, Other
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Re: Can this problem be solved quicker? [#permalink] New post 03 Jun 2011, 10:43
Expert's post
P = 2*3*5*7*11*13*17*19

Let's regroup it a bit and use approximation:

P = (2*5)*(3*7)*(11*19)*(13*17) ~ 10 * 20 * (10*20)* (15*15) ~ 10 * 2 * 10 * 2 * 100 * 2 * 100 ~ 8*10^6 --> ~10^7

OA should be C
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Re: Can this problem be solved quicker?   [#permalink] 03 Jun 2011, 10:43
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