OG 13 - Diagnostic - PS - 15

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OG 13 - Diagnostic - PS - 15

by rchetan_18 » Sun Feb 03, 2013 6:29 am
The product of all the prime numbers less than 20 is
closest to which of the following powers of 10 ?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5

How to solve this without multiplying all the prime numbers?

Thanks in advance
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by GMATGuruNY » Sun Feb 03, 2013 7:30 am
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.
Last edited by GMATGuruNY on Tue Mar 26, 2013 5:27 am, edited 1 time in total.
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by buzzdeepak » Mon Feb 04, 2013 5:39 pm
Thanks Mitch... your approach simplifies the solution and lot less to compute.

My approach was a bit lengthy:
2x3x5x7x11x13x17x19

=> 2x5 x 3x7 x 11x13 x 17x19
=> 10 x 2x10 x 143 x ~17x20
=> 10 x 2x10 x ~14x10 x ~3x100
=> 10 x 10 x 10 x 100 x 2x14x3
=> 10^5 x ~100
=> 10^7