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# The product of all the prime numbers less than 20 is closest to which

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Intern
Joined: 03 Jun 2011
Posts: 7
The product of all the prime numbers less than 20 is closest to which [#permalink]

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03 Jun 2011, 10:43
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Difficulty:

95% (hard)

Question Stats:

15% (02:10) correct 85% (01:23) wrong based on 161 sessions

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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) 10^9
(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!

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html
[Reveal] Spoiler: OA
CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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03 Jun 2011, 11:43
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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Manager
Joined: 05 Jun 2015
Posts: 84
Location: United States
WE: Engineering (Transportation)
Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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01 Sep 2015, 08:11
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P = 2*3*5*7*11*13*17*19
= 21 * (11 * 19) (13*17) *10
~ 21 * (10 * 20) (10 *20) * 10
~ 82 & 10 ^5
~ 10^ 7

Can some one edit the OA to C
Math Expert
Joined: 02 Sep 2009
Posts: 39672
Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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01 Sep 2015, 08:15
Olenkap82 wrote:
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

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!

We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.

# of different approximations are possible.

Approach #1:

2*5=10;
3*7=~20 (actually more than 20);
11*19=~200 (actually more than 200);
13*17=~200 (actually more than 200);

$$2*3*5*7*11*13*17*19\approx{10*20*200*200=8*10^6}\approx{10^7}$$.

Approach #2:

2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)

$$2*3*5*7*11*13*17*19\approx{10*50*100*200}=10^7$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html
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Re: The product of all the prime numbers less than 20 is closest to which   [#permalink] 01 Sep 2015, 08:15
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