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

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Intern
Joined: 08 Jun 2009
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The product of all the prime numbers less than 20 is closest to which [#permalink]

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12 Jun 2009, 20:28
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Difficulty:

95% (hard)

Question Stats:

39% (00:44) correct 61% (01:01) wrong based on 88 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-product-of-all-the-prime-numbers-less-than-20-is-closest-135192.html
[Reveal] Spoiler: OA

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

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12 Jun 2009, 23:12
Welcome to GMAT Club Jozu!

There is a neater way to post questions. You can learn how to post math symbols here: writing-mathematical-symbols-in-posts-72468.html. Usually, all you have to do is to highlight the text and hit the M button. Bu there are exceptions such as fractions.

You can also hide the Original Answer using the "Spoiler" functionality. I added it to your post. Here is the original question rewritten:

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) $$10^5$$
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Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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13 Jun 2009, 02:26
i found this method in another forum. thought i could share it with u.

2*3*5*7*11*13*17*19

7*11*13 2*5 17*19 * 3

1001 * 10 * (18-1))(18+1) 3

approximately 10^4 *(324-1) *3

10^4 * 323*3

9690000

nearest power 10 is 10^7

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

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16 Jun 2011, 20:45
how to solve this question using approximation method?

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

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04 Jun 2016, 06:19
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Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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04 Jun 2016, 07:03
1
KUDOS
Jozu wrote:
Is there any quick way to solve this question?

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

[Reveal] Spoiler:
OA is C

Product of Prime numbers less than 20 is 2*3*5*7*11*13*17*19
2*5=10 .

10*11*3*7*13*17*19 = 10*10*3*10*10*20*20 (approximately) ~ Product will be >10^6 <10^8 i.e. 10^7

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

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04 Jun 2016, 10:56
Jozu 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

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. One way:

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=~10*20*200*200=8*10^6=~10^7

Or:
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=~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] 04 Jun 2016, 10:56
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