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

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

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New post 14 Dec 2010, 18:18
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55% (02:04) correct 45% (01:00) wrong based on 42 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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New post 14 Dec 2010, 19:57
2*3*5*7*11*13*17*19

quick calculation:

3*10*77*13*17*19

231*10*13*17*19

231*10*221*19

231*221*190

Above steps did not take me much time, but after this I think one needs to be strong in multiplication!

If there is some short cut, it would be great to know....but I won't take the risk of some short cut which might result in wrong answer during the exam.

51051*190

=9699690

closer to 100,00000

which means 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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New post 14 Dec 2010, 20:15
My response from another thread:

Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19
Make groups
2*5 = 10
3*17 = 50 (approximately)
7*13 = 100 (approximately)
11*19 = 200 (approximately)
So you make 7 zeroes (the 2 and the 5 also make a 0). When you multiply all these, the answer will be close to 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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New post 15 Dec 2010, 06:50
"My response from another thread:

Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19
Make groups
2*5 = 10
3*17 = 50 (approximately)
7*13 = 100 (approximately)
11*19 = 200 (approximately)
So you make 7 zeroes (the 2 and the 5 also make a 0). When you multiply all these, the answer will be close to 10^7 "

Dear Karishma, a quick question on this:
when i actually multiply the numbers, i get 10^6..there are only 6 zeros from what I see. What am I overlooking ?
Thank you in advance!
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Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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New post 15 Dec 2010, 07:05
Expert's post
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0987654312 wrote:
"My response from another thread:

Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19
Make groups
2*5 = 10
3*17 = 50 (approximately)
7*13 = 100 (approximately)
11*19 = 200 (approximately)
So you make 7 zeroes (the 2 and the 5 also make a 0). When you multiply all these, the answer will be close to 10^7 "

Dear Karishma, a quick question on this:
when i actually multiply the numbers, i get 10^6..there are only 6 zeros from what I see. What am I overlooking ?
Thank you in advance!


The 5 of 50 and the 2 of 200 above multiply to make another 0.
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Re: The product of all the prime numbers less than 20 is closest to which [#permalink]

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

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New post 16 May 2016, 22:03
Robiou 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 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.

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);

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

Answer: C.

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)

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

Answer: C.

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] 16 May 2016, 22:03
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