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

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Intern
Status: What to know what someone's dream looks like? Observe a large pile of GMAT books. (c)
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The product of all the prime numbers less than 20 is closest to which [#permalink]

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14 Dec 2010, 18:18
3
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Difficulty:

55% (hard)

Question Stats:

53% (01:09) correct 47% (00:59) wrong based on 51 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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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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14 Dec 2010, 20:15

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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Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 16909 [0], given: 230 Intern Joined: 15 Nov 2010 Posts: 20 Kudos [?]: [0], given: 0 Re: The product of all the prime numbers less than 20 is closest to which [#permalink] ### Show Tags 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! Kudos [?]: [0], given: 0 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7612 Kudos [?]: 16909 [0], given: 230 Location: Pune, India Re: The product of all the prime numbers less than 20 is closest to which [#permalink] ### Show Tags 15 Dec 2010, 07:05 Expert's post 1 This post was BOOKMARKED 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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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 May 2016, 21:25
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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 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);

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

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] 16 May 2016, 22:03
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