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

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Manager
Joined: 01 Jan 2012
Posts: 50
Location: United States
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The product of all the prime numbers less than 20 is closest [#permalink]

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26 Jan 2012, 10:29
4
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10
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Difficulty:

75% (hard)

Question Stats:

51% (01:00) correct 49% (01:10) wrong based on 432 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

Last edited by Bunuel on 16 May 2016, 22:01, edited 3 times in total.
Math Expert
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Posts: 39753
Re: The product of all the prime numbers less than 20 is closest [#permalink]

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26 Jan 2012, 10:45
5
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monikaleoster 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

Suggest method of solution.
The correct ans is C

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.

P.S. Please format the questions properly.
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Re: The product of all the prime numbers less than 20 is closest [#permalink]

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23 Jun 2012, 21:52
2*3*5*7*11*13*17*19
2*19*3*17*5*13*7*11
38*51*65*77
By approximation
40*50*70*70
2000*4900
By approximation
2000*5000
10,000,000

Posted from my mobile device
Director
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Re: The product of all the prime numbers less than 20 is closest [#permalink]

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24 Jun 2012, 00:21
1
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melissawlim 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

Official Guide 12 Question

 Question: 15 Page: 22 Difficulty: 700

Find All Official Guide Questions

Video Explanations:

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

My approximation would be 2x5x(3x7)x(11x19)x(13x17)~10x20x200x15x15=10,000x4x225=10,000x900~10,000,000.

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Manager
Joined: 24 Jul 2010
Posts: 90
Re: The product of all the prime numbers less than 20 is closest [#permalink]

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23 Mar 2013, 12:00
GMATBLACKBELT wrote:
gablaze23 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

Okay I have the solution to this.
But I am just wondering whether there is a shortcut?

My solution... hall ass.. 2*3*5*7=210*11=2310*13=30030*17=510510*19=9699690

Did you actually calculate this with a pen and paper or you used a calculator?
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Re: The product of all the prime numbers less than 20 is closest [#permalink]

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07 Dec 2014, 13:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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21 Dec 2014, 08:24
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19

2* 5 = 10
11 = 10 approx.
3 * 7 = 21 = 20 approx = 10 *2 -Extra 2
19 = 10 * 2 - Extra 2
13 * 4 (2*2 extra) = 52 = 10 - Extra 5
17*5 = 105 - 100 approx
So 10 * 10 * 10 * 10 * 10 * 100 = 10^7 - C)
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Re: The product of all the prime numbers less than 20 is closest [#permalink]

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29 Apr 2015, 23:58
hard one
thank you Bunuel for the best solution
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Re: The product of all the prime numbers less than 20 is closest [#permalink]

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01 Jan 2016, 18:56
2*3*5*7*11*13*17*19
2*3*5*7=210
11 ~=10
13*17=221
19 ~= 20

210*10*221*20
=2^3*10^6
~=C
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Re: The product of all the prime numbers less than 20 is closest [#permalink]

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24 Jan 2016, 03:06
Dear Bunuel,
Thank you for elegant solution of the problem.
Could u plz share with similar questions,
Thanks
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Joined: 02 Sep 2009
Posts: 39753
Re: The product of all the prime numbers less than 20 is closest [#permalink]

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24 Jan 2016, 03:31
1
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Expert's post
studentsensual wrote:
Dear Bunuel,
Thank you for elegant solution of the problem.
Could u plz share with similar questions,
Thanks

Similar question: the-product-of-all-positive-even-numbers-less-than-or-equal-to-20-is-209969.html
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Re: The product of all the prime numbers less than 20 is closest   [#permalink] 24 Jan 2016, 03:31
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