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

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The product of all the prime numbers less than 20 is closest [#permalink] New post 26 Jan 2012, 09:29
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Difficulty:

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Question Stats:

53% (01:31) correct 47% (00:57) wrong based on 98 sessions
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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Jan 2012, 09:46, edited 1 time in total.
Edited the answer choices and added the OA
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Re: Help!! [#permalink] New post 26 Jan 2012, 09:45
Expert's post
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

Answer: C.

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.

Answer: C.

P.S. Please format the questions properly.
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The product of all the prime numbers less than 20 is closest [#permalink] New post 23 Jun 2012, 20:52
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

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Re: The product of all the prime numbers less than 20 is closest [#permalink] New post 23 Jun 2012, 23:21
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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

GMAT Official Guide 12

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.

Answer C
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The product of all the prime numbers less than 20 is closest to [#permalink] New post 23 Mar 2013, 11:00
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

Answer C


Did you actually calculate this with a pen and paper or you used a calculator?
The product of all the prime numbers less than 20 is closest to   [#permalink] 23 Mar 2013, 11:00
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6 Experts publish their posts in the topic The product of all the prime numbers less than 20 is closest Bunuel 13 02 Jul 2012, 01:21
1 Experts publish their posts in the topic The product of all the prime numbers less than 20 is closest melissawlim 7 20 Jan 2010, 05:27
1 Experts publish their posts in the topic The product of all the prime numbers less than 20 is closest JuliaS 2 21 Jan 2008, 21:05
2 The product of all the prime numbers less than 20 is closest gablaze23 9 02 Aug 2007, 07:07
The product of all the prime number less than 20 is closest Paul 4 06 Jan 2006, 17:20
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