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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
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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
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Last edited by

Bunuel on 16 May 2016, 22:01, edited 3 times in total.

Edited the answer choices and added the OA

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

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26 Jan 2012, 10:45
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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

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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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 10,000,000Posted from my mobile device

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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
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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

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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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

Answer C

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

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24 Jan 2016, 03:31
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