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the product of 5 smallest prime numbers

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by nafiul9090 » Wed Jul 04, 2012 8:46 am
The product of the Â…5 smallest two-digit prime numbers 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

any shortcut method?
Last edited by nafiul9090 on Wed Jul 04, 2012 4:46 pm, edited 1 time in total.
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by sandeep_thaparianz » Wed Jul 04, 2012 9:05 am
is it first five prime nos??
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by eagleeye » Wed Jul 04, 2012 9:12 am
The smallest two digit primes are 11, 13, 17, 19 and 23.

So their product = 11*13*17*19*23.

To approximate, put them in pairs. 11*19*13*17*23
11*19 is approx 10*20 = 200
13*17 is approx 10*20 = 200
23 is approx 25
multiplying 200*200*25 = 10^6.

So it is closest to 10^6.

Let me know if this helps :)
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by Bill@VeritasPrep » Wed Jul 04, 2012 10:07 am
eagleeye wrote:The smallest two digit primes are 11, 13, 17, 19 and 23.

So their product = 11*13*17*19*23.

To approximate, put them in pairs. 11*19*13*17*23
11*19 is approx 10*20 = 200
13*17 is approx 10*20 = 200
23 is approx 25
multiplying 200*200*25 = 10^6.

So it is closest to 10^6.

Let me know if this helps :)
Grouping and estimating is a great way to go, especially when the answers are so spread out. :)
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by Scott@TargetTestPrep » Thu Sep 27, 2018 4:16 pm
nafiul9090 wrote:The product of the Â…5 smallest two-digit prime numbers 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 the 5 smallest two-digit primes is 11 x 13 x 17 x 19 x 23, which we can approximate as the product 10 x 10 x 20 x 20 x 20 = 800,000. We see that this is closest to 1,000,000, or 10^6.

Answer: D

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