the product of 5 smallest prime numbers

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nafiul9090: Master | Next Rank: 500 Posts; Posts: 226; Joined: Thu Nov 25, 2010 12:19 amFollowed by: 2 members; Thanked: 3 times

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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Source: Beat The GMAT — Problem Solving | Wed Jul 04, 2012 8:46 am

sandeep_thaparianz: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Wed Mar 21, 2012 1:27 amFollowed by: 2 members; Thanked: 5 times

by sandeep_thaparianz » Wed Jul 04, 2012 9:05 am

is it first five prime nos??

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eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members; Thanked: 339 times; GMAT Score:770

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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Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8198; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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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