OG 11- diagnostic test 15

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Pugalenthi: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Fri Sep 25, 2009 9:26 am

OG 11- diagnostic test 15

by Pugalenthi » Mon May 14, 2012 11:40 am

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

The answer is C. Is there a way to find the answer without multiplying all the prime nos? Any help would be much appreciated

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Source: Beat The GMAT — Problem Solving | Mon May 14, 2012 11:40 am

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 am; Location: Pune, India; Thanked: 186 times; Followed by:29 members

by aneesh.kg » Mon May 14, 2012 12:14 pm

We're not concerned with the exact value, so we will make approximations and collect as many 0s as we can.

(2*3*5)*(7*11)*13*17*19
= (30*77)*(13*17)*(19)
~ 2200*200*20
~ 8.8 X 10^6
10^6 < 8.8 X 10^6 < 10^7
(8.8 X 10^6 is closer to 10^7 than 10^6)

[spoiler](C)[/spoiler] is the answer

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Mon May 14, 2012 8:35 pm

Pugalenthi 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

The answer is C. Is there a way to find the answer without multiplying all the prime nos? Any help would be much appreciated

We can regroup the numbers, 2, 3, 5, 7, 11, 13, 17, and 19, to multiply them.
2 * 3 * 5 * 7 * 11 * 13 * 17 * 19
= (2 * 5) * (3 * 7) * 11 * 13 * 17 * 19
= 10 * 21 * 11 * 13 * 17 * 19

Now approximating, we get 10 * 20 * 10 * 10 * 20 * 20 = 8 * 10^6, which is 10^7 appr.

The correct answer is C.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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