what is the least possible value of n?

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himu: Master | Next Rank: 500 Posts; Posts: 345; Joined: Sun Dec 21, 2008 10:57 pmFollowed by: 3 members; Thanked: 6 times

by himu » Mon Apr 08, 2013 8:15 pm

If n is a positive integer and
n3
is a multiple of 550, what is the least possible value of n?

8

27

81

110

125

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Source: Beat The GMAT — Problem Solving | Mon Apr 08, 2013 8:15 pm

vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Mon Apr 08, 2013 8:42 pm

my take D, 110

n^3 is a multiple of 550

n*n*n / 5*5*2*11
each n must have one 5 one 2 and one 11 hence 110

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Apr 08, 2013 8:49 pm

himu wrote:If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?

A. 8
B. 27
C. 81
D. 110
E. 125

550 = (2)(5)(5)(11)
This means that the prime factorization of n must have a 2, 5 and 11 in it.
So, the smallest value of n is (2)(5)(11) = [spoiler]110 = D[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Mon Apr 08, 2013 8:56 pm

himu wrote:If n is a positive integer and nÂ³ is a multiple of 550, what is the least possible value of n?

As nÂ³ is a multiple of 550, n must be multiple of 11.
Only option which is multiple of 11 is 110.

The correct answer is D.

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

Â§ GMAT with Gurome Â§ Admissions with Gurome Â§ Career Advising with Gurome Â§

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8176; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: what is the least possible value of n?

by Scott@TargetTestPrep » Sun Jul 26, 2020 2:50 pm

himu wrote: ↑
Mon Apr 08, 2013 8:15 pm
If n is a positive integer and
n3
is a multiple of 550, what is the least possible value of n?

8

27

81

110

125

Solution:

Let’s prime factorize 550:

550 = 55 x 10 = 5 x 11 x 5 x 2 = 2 x 5^2 x 11

Since n^3 must have its prime factors in multiplicities of 3, the least possible value of n^3 is 2^3 x 5^3 x 11^3 (i.e., n = 550 x 2^2 x 5 x 11^2) and hence the least possible value of n is 2 x 5 x 11 = 110.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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