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what is the least possible value of n?

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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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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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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]

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by Anju@Gurome » Mon Apr 08, 2013 8:56 pm
himu wrote:If n is a positive integer and n³ is a multiple of 550, what is the least possible value of n?
As n³ 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.
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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

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