what is the least possible value of n?

[himu]

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

[vipulgoyal]

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

[Brent@GMATPrepNow]

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

[Anju@Gurome]

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.

[Scott@TargetTestPrep]

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