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
what is the least possible value of n?
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vipulgoyal
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Brent@GMATPrepNow
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550 = (2)(5)(5)(11)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
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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Anju@Gurome
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As n³ is a multiple of 550, n must be multiple of 11.himu wrote:If n is a positive integer and n³ is a multiple of 550, what is the least possible value of n?
Only option which is multiple of 11 is 110.
The correct answer is D.
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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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