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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the smallest positive integer n such that n / 420 ca tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## What is the smallest positive integer n such that n / 420 ca ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [GMAT math practice question] What is the smallest positive integer n such that n / 420 can be expressed as a terminating decimal? A. 18 B. 21 C. 24 D. 30 E. 42 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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Max@Math Revolution wrote:
[GMAT math practice question]

What is the smallest positive integer n such that n / 420 can be expressed as a terminating decimal?

A. 18
B. 21
C. 24
D. 30
E. 42
A fraction will yield a terminating decimal if the prime-factorization of its denominator contains only 2's and/or 5's.
n/420 = n/(2*2*3*5*7).
For a terminating decimal to be yielded, the prime factors in red must CANCEL OUT with n, leaving only 2's and 5's in the denominator.
Thus, the smallest possible value for n = 21:
21/420 = (3*7)/((2*2*3*5*7) = 1/(2*2*5).
Since the prime-factorization in green contains only 2's and 5's, the resulting decimal will be terminating.

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n / 420 = n / {2^2*3^1*5^1*7^1}
The fraction will only be a terminating decimal if both 3 and 7 can be canceled out.
Thus, the smallest possible value of n is 3*7 = 21.

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