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What is the smallest positive integer n such that n / 420 can be expre

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Math Revolution GMAT Instructor
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New post 21 Mar 2019, 02:33
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  25% (medium)

Question Stats:

73% (01:08) correct 27% (01:32) wrong based on 22 sessions

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[GMAT math practice question]

What is the smallest positive integer \(n\) such that \(\frac{n}{420}\) can be expressed as a terminating decimal?

\(A. 18\)
\(B. 21\)
\(C. 24\)
\(D. 30\)
\(E. 42\)

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Re: What is the smallest positive integer n such that n / 420 can be expre  [#permalink]

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New post 21 Mar 2019, 02:48
MathRevolution wrote:
[GMAT math practice question]

What is the smallest positive integer \(n\) such that \(\frac{n}{420}\) can be expressed as a terminating decimal?

\(A. 18\)
\(B. 21\)
\(C. 24\)
\(D. 30\)
\(E. 42\)


420 = 2^2*3*5*7
so n/420 terminating decimal when divided by 2 & 5
so 3*7 = n = 21
we will then get terminating decimal
IMO B
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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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GPA: 3.82
Re: What is the smallest positive integer n such that n / 420 can be expre  [#permalink]

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New post 24 Mar 2019, 18:22
=>

\(\frac{n}{420} = \frac{n}{{2^2*3^1*5^1*7^1}}\)
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 \(3*7 = 21.\)

Therefore, the answer is B.
Answer: B
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Re: What is the smallest positive integer n such that n / 420 can be expre   [#permalink] 24 Mar 2019, 18:22
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