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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82
What is the smallest positive integer n such that n / 420 can be expre  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 73% (01:09) correct 27% (01:21) wrong based on 41 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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GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: What is the smallest positive integer n such that n / 420 can be expre  [#permalink]

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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
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the smallest positive integer n such that n / 420 can be expre  [#permalink]

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=>

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

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