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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
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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21 Mar 2019, 02:33
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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMAT Club Legend 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] ### Show Tags 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 Math Revolution GMAT Instructor 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] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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