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# If r, s are positive integers, is r/s a terminating decimal?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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If r, s are positive integers, is r/s a terminating decimal?  [#permalink]

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04 Feb 2016, 18:25
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15% (low)

Question Stats:

76% (00:47) correct 24% (01:10) wrong based on 145 sessions

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If r, s are positive integers, is r/s a terminating decimal?

1) 1/r is a terminating decimal
2) 1/s is a terminating decimal

* A solution will be posted in two days.

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7588 Re: If r, s are positive integers, is r/s a terminating decimal? [#permalink] ### Show Tags 04 Feb 2016, 19:15 MathRevolution wrote: If r, s are positive integers, is r/s a terminating decimal? 1) 1/r is a terminating decimal 2) 1/s is a terminating decimal * A solution will be posted in two days. Hi all, whether r/s is a terminating decimal will depend on value of s, if r/s is in its simplified form.. 1) 1/r is a terminating decimal nothing about s.. insuff 2) 1/s is a terminating decimal if 1/s is a terminating decimal.. when it is multiplied with r, it can be an integer or a terminating decimal.. so suff ans B _________________ CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2908 Location: India GMAT: INSIGHT Schools: Darden '21 WE: Education (Education) Re: If r, s are positive integers, is r/s a terminating decimal? [#permalink] ### Show Tags 05 Feb 2016, 07:03 MathRevolution wrote: If r, s are positive integers, is r/s a terminating decimal? 1) 1/r is a terminating decimal 2) 1/s is a terminating decimal * A solution will be posted in two days. Question : is r/s a terminating decimal? r/s will be a terminating decimal if in least form the fraction r/s has denominator made up of no prime factors other than 2 and/or 5 Statement 1: 1/r is a terminating decimal i.e. r contains no prime factor other than 2 and 5. But since we are seeking information primarily about denominator of fraction r/s therefore NOT SUFFICIENT Statement 2: 1/s is a terminating decimal i.e. s contains no prime factor other than 2 and 5 which is exactly what we were looking for therefore SUFFICIENT Answer: Option B _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Intern Joined: 07 Oct 2014 Posts: 9 If r, s are positive integers, is r/s a terminating decimal? [#permalink] ### Show Tags Updated on: 08 Feb 2016, 14:12 MathRevolution wrote: If r, s are positive integers, is r/s a terminating decimal? 1) 1/r is a terminating decimal 2) 1/s is a terminating decimal * A solution will be posted in two days. Decimal is terminating when it can be expressed as $$\frac{K}{2^n5^m}$$, where n, m are non-negative integers and k is an integer (e. g. 0.1 can be expressed as $$\frac{1}{2^15^1}$$; 0.015 can be expressed as $$\frac{15}{2^35^3}$$ or $$\frac{3}{2^35^2}$$ etc) 1) $$\frac{1}{r}$$ is a terminating decimal, thus, can be expressed as $$\frac{1}{2^n5^m}$$, $$r=2^n5^m$$. If s=5, then $$\frac{r}{s}=\frac{2^n5^m}{5}$$, terminating. If s=3, then $$\frac{r}{s}=\frac{2^n5^m}{3}$$, not terminating. Insufficient. 2) $$s=2^n5^m$$ $$\frac{r}{s}=\frac{r}{2^n5^m}$$. Since r, s are positive integers, then the expression is a terminating decimal for any r,s. Sufficient. B Originally posted by soloveva on 05 Feb 2016, 10:31. Last edited by soloveva on 08 Feb 2016, 14:12, edited 2 times in total. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7245 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If r, s are positive integers, is r/s a terminating decimal? [#permalink] ### Show Tags 08 Feb 2016, 00:11 Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. If r, s are positive integers, is r/s a terminating decimal? 1) 1/r is a terminating decimal 2) 1/s is a terminating decimal When you modify the original condition and the question, a terminating decimal is a fraction that only 2 and 5 are the prime factors of a denominator. So, you only need to figure out s from r/s. Therefore, the answer is B.  Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions. _________________ 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$149 for 3 month Online Course"
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Re: If r, s are positive integers, is r/s a terminating decimal?  [#permalink]

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18 Aug 2017, 15:07
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Re: If r, s are positive integers, is r/s a terminating decimal?   [#permalink] 18 Aug 2017, 15:07
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