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

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Math Revolution GMAT Instructor
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If r, s are positive integers, is r/s a terminating decimal? [#permalink]

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04 Feb 2016, 17:25
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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.
[Reveal] Spoiler: OA

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Joined: 02 Aug 2009
Posts: 5660
Re: If r, s are positive integers, is r/s a terminating decimal? [#permalink]

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04 Feb 2016, 18:15
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

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
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Re: If r, s are positive integers, is r/s a terminating decimal? [#permalink]

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05 Feb 2016, 06:03
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

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

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05 Feb 2016, 09:31
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

Last edited by soloveva on 08 Feb 2016, 13:12, edited 2 times in total.
Math Revolution GMAT Instructor
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Posts: 4905
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Re: If r, s are positive integers, is r/s a terminating decimal? [#permalink]

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07 Feb 2016, 23:11
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.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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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, 14:07
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Re: If r, s are positive integers, is r/s a terminating decimal?   [#permalink] 18 Aug 2017, 14:07
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