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

Question

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

* A solution will be posted in two days.

chetan2u · Answer

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

GMATinsight · Answer

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

soloveva · Answer

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

MathRevolution · Answer

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.

BrentGMATPrepNow · Answer

Target question :    Is r/s a terminating decimal?  
There's a nice rule that says something like, 
  If the prime factorization of the denominator contains only 2's and/or 5's, then the decimal version of the fraction will be a terminating decimal.  
So, r/s will be a terminating decimal if the prime factorization of s (the denominator) contains only 2's and/or 5's.

Statement 1 : 1/r is a terminating decimal  
If 1/r is a terminating decimal, then we know that the prime factorization of r contains only 2's and/or 5's. 
This, however, tells us nothing about about the value of the denominator in the fraction r/s
Consider these two pairs of conflicting values of r and s: 
Case a: r = 2 and s = 4, in which case  r/s = 2/4 = 0.5, which  is  a terminating decimal 
Case b: r = 2 and s = 3, in which case  r/s = 2/3 = 0.666.., which is  not  a terminating decimal 
Since we can't answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : 1/s is a terminating decimal  
If 1/s is a terminating decimal, then we know that the prime factorization of s contains only 2's and/or 5's. 
Since the prime factorization of s (the denominator) contains only 2's and/or 5's, we know that  the decimal version of the fraction  will be  a terminating decimal 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

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

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

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