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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?

by Max@Math Revolution » Thu Mar 15, 2018 11:41 pm
[GMAT math practice question]

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

1) 1/r^2 is a terminating decimal
2) 1/s^2 is a terminating decimal
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Source: — Data Sufficiency |
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by GMATinsight » Fri Mar 16, 2018 3:27 am
Max@Math Revolution wrote:[GMAT math practice question]

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

1) 1/r^2 is a terminating decimal
2) 1/s^2 is a terminating decimal
CONCEPT: Any fraction r/s will be a NON-terminating decimal if in least form the denominator of fraction has any prime factor other than 2 and 5

Question : Is r/s terminating?

Statement 1:1/r^2 is a terminating decimal
BUT no information about s is given which is the denominator of the given fraction hence
NOT SUFFICIENT

Statement 2: 1/s^2 is a terminating decimal
Denominator is made up of only prime factors 2 and 5 hence
SUFFICIENT

Answer: option B
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by Max@Math Revolution » Sun Mar 18, 2018 10:07 pm
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

We can modify the question as follows:
r/s is a terminating decimal if and only if s has no other prime factors than 2 and 5.
This is the same as condition 2). Condition 1) tells us nothing about the prime factors of s.

Therefore, B is the answer.


Answer: B
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