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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?  [#permalink]

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New post 15 Mar 2018, 23:52
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A
B
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E

Difficulty:

  35% (medium)

Question Stats:

68% (00:58) correct 32% (00:59) wrong based on 41 sessions

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[GMAT math practice question]

If \(r, s\) are positive integers, is \(\frac{r}{s}\) a terminating decimal?

1) \(\frac{1}{r^2}\) is a terminating decimal
2) \(\frac{1}{s^2}\) is a terminating decimal

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

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New post 16 Mar 2018, 00:49
Is it B?

Working:

For 1/(x^2) to be a terminating decimal, x has to be either power or a multiple of (1,2,5).

Stmt 1. Insufficient as terminating decimal depends on denominator.

Stmt 2. Sufficient, as s is a multiple or power of (1,2,5) and whatever is value of r, r/s will be terminating decimal.

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

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New post 18 Mar 2018, 22:17
=>

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:
\(\frac{r}{s}\) 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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Re: If r, s are positive integers, is r/s a terminating decimal? &nbs [#permalink] 18 Mar 2018, 22:17
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