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(1) \(\frac{r}{3s}=\frac{1}{4}\) --> \(\frac{r}{s}=\frac{3}{4}\), so \(\frac{s}{r}=\frac{4}{3}\) --> \(\frac{r}{s}=\frac{3}{4}<\frac{4}{3}=\frac{s}{r}\) thus answer to the question is YES. Sufficient.

(2) \(s=r+4\) --> so \(s>r\) as given that \(r>0\) --> \(s>r>0\) --> \(\frac{s}{r}>1>\frac{r}{s}\), thus answer to the question is YES. Sufficient.

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 > 0 and s > 0, is r/s < s/r?

(1) r/(3s) = 1/4 (2) s = r + 4

In inequalities, the sign does not change when a positive integer is multiplied on both sides. If we modify the question, r/x<s/r, or is r^2<s^2, of is r^2-s^2<0?, or (r-s)(r+s)<0? and r>0 and s>0, so we want to know whether r-s>0? For condition 1, in r/s=3/4, r and s are positive, so s>r, which answers the question 'yes' and is sufficient. For condition 2, s-r=4>0. s>r, so this also answers the question 'yes' and is sufficient. The answer becomes (D).

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 > 0 and s > 0, is r/s < s/r? [#permalink]

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01 Sep 2013, 14:09

First I restated the problem since we are given r and s are greater than 0 --> therefore, the question can be solved by answering whether or not r^2<s^2.

(1) r = (3/4)s [r<s, so r^2 < s^2] Sufficient AD/BCE - elminate BCE (3) s = r + 4 [r<s, so r^2 < s^2] Sufficent - elminate A ... answered D

Re: If r > 0 and s > 0, is r/s < s/r? [#permalink]

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01 Oct 2014, 05:30

Hello from the GMAT Club BumpBot!

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Re: If r > 0 and s > 0, is r/s < s/r? [#permalink]

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14 Nov 2015, 04:55

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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If r > 0 and s > 0, \(is \frac{r}{s} < \frac{s}{r}?\) The question stem tells us that both r and s are positive. What a relief, we can now do any operations on r and s without worrying about the polarity of the variable. Lets rephrase the statement Is \(\frac{r}{s} < \frac{s}{r}\)

THIS IS THE REAL QUESTION :- Is \(r^2 < s^2 ?\)

(1)\(\frac{r}{(3s)} = \frac{1}{4}\)

\(r=\frac{3}{4}*s\) Because r<s Therefore \(r^2 < s^2\) SUFFICIENT

(2) s = r + 4 Its obvious that s is bigger and r is smaller \(r<s\) and \(r^2<s^2\) SUFFICIENT

ANSWER IS D
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If r > 0 and s > 0, is r/s < s/r?
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18 Jul 2016, 05:51

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