If r > 0 and s > 0, is r/s < s/r? : GMAT Data Sufficiency (DS)
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# If r > 0 and s > 0, is r/s < s/r?

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

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17 Aug 2010, 08:02
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If r > 0 and s > 0, is r/s < s/r?

(1) r/(3s) = 1/4
(2) s = r + 4
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01 Nov 2010, 07:44
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cmugeria wrote:
If R > 0 and S > 0, Is r/s < s/r?

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

Since r and s are both positive, we can simplify the inequality to $$r^2 < s^2$$, and by taking the square root of both sides, $$r < s$$.

(1) $$4r = 3s$$
$$r = \frac{3}{4}s$$
So r < s. Sufficient.

(2) Since $$r = s - 4$$, $$r < s$$. Sufficient.
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17 Aug 2010, 08:21
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If r > 0 and S > 0, Is r/s < s/r?

Is $$\frac{r}{s}<\frac{s}{r}$$?

(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.

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

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17 Nov 2015, 09:29
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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.

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? 1) r/3s =1/4 2) s [#permalink]

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29 Nov 2011, 00:22
1. r/3s=1/4 so 3s = 4r , which is s>r - Sufficient
2. s=r+4 menas S>R - sufficient

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

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29 Jan 2013, 08:04
cmugeria wrote:
If r > 0 and s > 0, is r/s < s/r?

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

For 1 --- $$\frac{r}{s}$$= 3/4we can deduce from this

From 2.... s = r+4

substituting this in the question---

$$\frac{r}{4+r}$$<$$\frac{4+r}{r}$$
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Re: If r > 0 and s > 0, is r/s < s/r? [#permalink]

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01 Sep 2013, 13:09
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
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01 Oct 2014, 04:30
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Re: If r > 0 and s > 0, is r/s < s/r? [#permalink]

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14 Nov 2015, 03:55
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If r > 0 and s > 0, is r/s < s/r? [#permalink]

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18 Jul 2016, 04:51
cmugeria wrote:
If r > 0 and s > 0, is r/s < s/r?

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

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

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If r > 0 and s > 0, is r/s < s/r?   [#permalink] 18 Jul 2016, 04:51
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