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.

Answer: D.
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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.

1. r/3s=1/4 so 3s = 4r , which is s>r - Sufficient
2. s=r+4 menas S>R - sufficient

Answer - D

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

From 2.... s = r+4

substituting this in the question---

\(\frac{r}{4+r}\)<\(\frac{4+r}{r}\)

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

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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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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How do we arrive @ this..
r-s >0 ..I cant seem to figure it out
Thanks

how from here \(\frac{r}{3s}=\frac{1}{4}\) we got this \(\frac{r}{s}=\frac{3}{4}\) ????

By multiplying both sides by 3.
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I have a question here... so I simplified r/s <s/r and got r^2 - s^2 < 0 ( read equation1) and then for statement 2, I put the values s=r+4 on eq 1 and I got r<-2?

Though the stem says r>0...

So where did I do wrong?

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The statement can be rewritten as |r|<|s| i.e r/s<s/r => r^2<s^2 => |r|<|s|.
We need to prove magnitude of r is less than magnitude of s.

Statement 1: r/3s<1/4 => r/s=3/4=> |r|<|s| Sufficient.
Statement 2:s=r+4 Since, both r and s are >0 => |r|<|s|. Sufficient.

Answer D.

VeritasKarishma Bunuel Is the approach correct? Please reply.

Could you tell me how did we get the highlighted part? it seems that we did not get the highlighted part dividing 0 by r, right?

Divide by r and then by s.
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If R > 0 and S > 0 and if I have R^2 < S^2 then can I conclude that R < S OR R > -S

Given, r>0 and s>0

Let’s look at the target question..

Is r/s<s/r ?

Or

Is (r^2 - s^2)/sr < 0 ?

Or

In the above expression, sr cannot be negative, ie will always be positive and for the entire above expression to be negative, the numerator must be negative, so now the target question becomes — is r^2<s^2 ?


Statement 1 —

this one is pretty straightforward — r/3s -1/4=0 —> (4r-3s)/ 12s = 0 —> 4r = 3s—>
r/s=3/4 or s/r=4/3 .. therefore r/s<s/r .. sufficient

Statement 2 —

We need to check whether r^2<s^2

S=r+4 —> r^2 will always be less than s or (r+4)^2 .. therefore sufficient

Answer is D

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