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Algebra - Ratios

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Source: — Data Sufficiency |

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by Anurag@Gurome » Thu Jan 13, 2011 11:15 pm
anirudhbhalotia wrote:If r> 0 and s>0, is r/s < s/r ?

1. r/3s = 1/4
2. s = r + 4
Statement 1: (r/3s) = 1/4
Implies, (r/s) = 3/4 => (s/r) = 4/3
Hence, (r/s) < (s/r)

Sufficient

Statement 2: s = (r + 4)
Dividing both side by r, (s/r) = 1 + (4/r) > 1
And dividing both side by s, 1 = (r/s) + (4/s) => (r/s) = 1 - (4/s) < 1

Hence (r/s) < (s/r)

Sufficient

The correct answer is D.
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by MAAJ » Fri Jan 14, 2011 5:11 am
For the second statement you can also do this:

(r/s) < (s/r) ?

Because they are both positive, you can cross-multiply

r²< s² ?

Statement 2 tell us that s= r+4 so:

r² < (r+4)² ?

Because "r" is a positive number, r² will always by less than (r+4)², making this statement sufficient.
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by anirudhbhalotia » Sun Jan 16, 2011 2:10 am
MAAJ wrote:For the second statement you can also do this:

(r/s) < (s/r) ?

Because they are both positive, you can cross-multiply

r²< s² ?

Statement 2 tell us that s= r+4 so:

r² < (r+4)² ?

Because "r" is a positive number, r² will always by less than (r+4)², making this statement sufficient.
Cool!

Was a bit confused as to how did Anurag suffice the 2nd statement!
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by ankur.agrawal » Sun Jan 16, 2011 3:00 am
MAAJ wrote:For the second statement you can also do this:

(r/s) < (s/r) ?

Because they are both positive, you can cross-multiply

r²< s² ?

Statement 2 tell us that s= r+4 so:

r² < (r+4)² ?

Because "r" is a positive number, r² will always by less than (r+4)², making this statement sufficient.

For the statement 2 we can do this:

s=r+4: putting this value:

r/r+4<r+4/r. From this it is clear that LHS will be <1 & RHS will be >1.
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by vikrambansal » Mon May 18, 2015 5:28 pm
Can we simplify r/s < s/r

= r^2 < s^2 (cross multiply. No change in inequality as both r & s are +ve)

= r < s (taking square root)
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by Brent@GMATPrepNow » Mon May 18, 2015 5:41 pm
vikrambansal wrote:Can we simplify r/s < s/r

= r^2 < s^2 (cross multiply. No change in inequality as both r & s are +ve)

= r < s (taking square root)
Perfect!
The KEY is that r and s are both POSITIVE

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