If r and s are positive, the value of (2r + 3s)/(r + s) is ?

Question

If r and s are positive, the value of  \frac{2r+3s}{r+s}  is ?

A. 0.15 
B. Between 0.5 and 1.5 
C. Between 2 and 3 
D. Between 3 and 3.5 
E. Between 3.5 and 5

BrentGMATPrepNow · Accepted Answer

There's a nice (and often-tested) fraction property that says:    (x + y)/z = x/z + y/z

Let's see this property in action!

Take: (2r + 3s)/(r + s)
Rewrite numerator as follows: ( 2r + 2s  + s)/(r+s)
Apply above   property   to get: ( 2r + 2s )/(r + s) + s/(r + s)
Factor the numerator of first fraction to get: ( 2(r + s) )/(r + s) + s/(r + s)
Simplify first fraction to get: 2 +  s/(r + s) 
Since r and s are positive, we know that s < r + s
So,  s/(r + s)  must be a fraction that's  less than 1 
We get: 2 +  some fraction less than 1 
In other words, we get: 2.something

Answer: C

RELATED VIDEO FROMM OUR COURSE
 https://www.youtube.com/watch?v=hnpJiUoFY_Q

rahul16singh28 · Answer

The fraction can be written as -

2 + \frac{s}{r+s} .

Hence, C.

GMATBusters · Answer

As r and s are positive,

2r+2s < 2r+3s < 3r+3s

or,  \frac{2r+2s}{r+s} < \frac{2r+3s}{r+s} < \frac{3r+3s}{r+s}

or,  2<\frac{2r+3s}{r+s}<3

Hence answer is C

AkshdeepS · Answer

Take r = 2 and s = 3

\frac{2*2 + 3*3}{(2 + 3)}  =  \frac{13}{5}  =  2.6

Take r = 4 and s = 4

\frac{2*4 + 3*4}{(4 + 4)}  =  \frac{20}{8} =  2.5

Take r = 1.5 and s = 1.5

\frac{2*1.5 + 3*1.5}{(1.5 + 1.5)} = \frac{7.5}{3} = 2.5

Hence C

KSBGC · Answer

This question is designed to test weighted average method.

Between weight 2 and 3 , 3 is greater integer.

Approximate result will be closer to 3 and greater than 2.

C is the correct answer.

eaat · Answer

For this question, why can't we just assume r = 1, and s = 1? Then it's 5/2 =2.5 which is C...

Krunaal · Answer

You can, your approach is valid too.

If r and s are positive, the value of (2r + 3s)/(r + s) is ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If r and s are positive, the value of (2r + 3s)/(r + s) is ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards