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

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

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

by VJesus12 » Fri Dec 11, 2020 1:44 am

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If $r$ and $s$ are positive, the value of $\dfrac{2r+3s}{r+s}$ 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

Answer: C

Source: Economist

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Source: Beat The GMAT — Problem Solving | Fri Dec 11, 2020 1:44 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

Re: If $r$ and $s$ are positive, the value of $\dfrac{2r+3s}{r+s}$ is

by deloitte247 » Sun Dec 13, 2020 6:27 am

$$\frac{2r+35}{r+5}=\frac{2r}{r+s}+\frac{3s}{r+s}$$
$$=>\frac{2r+2s}{r+s}+5$$
$$=>\frac{2r+2s}{r+s}+\frac{5}{r+s}$$
$$=>\frac{2\left(r+s\right)}{r+s}+\frac{5}{r+s}$$
$$2+\frac{5}{r+s}$$
$$Since\ r\ and\ s\ are\ positive,$$
$$definitely;\ \left(r+s\right)>5$$
$$so\ \frac{5}{\left(r+s\right)}=>a\ fraction\ less\ than\ 1$$
$$0.1\le\left(\frac{s}{r+s}\right)\le0.9$$
$$value\ of\ 2+\frac{s}{r+s}=>\ 2.1\le\frac{2r+3s}{r+s}\le2.9$$
$$Answer\ =\ between\ 2\ and\ 3$$
$$Answer\ =\ C$$