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

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Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1195
Location: India
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WE: Business Development (Energy and Utilities)
If r and s are positive, the value of (2r + 3s)/(r + s) is ?  [#permalink]

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18 Sep 2018, 07:34
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Question Stats:

100% (01:00) correct 0% (00:00) wrong based on 40 sessions

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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

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Location: Malaysia
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Re: If r and s are positive, the value of (2r + 3s)/(r + s) is ?  [#permalink]

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18 Sep 2018, 07:37
gmatbusters wrote:
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

The fraction can be written as -

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

Hence, C.
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Re: If r and s are positive, the value of [m][fraction]2r+3s/r+s[/fraction  [#permalink]

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18 Sep 2018, 08:02
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Top Contributor
gmatbusters wrote:
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

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

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Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1195
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If r and s are positive, the value of (2r + 3s)/(r + s) is ?  [#permalink]

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18 Sep 2018, 21:16
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, $$2<\frac{2r+3s}{r+s}<3$$

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Re: If r and s are positive, the value of (2r + 3s)/(r + s) is ?  [#permalink]

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18 Sep 2018, 22:22
gmatbusters wrote:
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

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
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Re: If r and s are positive, the value of (2r + 3s)/(r + s) is ? &nbs [#permalink] 18 Sep 2018, 22:22
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