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

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

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New post 18 Sep 2018, 08:34
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A
B
C
D
E

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Question Stats:

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

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New post 18 Sep 2018, 08:37
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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New post 18 Sep 2018, 09:02
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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

Answer: C

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

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New post 18 Sep 2018, 22:16
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, \(2<\frac{2r+3s}{r+s}<3\)



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

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New post 18 Sep 2018, 23:22
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, 23:22
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