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# If a + b = 5c, then which of the following represents the average (ari

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Joined: 02 Sep 2009
Posts: 43804
If a + b = 5c, then which of the following represents the average (ari [#permalink]

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10 May 2017, 01:32
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95% (00:34) correct 5% (03:03) wrong based on 37 sessions

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If a + b = 5c, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of c?

A. 3c + 1
B. 2c
C. 5c
D. c/3
E. 3c/2
[Reveal] Spoiler: OA

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Re: If a + b = 5c, then which of the following represents the average (ari [#permalink]

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10 May 2017, 01:42
If a + b = 5c, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of c?

a+b = 5c
Average of a,b,c = $$\frac{a+b+c}{3}$$
= $$\frac{5c+c}{3}$$ (given a+b = 5c)
= $$\frac{6c}{3}$$ = 2c ... Answer B

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Re: If a + b = 5c, then which of the following represents the average (ari [#permalink]

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10 May 2017, 05:03
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Bunuel wrote:
If a + b = 5c, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of c?

A. 3c + 1
B. 2c
C. 5c
D. c/3
E. 3c/2

We can solve questions like this (VIACs - Variables in the Answer Choices) by using algebra (as sashiim20 has done), or by using the INPUT-OUTPUT approach.

Let's use the INPUT-OUTPUT approach
First find numbers that meet the given condition: a + b = 5c
One option is a = 0, b = 5 and c = 1

Given these values, the average of a, b and c = (0 + 5 + 1)/3 = 2

So, when we INPUT a = 0, b = 5 and c = 1, the OUTPUT (the average of a, b and c) is 2

In this question, we care only about the value of c.
So, let's take the answer choices and plug in c = 1, and see which one yields an OUTPUT of 2

A. 3(1)+ 1 = 4 Not a match. ELIMINATE
B. 2(1) = 2 a match. KEEP
C. 5(1) = 5 Not a match. ELIMINATE
D. c = 1/3 = 1/3 Not a match. ELIMINATE
E. 3(1)/2 = 3/2 Not a match. ELIMINATE

[Reveal] Spoiler:
B

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Re: If a + b = 5c, then which of the following represents the average (ari [#permalink]

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10 May 2017, 07:52
Given a + b = 5c
a+b+c = 5c+c=6c
average
(a+b+c)/3=6c/3
=2c
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Re: If a + b = 5c, then which of the following represents the average (ari [#permalink]

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12 May 2017, 12:36
Bunuel wrote:
If a + b = 5c, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of c?

A. 3c + 1
B. 2c
C. 5c
D. c/3
E. 3c/2

We are given that a + b = 5c and need to determine: (a + b + c)/3. So we have:

(5c + c)/3 = 6c/3 = 2c

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Re: If a + b = 5c, then which of the following represents the average (ari   [#permalink] 12 May 2017, 12:36
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