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The average of a, b, and c is 8, and the average of a and b is 10. If

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The average of a, b, and c is 8, and the average of a and b is 10. If [#permalink]

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New post 27 Dec 2017, 23:25
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The average of a, b, and c is 8, and the average of a and b is 10. If the average of a and c is 6, what is the value of a – c ?

A. 8
B. 7
C. 6
D. 5
E. 4
[Reveal] Spoiler: OA

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Kudos [?]: 139606 [0], given: 12794

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Re: The average of a, b, and c is 8, and the average of a and b is 10. If [#permalink]

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New post 28 Dec 2017, 03:13
Bunuel wrote:
The average of a, b, and c is 8, and the average of a and b is 10. If the average of a and c is 6, what is the value of a – c ?

A. 8
B. 7
C. 6
D. 5
E. 4


We'll start by writing by writing all our information as equations and then simplify them.
This is a Precise approach.

(a+b+c)/3 = 8 --> a+b+c=24
(a+b)/2 = 10 --> a+b=20
(a+c)/2 = 6 --> a+c=12

We'll subtract the first two equations to get c = 4
and substitute c=4 into our third equation to get a = 8
then a - c = 4

(E) is our answer.
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The average of a, b, and c is 8, and the average of a and b is 10. If [#permalink]

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New post 28 Dec 2017, 04:36
Bunuel wrote:
The average of a, b, and c is 8, and the average of a and b is 10. If the average of a and c is 6, what is the value of a – c ?

A. 8
B. 7
C. 6
D. 5
E. 4

Substituting twice.

\(\frac{a + b + c}{3} = 8\)
\(a + b + c = 24\)

\(\frac{a + b}{2} = 10\)
\(a + b = 20\)

\(20 + c = 24\)
\(c = 4\)

\(\frac{a + c}{2} = 6\)
\(a + c = 12\)
\(c = 4\)
\(a = 8\)

\((a - c) = (8 - 4) = 4\)

Answer E
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Kudos [?]: 0 [0], given: 4

Re: The average of a, b, and c is 8, and the average of a and b is 10. If [#permalink]

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New post 28 Dec 2017, 04:54
a+b+c/3 =8 ==> a+b+c= 24
add a+b/2 and a+c/2 => 2a+b+c= 32=> a+24=32=>a= 8
8+c/2=6=>c=4
a-c=4

Kudos [?]: 0 [0], given: 4

Re: The average of a, b, and c is 8, and the average of a and b is 10. If   [#permalink] 28 Dec 2017, 04:54
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