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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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Math Expert
Joined: 02 Sep 2009
Posts: 43334

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

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

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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

examPAL Representative
Joined: 07 Dec 2017
Posts: 117

Kudos [?]: 21 [0], given: 3

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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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

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Kudos [?]: 21 [0], given: 3

VP
Joined: 22 May 2016
Posts: 1255

Kudos [?]: 465 [0], given: 683

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

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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.

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

$$\frac{a + b}{2} = 10$$
$$a + b = 20$$

$$20 + c = 24$$
$$c = 4$$

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

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

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Kudos [?]: 465 [0], given: 683

Intern
Joined: 21 Jul 2017
Posts: 1

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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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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