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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: 50007
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, 00:25
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95% (01:24) correct 5% (01:21) wrong based on 37 sessions

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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

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Joined: 07 Dec 2017
Posts: 721
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, 04:13
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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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, 05:36
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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Joined: 21 Jul 2017
Posts: 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, 05:54
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
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Joined: 12 Jan 2018
Posts: 21
Location: India
Concentration: General Management, Marketing
WE: Engineering (Energy and Utilities)
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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02 Feb 2018, 05:26
The correct option is E (Just tests your knowledge of averages) . This is a fairly easy question. What could the level of this question be? It looks like something lesser than a 500.
Senior Manager
Joined: 17 Oct 2016
Posts: 322
Location: India
Concentration: Operations, Strategy
GPA: 3.73
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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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02 Feb 2018, 05:30
ManasviHP wrote:
The correct option is E (Just tests your knowledge of averages) . This is a fairly easy question. What could the level of this question be? It looks like something lesser than a 500.

May be you will get this question if you flunk tougher questions continuously.

Posted from my mobile device
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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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02 Feb 2018, 07:23
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

$$a + b + c = 24$$--------------------> (I)
$$a + b = 20$$------------------------->(II)
$$a + c = 12$$------------------------->(III)

From (I) and (II) we get $$c = 4$$
From (II) and (III) we get $$b = 12$$

Hence $$a = 8$$

Thus, $$a - c = 8 - 4$$

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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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05 Feb 2018, 10:18
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 can create the equations:

(a + b + c)/3 = 8

a + b + c = 24

and

(a + b)/2 = 10

a + b = 20

and

(a +c)/2 = 6

a + c = 12

Substituting, we obtain:

20 + c = 24

c = 4

Thus, a + 4 = 12, so a = 8.

Finally, we have a - c = 8 - 4 = 4.

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Re: The average of a, b, and c is 8, and the average of a and b is 10. If &nbs [#permalink] 05 Feb 2018, 10:18
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