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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 28 Dec 2017, 00:25
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A
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E

Difficulty:

  15% (low)

Question Stats:

86% (00:50) correct 14% (00:17) wrong based on 35 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
[Reveal] Spoiler: OA

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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, 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

(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, 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.

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

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

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

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

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

Answer E
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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, 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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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 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.
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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 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.

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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 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, \(a - c = 8 - 4\)

Answer will be (E) 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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New post 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.

Answer: E
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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] 05 Feb 2018, 10:18
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