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The average (arithmetic mean) of two integers a and b is 8. If the av

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The average (arithmetic mean) of two integers a and b is 8. If the av [#permalink]

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New post 05 May 2017, 03:13
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The average (arithmetic mean) of two integers a and b is 8. If the average (arithmetic mean) of integers b and c is 13, what is the positive difference between a and c?

A. 26
B. 21
C. 10
D. 5
E. It cannot be determined from the information given.

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Re: The average (arithmetic mean) of two integers a and b is 8. If the av [#permalink]

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New post 05 May 2017, 07:42
From the question,
a+b=16
Therefore, b=16-a and
b+c=26
Therefore, b=26-c
Equating both RHS as LHS are equal
16-a=26-c
-a+c=10

Hence IMO C

But it can also be that the integers are negative since it is not specified whether they are positive or not!
This may lead to answer choice E

Please tell me if I am doing it correctly
Thanks

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Re: The average (arithmetic mean) of two integers a and b is 8. If the av [#permalink]

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New post 05 May 2017, 09:12
Bunuel wrote:
The average (arithmetic mean) of two integers a and b is 8. If the average (arithmetic mean) of integers b and c is 13, what is the positive difference between a and c?

A. 26
B. 21
C. 10
D. 5
E. It cannot be determined from the information given.


a + b = 16
b + c = 26

Now, ( a + b ) - ( b + c ) = 16 - 26

Or, a - c = - 10

So, The positive difference between a and c is 10, answer must be (C) 10
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Re: The average (arithmetic mean) of two integers a and b is 8. If the av [#permalink]

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New post 05 May 2017, 12:21
Given data
(a+b)/2 = 8
(b+c)/2 = 13

From this a+b=16 & b+c=26
So, 16-a = 26-c(by equating the value of b in both the equation)
c-a = 10 which is the positive difference between a and c(Option C)


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The average (arithmetic mean) of two integers a and b is 8. If the av [#permalink]

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New post 07 May 2017, 11:47
a + b = 16
b + c = 26
add both the equations...
( a + b ) - ( b + c ) = 16 - 26

a - c = - 10

ans C
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Re: The average (arithmetic mean) of two integers a and b is 8. If the av [#permalink]

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New post 12 May 2017, 13:10
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Bunuel wrote:
The average (arithmetic mean) of two integers a and b is 8. If the average (arithmetic mean) of integers b and c is 13, what is the positive difference between a and c?

A. 26
B. 21
C. 10
D. 5
E. It cannot be determined from the information given.


We are given that the average of a and b is 8. Thus:

8 = (a + b)/2

16 = a + b

We are also given that the average of b and c is 13. Thus:

13 = (b + c)/2

26 = b + c

If we subtract 16 = a + b from 26 = b + c, we have:

10 = c - a

Answer: C
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Re: The average (arithmetic mean) of two integers a and b is 8. If the av [#permalink]

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New post 13 May 2017, 19:09
1
Hi All,

It's looks like all of the other posters in this thread used an algebraic approach to this question, which is fine. It can also be solved rather easily by TESTing VALUES.

To start, we're told that the average (arithmetic mean) of two integers A and B is 8. This mean that the SUM of A and B is 16.

Let's TEST....
A = 0
B = 16

Next, we're told that the average (arithmetic mean) of integers B and C is 13. This means that the SUM of B and C is 26. Since we already have a value for B (it's 16), we now have a corresponding value for C...

C = 10

The question asks for the positive difference between A and C. Since A=0 and C=10, the positive difference is 10.

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Re: The average (arithmetic mean) of two integers a and b is 8. If the av   [#permalink] 13 May 2017, 19:09
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