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In a set of three numbers, the average of first two numbers

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In a set of three numbers, the average of first two numbers [#permalink] New post 11 Apr 2019, 16:15
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In a set of three numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?

(A) 2

(B) 2.5

(C) 3

(D) 3.5

(E) 4
[Reveal] Spoiler: OA

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Re: In a set of three numbers, the average of first two numbers [#permalink] New post 13 Apr 2019, 03:40
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When given averages, it's often useful to think in terms of sums. So if the average of the first two numbers is 2, then their sum is 4.

Let's call our numbers a, b, and c. Thus:

a + b = 4
b + c = 6
a + c = 8

We now have three variables and three equations, which we can solve in many ways. Feel free to follow your own method. I'm going to subtract these two equations:

c + b = 6
a + b = 4

c - a = 2

Now I'll subtract that from the last equation:

c + a = 8
c - a = 2

2a = 6

a = 3

Nice. If a = 3, then (using the original equations) b = 1, and c = 5. Their average is \(\frac{3+1+5}{3} = 3\).
Re: In a set of three numbers, the average of first two numbers   [#permalink] 13 Apr 2019, 03:40
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In a set of three numbers, the average of first two numbers

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