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GRE Math Challenge #11- If a + 2b= 14 and 5a + 4b =16 [#permalink]
Expert's post 00:00

Question Stats: 100% (01:04) correct 0% (00:00) wrong based on 9 sessions
If a + 2b= 14 and 5a + 4b =16, what is the average (arithmetic mean) of a and b?

5/2

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Sandy
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Re: GRE Math Challenge #11- If a + 2b= 14 and 5a + 4b =16 [#permalink]
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Expert's post
sandy wrote:
If a + 2b = 14 and 5a + 4b =16, what is the average (arithmetic mean) of a and b?

5/2

The average (arithmetic mean) of a and b = (a + b)/2

The slow approach to answer this question is to solve the system of equations to find the individual values of a and b.

The fast approach is to recognize that we need only find the SUM of a and b

Here's what I mean...

Given:
a + 2b = 14
5a + 4b =16

ADD the two equations to get:
6a + 6b = 30

Factor to get:
6(a + b) = 30

Divide both sides by 6 to get:
a + b = 5

Divide both sides by 2 to get:
(a + b)/2 = 5/2

Perfect!
The average (arithmetic mean) of a and b = (a + b)/2, and we can see that (a + b)/2 = 5/2

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Brent Hanneson – Creator of greenlighttestprep.com  Re: GRE Math Challenge #11- If a + 2b= 14 and 5a + 4b =16   [#permalink] 01 Sep 2017, 13:44
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