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If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithm

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If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithm [#permalink] New post 16 Aug 2018, 09:36
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If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean) of a and b ?

A) 0.1
B)0.5
C)1
D)2.5
E)5
[Reveal] Spoiler: OA
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Re: If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithm [#permalink] New post 17 Aug 2018, 06:54
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amorphous wrote:
If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean) of a and b ?

A) 0.1
B)0.5
C)1
D)2.5
E)5


We COULD solve this system of equations for a and b, but this could take some time.
Also recognize that, to find the average of a and b, we need only find the SUM, a + b

GIVEN:
12a + 3b = 1
–2a + 7b = 9


ADD the two equations to get: 10a + 10b = 10
Divide both sides by 10 to get: a + b = 1

What is the average (arithmetic mean) of a and b?
Average = (a + b)/2 = 1/2 = 0.5

Answer: B

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithm [#permalink] New post 17 Aug 2018, 16:05
Taking the sum works the fastest here, as against substituting values.
Re: If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithm   [#permalink] 17 Aug 2018, 16:05
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If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithm

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