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

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Bunuel
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If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean) [#permalink] New post   17 Aug 2018, 06:01
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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
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B
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If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean) [#permalink] New post   17 Aug 2018, 06:10
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Bunuel 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


Adding the given equations:-
12a+3b+7b-2a=10
Or, 10a+10b=10
Or, 10(a+b)=10
Or, a+b=1
So, average of a and b is 0.5.

Ans. (B)
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Re: If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean) [#permalink] New post   17 Aug 2018, 06:09
Multiplying equation 2 by 6 gives 42b-12a=54.
Now adding this to eqn 1 gives 45b=55. Hence b = \(\frac{11}{9}\).
replacing this in eqn 1 gives a = \(\frac{-2}{9}\).
The average of a+b gives 0.5.
B is the answer.
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If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean) [#permalink] New post   17 Aug 2018, 06:57
Bunuel 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


In order to find the arithmetic mean, we need the value of a+b

P.S In the GMAT, most of the times, this kind of question can be done by a very straightforward
approach. You either have to add or subtract the two statements. Sometimes, you might have
to add twice the second statement to the first statement. Try these combinations before you go
ahead and find individual values for a & b.

Here, the simple addition of both the statements will lead us to the answer.

12a + 3b + 7b – 2a = 9 + 1 -> 10(a + b) = 10 -> a + b = 1

Therefore, the average of a and b is \(\frac{a+b}{2} = \frac{1}{2}\) = 0.5(Option B)
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Re: If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean) [#permalink] New post   18 Aug 2018, 09:55
by adding both equations
10a + 10b = 10
a + b = 1
so arithmetic mean is 0.5
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Re: If 12a + 3b = 1 and 7b – 2a = 9, what is the average (arithmetic mean) [#permalink]
18 Aug 2018, 09:55
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