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Average of a,b

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by debmalya_dutta » Wed Jun 09, 2010 3:33 pm
If 2a - b = 3c, where a, b, and c are integers, which of the following could be the average (arithmetic mean) of a and b?

a. -2
b. 0
c. 1
d. 10
e. 12
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by gmatjedi » Wed Jun 09, 2010 4:12 pm
a+b / 2 = m

a+b=2m

a= 3c+b / 2

substitute a into above equation

3c+b / 2 + 2b/2= 2m

= 3c+3b / 2 = 2m
= c+b=4m/3

therefore m has to be divisible by 3
only number among answer choices that contains factor of 3 is 12
answer e
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by hardik.jadeja » Thu Jun 10, 2010 6:07 am
0 is also one of the possible answer.

2a - b = 3c
b = 2a - 3c
a + b = 3a - 3c ......... (adding a to both sides)
(a + b)/2 = (3/2) (a - c) ........... (diving both sides by 2)

Now if a = c then a = -b and in that case arithmetic mean is 0

Correct me if i am missing something. What is the source of this problem?
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