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The average of 5 consecutive integer is 12, What will be the average of the only even number among those five?

12 8 10 9

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2 solutions

Let x x be the first integer. Then the integers in order are x , x + 1 , x + 2 , x + 3 x,x+1,x+2,x+3 and x + 4 x+4 . Then we have

x + x + 1 + x + 2 + x + 3 + x + 4 5 = 12 \dfrac{x+x+1+x+2+x+3+x+4}{5}=12

5 x + 10 = 60 5x+10=60

5 x = 50 5x=50

x = 10 x=10

The integers are 10 , 11 , 12 , 13 10,11,12,13 and 14 14 .

The average of the even integers is 10 + 12 + 14 3 = 36 3 = 12 \dfrac{10+12+14}{3}=\dfrac{36}{3}=\boxed{12} .

Abishek Nathan
Feb 2, 2015

Since the average of five CONSECUTIVE INTEGERS is 12, those 5 numbers should be around "12". So the numbers are 10, 11, 12, 13, 14 whose average is 12 and average of even numbers is 12.

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