The average number of 8 numbers is 80. If 3 equal numbers are added to the 8 original numbers, the new average is 83. Of the 11 numbers , 3 of them must be ...

Question

Answer choices:

a) 89

b)90

c)92

d)91

e)93

 

Which 3? Help!

Answer 1

The average is defined as the sum of the numbers divided by the quantity of numbers.

 

Average = sum / quantity

 

sum = Average * quantity

sum = 80 * 8

sum = 640

 

This means that the sum of the 8 numbers is 640.  Now if we add 3 equal numbers to the original numbers, the average is 83.

 

83 = (sum + x + x + x) / (8 + 3)

 

where x is the equal numbers.

 

 

83 = (640 + 3x) / 11

 

 

Solve for x from this equation.

 

913 = 640 + 3x

 

273 = 3x

 

91 = x

 

 

Answer is (d).

Answer 2

Remember that the numerical average is (sum of the numbers)/(count of numbers).

 

Given the (average) and the (count of the numbers), we can compute the (sum of the numbers).

 

If the average of 8 numbers is 80, then the sum of those numbers must be 640.

For the sum of 11 numbers to have an average of 83, then the sum of those numbers must be 913.

 

For 3 equal numbers to add (913-640)=273 to the total, they must each be 273/3=91.  Only the three just added must be 91, even though others in the original set of 8 numbers may be 91.