The average of 5 numbers is 15. Find a number which should be included in these numbers to make the average 16.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 21
The total of a set of numbers = average × how many numbers there are. The new number is whatever raises the total from the old one to the new one.
Total of the 5 numbers: \(5\times15=75\)
Total needed for 6 numbers with average 16: \(6\times16=96\)
Number to be included: \(96-75=21\)
Shortcut:
The new number must equal the new average and also give each of the 5 old numbers the rise of 1: \(16+5\times1=21\)