The average (arithmetic mean) of five numbers is 20. When one of the numbers is removed, the average of the remaining four numbers is 18. What is the value of the number that was removed?
- A22
- B24
- C26
- D28
- E30
Averages: work with sums, not averages
Try it before you scroll. Two minutes on the clock, then commit to an answer.
Correct answer: D
Averages are awkward to subtract, but sums subtract cleanly. Convert both averages to sums:
- Sum of all five numbers: 5 × 20 = 100.
- Sum of the remaining four: 4 × 18 = 72.
The removed number is the difference: 100 − 72 = 28.
Sanity check: removing a number above the original average pulls the average down. The average fell from 20 to 18, so the removed number must be above 20. All five choices are, which means this check alone cannot finish the problem, but it does tell you the direction is right. The removed value 28 is 8 above the old average, and the other four numbers each give up 2 points of average to cover that 8: 4 × 2 = 8. Consistent.
Trap (A), 22, comes from averaging 20 and 18 and rounding. Trap (E), 30, comes from dividing 100 − 72 by the wrong count or from 5 × 20 − 4 × 18 computed as 100 − 70.