The average of 9 numbers is 63. When one number is removed, the average becomes 60. What number was removed?

Correct — A. Turn both averages into totals.

Total of the 9 numbers: 9 × 63 = 567
Total of the 8 left: 8 × 60 = 480
Number removed: 567 − 480 = 87 → option (a)

Why the others are wrong

• (b)
  90 — 90 = 63 + 9 × 3 spreads the fall of 3 over all nine numbers, but only eight remain. Check: 567 − 90 = 477, an average of 59.625.
• (c)
  84 — 84 leaves 567 − 84 = 483 for the eight numbers, an average of 60.375, not 60.
• (d)
  78 — 78 is too small to pull the average down to 60. The remaining eight would total 489, an average of 61.125.

Total = average × count turns an average problem into subtraction. The removed number is the old total minus the new total.

Shortcut: the average fell by 3 across the 8 numbers that remain, so the removed number sits 8 × 3 = 24 above the old average: 63 + 24 = 87.

Key facts

• Sum = average × count.
• Removed value = old sum − new sum.
• If removing one value lowers the average by d, that value = old average + (remaining count × d).

Common traps

• Multiplying the fall by 9, the original count, instead of 8. That gives 90.
• Expecting the removed number to be below 63. The average fell, so the removed number was above it.

No directly related past PYQ was found.