Single correct option
Consider a set of 15 numbers whose average is 40. The first nine of these numbers average 38 and the last seven average 43. Find the value of the ninth number, which lies in both groups.
- A. 41
- B. 43
- C. 45
- D. 39
Show answer and solution
Answer: (B) 43
Sum of all 15 numbers = 15 × 40 = 600.
Sum of first nine = 9 × 38 = 342; sum of last seven = 7 × 43 = 301.
The ninth number is counted in both groups (9 + 7 = 16, one more than 15), so 342 + 301 = 600 + (9th number) ⇒ 9th number = 643 − 600 = 43.
Tip: Whenever two overlapping groups together cover the whole set with one element shared, (sum of groups) − (total) = the shared element.
Sum of first nine = 9 × 38 = 342; sum of last seven = 7 × 43 = 301.
The ninth number is counted in both groups (9 + 7 = 16, one more than 15), so 342 + 301 = 600 + (9th number) ⇒ 9th number = 643 − 600 = 43.
Tip: Whenever two overlapping groups together cover the whole set with one element shared, (sum of groups) − (total) = the shared element.
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