Single correct option
The average of 15 numbers is 34. The average of the first eight numbers is 32 and the average of the last eight numbers is 36. What is the eighth number?
- A. 34
- B. 36
- C. 32
- D. 38
Show answer and solution
Answer: (A) 34
The eighth number belongs to both the 'first eight' and the 'last eight', so it is counted twice when the two group sums are added.
Sum of first eight = 8 × 32 = 256. Sum of last eight = 8 × 36 = 288. Sum of all 15 = 15 × 34 = 510.
Eighth number = 256 + 288 − 510 = 34.
Tip: Overlapping-group averages: (sum of groups) − (total) = the overlapping element(s).
Sum of first eight = 8 × 32 = 256. Sum of last eight = 8 × 36 = 288. Sum of all 15 = 15 × 34 = 510.
Eighth number = 256 + 288 − 510 = 34.
Tip: Overlapping-group averages: (sum of groups) − (total) = the overlapping element(s).
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