Set of 30 numbers, average of 1st 10 numbers = average of last 20 numbers. The…
2023
Set of 30 numbers, average of 1st 10 numbers = average of last 20 numbers. The sum of the last 20 numbers is ?
- A.
Sum of 1st ten numbers
- B.
Can't be determined
- C.
2* sum of first ten numbers
- D.
2* sum of last ten numbers
Attempted by 179 students.
Show answer & explanation
Correct answer: C
Key idea: use algebra to relate the sums via the equal averages.
Let S be the sum of the first ten numbers. Their average is S/10.
Let T be the sum of the last twenty numbers. Their average is T/20.
Since the averages are equal, S/10 = T/20. Multiply both sides by 20 to get 2S = T.
Conclusion: The sum of the last twenty numbers equals twice the sum of the first ten numbers.
Quick example: if the sum of the first ten numbers is 30 (average 3), then the last twenty also have average 3, so their sum is 20×3 = 60, which is 2×30.