Problem 14 · 2011 Math Kangaroo
Hard
Arithmetic & Operations
total-then-dividesum-constraint
The list 17, 13, 5, 10, 14, 9, 12, 16 gives the points scored in a test. Which two scores can be removed without changing the average value of the list?
Show answer
Answer: E — 14 and 10
Show hints
Hint 1 of 2
First find the current average of the list.
Still stuck? Show hint 2 →
Hint 2 of 2
Two numbers can be dropped without changing the mean exactly when their sum is twice the mean.
Show solution
Approach: removing two numbers keeps the mean only if their sum equals 2×mean
- The eight scores total 96, so the average is 96/8 = 12.
- To keep the average 12 after removing two of them, the removed pair must sum to 2×12 = 24.
- Among the listed pairs, only 14 and 10 add to 24.
Mark:
· log in to save