Problem 10 · Compare pair averages using totals · 4 points
Made by AI and not reviewed by a real person.
If you choose two different weeks from the chart, how many pairs have an average strictly greater than the average for all four weeks?
- 0
- 3
- 4
- 1
- 2
Show a hint
- Pair the tallest bar with the shortest, then pair the two leftover bars. What useful comparison do those pairs give you?
- The four-week average is 42.5, so a two-week pair needs a total greater than 85.
Show the answer and solution
Answer: E — 2
The four weeks total 170 tickets, giving an average of 42.5. Only weeks 2 and 4 (45 + 55 = 100) and weeks 3 and 4 (40 + 55 = 95) total more than 85, so the answer is 2. Weeks 1 and 4 and weeks 2 and 3 each total exactly 85; counting them would mistake an equal average for a greater one.