Problem 11 · 2011 AMC 8
Easy
Arithmetic & Operations
average-of-differences
The graph shows the number of minutes studied by both Asha (black bar) and Sasha (grey bar) in one week. On the average, how many more minutes per day did Sasha study than Asha?
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Answer: A — 6 minutes.
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Hint 1 of 2
The average difference equals the difference of the totals, so you can just compare the two weekly totals — the days some days are negative is fine, they cancel in the total.
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Hint 2 of 2
Average daily gap = (Sasha's total for the week − Asha's total) ÷ 5 days.
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Approach: compare weekly totals, then divide by the number of days
- Read each day's gap (Sasha − Asha): +10, −10, +20, +30, −20. They add to +30 for the week — the negatives (days Asha studied more) correctly subtract.
- Spread that over 5 days: 30 ÷ 5 = 6 minutes per day.
- Why this works: averaging the daily differences is the same as (sum of differences)÷5, which equals (Sasha's weekly total − Asha's weekly total)÷5 — you never have to average each person separately.
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