Problem 17 · 2015 Math Kangaroo
Medium
Algebra & Patterns
total-then-dividesubstitution
The 10 participants of a test achieve on average 6 points. Exactly 6 of the participants passed the test. The average of the participants that passed the test was 8 points. What is the average of the participants that did not pass the test?
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Answer: C — 3
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Hint 1 of 2
Turn each average into a total number of points.
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Hint 2 of 2
Total points minus the passers' points gives the failers' points; divide by how many failed.
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Approach: use totals, not averages, then divide
- All 10 participants total 10 * 6 = 60 points.
- The 6 who passed total 6 * 8 = 48 points.
- The 4 who failed total 60 - 48 = 12 points, so their average is 12 / 4 = 3.
- So the failers averaged 3 (C).
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