Problem 13 · 2012 Math Kangaroo
Medium
Logic & Word Problems
complementary-counting
A travel agency organises four different trips for a certain group. Each trip has a participation rate of 80%. What is the minimum percentage of the group which has taken part in all four roundtrips?
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Answer: D — 20 %
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Hint 1 of 2
Count who could MISS a trip rather than who takes it.
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Hint 2 of 2
Spread the 20% who skip each trip over different people to make the all-four group as small as possible.
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Approach: bound the overlap using the missers
- Each trip is skipped by 20% of the group.
- Across four trips at most 4×20% = 80% skip at least one trip.
- So at least 100% − 80% = 20% took part in all four.
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