Problem 18 · 2017 Math Kangaroo
Hard
Logic & Word Problems
Algebra & Patterns
sum-constraintsubstitution
During our holidays it rained on 7 days. If it rained before noon, then there was no rain in the afternoon. If it rained in the afternoon, there was no rain before noon. There were 5 days without rain before noon and six days without rain in the afternoon. How many days long was our holiday?
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Answer: C — 9
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Hint 1 of 2
Each rainy day rains either only the morning or only the afternoon, never both.
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Hint 2 of 2
Count days with no morning rain and no afternoon rain in terms of the total.
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Approach: set up the dry-half counts against the total number of days
- Each of the 7 rainy days has rain in exactly one half, so morning-rain + afternoon-rain days = 7.
- If the holiday is N days: dry mornings = N − (morning-rain) = 5 and dry afternoons = N − (afternoon-rain) = 6.
- Adding: 2N − 7 = 11, so 2N = 18 and N = 9, choice C.
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