Problem 30 · 2025 Math Kangaroo
Stretch
Logic & Word Problems
work-backwardsum-constraint
Annie, Bibi, Clara and Doris each live on a different floor of a four-storey building, and other people live there too. 25 people live above Annie, 5 people live below Bibi, 17 people live below Clara, and 22 people live above Doris. How many people live in the building in total?
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Answer: A — 27
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Hint 1 of 2
For any resident, (people above) + (themselves) + (people below) is the whole building, so each clue tells you both an 'above' and a 'below' count once you call the total \(N\).
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Hint 2 of 2
Annie has the most people above her, so she is the lowest of the four friends; rank the four and make their above/below counts line up.
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Approach: rank the four friends and reconcile the counts
- Annie has 25 people above her — the most of the four — so she is the lowest friend, and the most people above means the fewest below; in fact only Clara (17 below) and the others can sit above her.
- Ranking everyone in one line, Annie is 26th from the top, Doris 23rd, Bibi has 5 below and Clara 17 below; fitting these together with one person below Annie forces the total.
- The counts only agree when the building holds 27 people, which is (A).
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