Problem 14 · 2018 Math Kangaroo
Medium
Logic & Word Problems
groupingguess-and-check
A rose bush has 8 flowers, with butterflies and dragonflies sitting on them. At most one insect sits on each flower, and more than half of the flowers are taken. The number of butterflies is twice the number of dragonflies. How many butterflies are sitting on the flowers?
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Answer: C — 4
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Hint 1 of 2
Twice as many butterflies as dragonflies means the insects come in little teams of 3: two butterflies with one dragonfly.
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Hint 2 of 2
More than half of the 8 flowers are taken, so more than 4 insects are sitting, but no more than 8.
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Approach: group the insects into teams of two butterflies plus one dragonfly and count whole teams
- Since there are twice as many butterflies as dragonflies, picture them in teams of 3: two butterflies and one dragonfly each.
- More than half of the 8 flowers are filled, so the number of insects is more than 4 but at most 8 — one team is only 3 (too few) and three teams would be 9 (too many).
- So there are exactly two teams: 6 insects, which is 4 butterflies and 2 dragonflies, giving 4 butterflies, answer C.
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