Problem 12 · 2022 Math Kangaroo
Hard
Arithmetic & Operations
division
2022 tiles are placed in one long row. Adam removes every sixth tile. Then Beate removes every fifth of the remaining tiles. Subsequently Cora removes every fourth of the remaining tiles. How many tiles are left?
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Answer: D — 1011
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Hint 1 of 2
After removing every k-th tile, the fraction (k-1)/k of the tiles survive.
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Hint 2 of 2
Multiply 2022 by 5/6, then 4/5, then 3/4 in turn.
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Approach: multiply by the surviving fractions in order
- Removing every 6th leaves 2022 * 5/6 = 1685.
- Removing every 5th of those leaves 1685 * 4/5 = 1348.
- Removing every 4th of those leaves 1348 * 3/4 = 1011.
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