Problem 14 · 2024 Math Kangaroo
Hard
Logic & Word Problems
work-backwardoff-by-one
Andrew throws arrows at a target. He starts with 10 arrows. Each time he hits the target, he gets 2 more arrows. In total Andrew throws 20 arrows, and then he has run out of arrows. How many times did Andrew hit the target?
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Answer: B — 5
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Hint 1 of 3
He only started with 10 arrows, but he threw 20, so where did the extra arrows come from?
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Hint 2 of 3
Every hit is like a little gift of 2 more arrows.
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Hint 3 of 3
Figure out how many extra arrows he earned, then see how many hits that took.
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Approach: count the extra arrows the hits gave him
- He started with 10 arrows but threw 20 in total, so 10 extra arrows must have come from hitting the target.
- Each hit gives 2 extra arrows, so we count by twos: 2, 4, 6, 8, 10 — that takes 5 hits to reach 10 extra arrows.
- So Andrew hit the target 5 times.
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