Problem 12 · 2011 Math Kangaroo
Medium
Logic & Word Problems
sum-constraint
Marie has 9 pearls which weigh, in order, 1 g, 2 g, 3 g, 4 g, 5 g, 6 g, 7 g, 8 g and 9 g. She makes four rings, each with two pearls. The pearls on those rings weigh, in order, 17 g, 13 g, 7 g and 5 g. How much does the pearl which has not been used weigh?
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Answer: C — 3 g
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Hint 1 of 2
You do not need to figure out the actual pairs — think about totals.
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Hint 2 of 2
Subtract the combined ring weight from the weight of all nine pearls.
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Approach: the unused pearl is the total minus the four ring sums
- The pearls 1..9 weigh 1+2+...+9 = 45 g in total.
- The four rings weigh 17+13+7+5 = 42 g and use 8 pearls.
- So the single unused pearl weighs 45−42 = 3 g.
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