Problem 16 · 2022 Math Kangaroo
Hard
Logic & Word Problems
sum-constraint
Lisa has four dogs of different weights. Each dog weighs a whole number of kilograms. All four dogs together weigh 60 kg, and the second heaviest dog weighs 28 kg. How heavy is the third heaviest dog?
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Answer: A — 2 kg
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Hint 1 of 2
The heaviest dog weighs more than 28 kg, so it already uses up a big chunk of the 60 kg.
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Hint 2 of 2
After the heaviest and the 28 kg dog, very little weight is left for the two lightest, who must still be different whole numbers.
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Approach: see how little weight is left for the two smallest dogs
- The heaviest, the 28 kg dog, and the two lightest add to 60 kg, so the heaviest plus the two lightest make 60 − 28 = 32 kg.
- The heaviest is more than 28, so it is at least 29 kg, leaving at most 3 kg for the two lightest together.
- Two different whole numbers adding to at most 3 can only be 2 and 1, so the third heaviest is 2 kg.
- So the answer is A.
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