Problem 17 · 2017 Math Kangaroo
Hard
Algebra & Patterns
Logic & Word Problems
substitution
Four brothers have different heights. Tobias is as many centimeters smaller than Viktor, as he is taller than Peter. Oskar on the other hand is equally many centimeters smaller than Peter. Tobias is 184 cm tall, and on average the four brothers are 178 cm tall. How tall is Oskar?
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Answer: A — 160 cm
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Hint 1 of 2
Write everyone's height as Tobias plus or minus a single difference d.
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Hint 2 of 2
Use the average to pin down d.
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Approach: express all four heights in terms of one difference, then use the average
- Let d be the common difference. Viktor = 184 + d, Peter = 184 − d, and Oskar = Peter − d = 184 − 2d.
- The average is 178, so the sum is 712: (184+d) + 184 + (184−d) + (184−2d) = 736 − 2d = 712.
- Thus 2d = 24, d = 12, and Oskar = 184 − 24 = 160 cm, choice A.
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