Problem 14 · 2024 Math Kangaroo
Hard
Algebra & Patterns
estimate-and-pick
We are given two positive numbers x and y with x < y. Which of the following expressions has the biggest value?
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Answer: A — x + 3y4
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Hint 1 of 2
Each option is a weighted average of x and y; with y larger, more weight on y makes it bigger.
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Hint 2 of 2
Compare how much weight each expression puts on y and pick the one with the most.
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Approach: compare weights on the larger value y
- Each expression is a weighted average of x and y, and y > x.
- Putting more weight on y makes the value larger.
- (x + 3y)/4 weights y the most (3/4), so it is the biggest — option A.
Mark:
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