Problem 23 · 2011 Math Kangaroo
Stretch
Algebra & Patterns
estimate-and-pick
The numbers x and y are both greater than 1. Which of the following numbers is biggest?
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Answer: B — \(\dfrac{x}{y-1}\)
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Hint 1 of 2
Rewrite each option as x over an 'effective denominator' by dividing numerator and denominator alike.
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Hint 2 of 2
The biggest fraction comes from the smallest effective denominator.
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Approach: reduce each to x over an effective denominator
- Dividing out the common factor, the options equal x over y+1, y−1, y+½, y−½, y+⅓.
- Since x > 0, the largest value corresponds to the smallest denominator.
- The smallest of those denominators is y−1.
- So the biggest number is x/(y−1), choice (B).
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