Problem 19 · 2011 Math Kangaroo
Hard
Algebra & Patterns
substitution
The positive number a is smaller than 1 and the number b is greater than 1. Which of the following numbers is biggest?
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Answer: B — a + b
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Hint 1 of 2
Test a typical case like a = 0.5, b = 2 to see which expression wins.
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Hint 2 of 2
Adding the positive a always beats b, while multiplying by a small a does not.
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Approach: compare the expressions using a<1
- Since a is between 0 and 1, multiplying or dividing by it shrinks things, so a×b < b and a÷b < b.
- But a+b is larger than b because a is positive.
- So a+b is the biggest of the five.
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