Problem 12 · 2017 Math Kangaroo
Hard
Algebra & Patterns
substitution
The positive number p is smaller than 1, and the number q is greater than 1. Which of the following numbers is the biggest?
Show answer
Answer: B — \(p + q\)
Show hints
Hint 1 of 2
Since p is less than 1 and q is greater than 1, test the options with a simple example like p = 1/2, q = 2.
Still stuck? Show hint 2 →
Hint 2 of 2
Dividing by q (>1) shrinks a value, and adding two positives beats either one alone.
Show solution
Approach: compare the expressions using the size constraints on p and q
- p < 1 < q, both positive. Then p/q < p (dividing by something bigger than 1), and p < q.
- Also p + q is larger than q alone since p > 0, and larger than the product p x q for such values.
- So the biggest expression is p + q.
Mark:
· log in to save