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MathNet 2003 — Part 02 Question 8

Math Olympiad Vault · MathNet 2003 — Part 02

Question 8

Given two numbers $x$ and $y$ with $0 \lt x \lt 1$, $0 \lt y \lt 1$ which of the following statements is always true?
  1. $x + y \lt 1$
  2. $\frac{x}{y} \lt 1$
  3. $x + y \gt 1$
  4. $x^{2} + y^{2} \gt 1$
  5. $x \lt \frac{1}{y}$.