, 2003

Algebra Difficulty 4.0 AMC 10/12 Find the answer Italy

Problem:

Given two numbers $x$ and $y$ with $0 < x < 1$ , $0 < y < 1$ , which of the following statements is always true?

Pick one

Solution

Solution:

The answer is $\mathbf{(E)}$ . This statement is always true, since $x < 1$ , while $\frac{1}{y} > 1$ . For $x = \frac{1}{2}$ , $y = \frac{1}{3}$ the hypotheses of the text are satisfied, but (B), (C) and (D) are false. Finally $x = y = \frac{3}{4}$ provides a counterexample for (A).

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Source: MathNet, licensed CC-BY-4.0. Statement translated into English from it; metadata (topic, difficulty) added by this project.