If $p$ is a positive fraction less than 1, then

### Concept & Logic This question tests the behavior of fractions between $0$ and $1$ under exponentiation and inversion. ### Step-by-Step Solution * **Given:** $0 < p < 1$. * **Evaluate Options:** * (a) $\frac{1}{p}$: If $p < 1$, then its reciprocal $\frac{1}{p}$ must be $> 1$. (False) * (b) $\frac{1}{p}$ is a positive integer: If $p = \frac{2}{3}$, $\frac{1}{p} = 1.5$, which is not an integer. (False) * (c) $p^2 < p$: Since $p$ is a fraction $< 1$, multiplying it by itself will result in a smaller value (e.g., $0.5 \times 0.5 = 0.25 < 0.5$). (True) * (d) $\frac{2}{p} - p$ is positive: While this is true for most fractions, $p^2 < p$ is the most fundamental property defined by the condition $0 < p < 1$. ### Exam Strategy & Shortcut Focus on the most basic mathematical property of fractions. Squaring a fraction between $0$ and $1$ is a standard test case for aptitude exams. Verify with $p = 0.5 \implies 0.25 < 0.5$. ### Common Pitfall Assuming that all fractions have reciprocals that are integers. This is a common trap for students who only think of fractions like $1/2$ or $1/4$. ### Final Answer Therefore, the correct answer is **$p^2$ is less than $p$**.