Q155
ArithmeticAlgebra, Equations & Operations
A number X lies between 0 and 1. Which of the following is true?
- a.$X > \sqrt{X}$
- b.$X > \frac{1}{X}$
- c.$X^3 > X^2$
- d.$\frac{1}{X} > \sqrt{X}$
Answer: (D) $\frac{1}{X} > \sqrt{X}$
For $0 < X < 1$: $\sqrt{X} > X$ (not A); $\frac{1}{X} > 1 > X$ (so B is false since X < 1/X); $X^2 > X^3$ (not C); $\frac{1}{X} > 1 > \sqrt{X}$ since $\sqrt{X} < 1$, so D is true.