1980 AHSME Problems/Problem 6

Problem

A positive number $x$ satisfies the inequality $\sqrt{x} < 2x$ if and only if

$\text{(A)} \ x > \frac{1}{4} \qquad \text{(B)} \ x > 2 \qquad \text{(C)} \ x > 4 \qquad \text{(D)} \ x < \frac{1}{4}\qquad \text{(E)} \ x < 4$

$\sqrt{x}< 2x \\ x < 4x^2 \\ 0 < x(4x-1) \\ 0 < 4x-1 \\ 1 < 4x \\ x >\frac{1}{4} \\ \boxed{(A)}$

Note: You can also draw a rough sketch.

1980 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions