Difference between revisions of "1980 AHSME Problems/Problem 6"
Mrdavid445 (talk | contribs) (Created page with "==Problem== A positive number <math>x</math> satisfies the inequality <math>\sqrt{x} < 2x</math> if and only if <math>\text{(A)} \ x > \frac{1}{4} \qquad \text{(B)} \ x > 2 \qqu...") |
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A positive number <math>x</math> satisfies the inequality <math>\sqrt{x} < 2x</math> if and only if | A positive number <math>x</math> satisfies the inequality <math>\sqrt{x} < 2x</math> if and only if | ||
| − | <math>\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</math> | + | |
| + | <math>\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</math> | ||
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| + | == Solution == | ||
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| + | <math> \sqrt{x}< 2x \\ x < 4x^2 \\ 0 < x(4x-1) \\ 0 < 4x-1 \\ 1 < 4x \\ x >\frac{1}{4} \\ \boxed{(A)}</math> | ||
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| + | Note: You can also draw a rough sketch. | ||
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| + | == See also == | ||
| + | {{AHSME box|year=1980|num-b=5|num-a=7}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 14:40, 20 March 2018
Problem
A positive number 
satisfies the inequality 
if and only if
Solution
Note: You can also draw a rough sketch.
See also
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
