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National and Regional Contests
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MAA AMC
AMC 12/AHSME
1980 AMC 12/AHSME
6
Inequality
Inequality
Source:
December 30, 2005
inequalities
Problem Statement
A positive number
x
x
x
satisfies the inequality
x
<
2
x
\sqrt{x} < 2x
x
<
2
x
if and only if
(A)
x
>
1
4
(B)
x
>
2
(C)
x
>
4
(D)
x
<
1
4
(E)
x
<
4
\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
(A)
x
>
4
1
(B)
x
>
2
(C)
x
>
4
(D)
x
<
4
1
(E)
x
<
4
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