AHSME 1952 Problem 45

If $a$ and $b$ are two unequal positive numbers, then: $\text{(A) } \frac{2ab}{a+b}>\sqrt{ab}>\frac{a+b}{2} \text{(B) } \sqrt{ab}>\frac{2ab}{a+b}>\frac{a+b}{2} \\ \text{(C) } \frac{2ab}{a+b}>\frac{a+b}{2}>\sqrt{ab} \text{(D) } \frac{a+b}{2}>\frac{2ab}{a+b}>\sqrt{ab} \\ \text{(E) } \frac {a + b}{2} > \sqrt {ab} > \frac {2ab}{a + b}$