MathDB
Easy Function

Source: 1968 AHSME Problem #4

August 31, 2011
functionAMC

Problem Statement

Define an operation ∗* for positve real numbers as a∗b=aba+ba*b=\dfrac{ab}{a+b}. Then 4∗(4∗4)4*(4*4) equals:
<spanclass=′latex−bold′>(A)</span> 34<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 43<spanclass=′latex−bold′>(D)</span> 2<spanclass=′latex−bold′>(E)</span> 163<span class='latex-bold'>(A)</span>\ \frac{3}{4} \qquad <span class='latex-bold'>(B)</span>\ 1 \qquad <span class='latex-bold'>(C)</span>\ \dfrac{4}{3} \qquad <span class='latex-bold'>(D)</span>\ 2 \qquad <span class='latex-bold'>(E)</span>\ \dfrac{16}{3}
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