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Spade Operation

Source: AMC 10 2010A Problem 6

February 10, 2010
AMC

Problem Statement

For positive numbers x x and y y the operation ♠(x,y) \spadesuit(x,y) is defined as \spadesuit(x,y)\equal{}x\minus{}\frac1yWhat is ♠(2,♠(2,2)) \spadesuit(2,\spadesuit(2,2))? <spanclass=′latex−bold′>(A)</span> 23<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 43<spanclass=′latex−bold′>(D)</span> 53<spanclass=′latex−bold′>(E)</span> 2 <span class='latex-bold'>(A)</span>\ \frac23 \qquad <span class='latex-bold'>(B)</span>\ 1 \qquad <span class='latex-bold'>(C)</span>\ \frac43 \qquad <span class='latex-bold'>(D)</span>\ \frac53 \qquad <span class='latex-bold'>(E)</span>\ 2
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