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AHSME 1969 Problem 4

    Let a binary operation ⋆\star on ordered pairs of integers be defined by (a,b)⋆(c,d)=(a−c,b+d)(a,b)\star (c,d)=(a-c,b+d). Then, if (3,3)⋆(0,0)(3,3)\star (0,0) and (x,y)⋆(3,2)(x,y)\star (3,2) represent identical pairs, xx equals: (A) −3(B) 0(C) 2(D) 3(E) 6\text{(A) } -3 \text{(B) } 0 \text{(C) } 2 \text{(D) } 3 \text{(E) } 6

    Dataset text NuminaMath-1.5. Quoted with source.

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