1969 AHSME Problems/Problem 4

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Problem

Let a binary operation $\star$ on ordered pairs of integers be defined by $(a,b)\star (c,d)=(a-c,b+d)$. Then, if $(3,3)\star (0,0)$ and $(x,y)\star (3,2)$ represent identical pairs, $x$ equals:

$\text{(A) } -3\quad \text{(B) } 0\quad \text{(C) } 2\quad \text{(D) } 3\quad \text{(E) } 6$

Solution

Performing the operation based on the definition, $(3,3)\star(0,0) = (3,3)$ and $(x,y)\star(3,2)=(x-3,y+2)$. Because the outputs are identical pairs, they must equal each other, so $3 = x-3$. Solving for x yields $x = 6$, which is answer choice $\boxed{\textbf{(E)}}$.

See also

1969 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
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