1993 AHSME Problems/Problem 4

Problem

Define the operation " $\circ$ " by $x\circ y=4x-3y+xy$ , for all real numbers $x$ and $y$ . For how many real numbers $y$ does $3\circ y=12$ ?

$\text{(A) } 0\quad \text{(B) } 1\quad \text{(C) } 3\quad \text{(D) } 4\quad \text{(E) more than 4}$

Solution

Note that $3 \circ y = 4 \cdot 3 - 3y + 3y = 12$ , so $3 \circ y = 12$ is true for all values of $y$ . Thus there are more than four solutions, and the answer is $\fbox{E}$

1993 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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1993 AHSME Problems/Problem 4

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