1992 AHSME Problems/Problem 10

Problem

The number of positive integers $k$ for which the equation $kx-12=3k$ has an integer solution for $x$ is

$\text{(A) } 3\quad \text{(B) } 4\quad \text{(C) } 5\quad \text{(D) } 6\quad \text{(E) } 7$

$\fbox{D}$

$kx -12 = 3k$

$-12=3k-kx$

$-12=k(3-x)$

$\frac{-12}{k}=3-x$

Positive factors of $-12$ : $1,2,3,4,6,12$

6 factors, each of which have an integer solution for $x$ in $\frac{-12}{k}=3-x$

1992 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
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