1992 AHSME Problems/Problem 10: Difference between revisions

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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
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
All AHSME Problems and Solutions

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 == Solution ==
 <math>\fbox{D}</math>
+<math>kx -12 = 3k</math>
+<math>-12=3k-kx</math>
+<math>-12=k(3-x)</math>
+<math>\frac{-12}{k}=3-x</math>
+Positive factors of <math>-12</math>:
+<math>1,2,3,4,6,12</math>
+factors, each of which have an integer solution for <math>x</math> in <math>\frac{-12}{k}=3-x</math>
 == See also ==