1992 AHSME Problems/Problem 10

Revision as of 20:49, 2 March 2017 by Xiej (talk | contribs) (Solution)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

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

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

Solution

$\fbox{D}$

$kx -12 = 3k$

$-12=3k-kx$

$-12=k(3-x)$

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

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

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

See also

1992 AHSME (ProblemsAnswer KeyResources)
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS