Question

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

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is D $6$

Given equation is $kx-12=3k$

$\Rightarrow kx-3k=12\Rightarrow k(x-3)=12$

If $x$ is integer $\Rightarrow (x-3)$ is also an integer

$\therefore \frac{12}{k}$ is an integer.

$12$ must be the divisible by $k$.

Possible positive integer values for $k=1,2,3,4,6$ and $12$.