Question

If $mn=3(m+1)+n$ and $m$ and $n$ are integers, $m$ could be any of the following values EXCEPT:

• A. $2$
• B. $3$
• C. $4$
• D. $5$
• E. $7$

Answer 1

The correct option is D $5$

First you need to solve for $n$. The reason you solve for $n$ is that the answer choices list possible values for $m$, the other variable. IF you solve for $n$, then you can plug the possible values for $m$ into the formula and see when you get a non-integer for $n$, since $n$ must be an integer.

$mn=3(m+1)+n$

$mn-n=3(m+1)$

$n(m-1)=3(m+1)$

$n=\frac{3(m+1)}{(m-1)}$

$m$ $n=\frac{3(m+3)}{(m-1)}$

$2$ $n=\frac{3(2+1)}{(2-1)}=9$

$3$ $n=\frac{3(3+1)}{(3-1)}=6$

$4$ $n=\frac{3(4+1)}{(4-1)}=5$

$5$ $n=\frac{3(5+1)}{(5-1)}=\frac{18}{4}=\frac{9}{2}$

$7$ $n=\frac{3(7+1)}{(7-1)}=4$

Only a value of $5$ for $m$ does not produce an integer for $n$