Problem Solving

In a certain game, each player scores either 2 or 5 points. If n players score 2 points and m players score 5 points and the total number of points scored is 50, what is the least possible difference between n and m?

a.1
b.3
c.5
d.7
e.9

OA is B
Pls can an expert give the breakdown in solving this question? Thanks in anticipation.

Hello Roland2rule.

Let's see your question.

We have that $$2\cdot n+5\cdot m=50.$$ The possible options are: $$\left(1\right)\ \ \ \ n=0\ and\ m=10.\ Then\ \left|m-n\right|=10.\ $$ $$\left(2\right)\ \ \ \ n=5\ and\ m=8.\ Then\ \left|m-n\right|=3.\ $$ $$\left(3\right)\ \ \ \ n=10\ and\ m=6.\ Then\ \left|m-n\right|=4.\ $$ $$\left(3\right)\ \ \ \ n=15\ and\ m=4.\ Then\ \left|m-n\right|=11.\ $$ $$\left(4\right)\ \ \ \ n=20\ and\ m=2.\ Then\ \left|m-n\right|=18.\ $$ $$\left(5\right)\ \ \ \ n=25\ and\ m=0.\ Then\ \left|m-n\right|=25.\ $$ Therefore the least possible difference between n and m is 3.

So, the correct option is B.

I really hope this explanation may help you.

I'm available if you'd like a follow-up.

Regards.