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.
Arithmetic
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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.
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.
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We can create the equation:BTGmoderatorRO wrote: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
2n + 5m = 50
Since 2n and 50 are even, then 5m must also be even. Since 5 is not even, m must be even. Therefore, m could be 0, 2, 4, 6, 8, 10.
Since we want the least possible difference between n and m, let's let m = 6, and we have:
2n + 5(6) = 50
2n = 20
n = 10
We see the difference between n and m is 4.
If m = 8, then we have:
2n + 5(8) = 50
2n = 10
n = 5
We see the difference between n and m is 3.
If m = 10, then we have:
2n + 5(10) = 50
2n = 0
n = 0
We see the difference between n and m is 10.
Thus, the smallest possible difference between n and m is 3 (when n = 5 and m = 8).
Answer: B
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