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Arithmetic

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by BTGmoderatorRO » Sun Dec 17, 2017 5:02 am
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.
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by EconomistGMATTutor » Sun Dec 17, 2017 7:44 am
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.
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by Scott@TargetTestPrep » Sat Sep 21, 2019 11:20 am
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
We can create the equation:

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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