Question

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

a. 1

b. 3

c. 5

d. 7

e. 9

Please show work!

Answer 1

b. 3

Explanation:

Here, n players score 2 points and m players score 5 points,

So, total scores = 2n + 5m,

According to the question,

The total number of points is 50,

⇒ 2n + 5m = 50

Since, n and m can be any positive integers including 0 ( because number of players can not be negative or in fraction )

Also, for the positive integer value of m, n must be the multiple of 5 less than or equal to 25,

Thus, the possible values of m and n are,

(5,8), (10, 6), (15, 4), (25,0),

Since, 8-5 < 10-6 < 15-4 < 25-0

Hence, the least possible positive difference between n and m is 3.

Option 'b' is correct.