In a tournament, a win fetches two points; a draw, one point; and a loss, no points. Fischer, who played 20 matches, had exactly three draws, at least one loss and at least one win. What could be his maximum and minimum scores possible, respectively?

Correct option is C

Given:

Fischer played 20 matches.

He had exactly 3 draws.

He had at least 1 win and at least 1 loss.

A win gives 2 points.

A draw gives 1 point.

A loss gives 0 points.

Solution:

Since Fischer played 20 matches and had 3 draws, he played 20 - 3 = 17 matches that were either wins or losses.

To maximize Fischer's score, we need to maximize the number of wins. Since he had at least one loss,

the maximum number of wins he could have is 17 - 1 = 16.

Number of wins = 16

Number of draws = 3

Number of losses = 1

Maximum score = (16 wins $$\times$$​2 points/win) + (3 draws $$\times$$ 1 point/draw) + (1 loss $$\times$$ 0 points/loss) = 32 + 3 + 0 = 35​​

Minimum Possible Score:

To minimize Fischer's score, we need to maximize the number of losses. Since he had at least one win, the maximum number of losses he could have is 17 - 1 = 16.

Number of wins = 1

Number of draws = 3

Number of losses = 16

Minimum score = (1 win $$\times$$ 2 points/win) + (3 draws $$\times$$ 1 point/draw) + (16 losses $$\times$$ 0 points/loss) = 2 + 3 + 0 = 5​​​

Maximum possible score: 35

Minimum possible score: 5