Question

In a particular card game, the minimum score a player can achieve in a single game is 20, and the maximum score possible in a single game is 52. If a player plays three games and scores a total of 141 points, calculate the least number of points that the player could have scored in one of the games.
A.35
B.36
C.37
D.38

Answer 1

Hint: We can assume that out of three games, the player will score the maximum points in the two games. Then we can find their sum and subtract it from the total score. Then if the difference is greater than the minimum points scored in a round, then it will be the required point. If the difference is less than the minimum point, then the minimum point will be the required number of points.

Complete step-by-step answer:
We are given a game which the maximum score a player can achieve is 52 and minimum point a player can score is 20 points.
We are given that a player scored a total of 141 in 3 rounds.
We know that the total point is given by the sum of the points collected in each of the three rounds.
So, the minimum score is obtained in one game when the points scored in other games are maximum. It is given that 52 is the maximum point obtained in a game.
Let x be the minimum points scored in the game. Then we can write the total points as,
 \[141 = 52 + 52 + x\]
 \[ \Rightarrow 141 = 104 + x\]
Now we can solve for x.
 \[ \Rightarrow x = 141 - 104\]
 \[ \Rightarrow x = 37\]
As x is greater than the minimum points scored in a round, it is the required value.
Therefore, the least number of points that the player could have scored in one of the games is 37.
So, the correct answer is option C which is 37.

Note: We must make sure that the value we found out must lie between the maximum and minimum scores obtained in one round which is given by 52 and 20. As the options are given, we can find the value of x by the method of trial and error. We can note that the order of obtaining points in each round is more important