M09-23

Official Solution:


A chess player won 25% of his first 20 games and won all of his remaining games. What is the ratio of the games he won to the games he lost, assuming no draws occurred?

(1) If the player had won 25% of all his games, he would have lost 30 more games than he actually lost.

The player won 25% of his first 20 games and 100% of the remaining games. To have won 25% of the total matches, he should have won 25% of the remaining games (instead of 100%, thus 75% less). Therefore, 75% losses in the remaining games would result in 30 more losses: \(0.75*R=30\), where \(R\) is the number of the remaining games. We have only one unknown, \(R\), hence we can solve for it and thus we'll have all the information needed to calculate the ratio. Sufficient.

(2) The player won 75% of all the games he played.

From this, we can formulate: \(0.25*20+1*R=0.75*(20+R)\). Similarly, here, with only one unknown \(R\), we can solve for it. This will give us all the necessary information to determine the ratio. Sufficient.


Answer: D