M09-23

Question

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

Bunuel · Accepted Answer

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

louwi · Answer

Number of wins: 25% of 20+ All the rest of the games (T-20)===> 5+(T-20)
Number of Loss: 75% of 20====> 15 Games

A) 75% T = 45 Loss (15+30), so total games, T=60

W:L= 45:15=3

Sufficient

B) 75%T=5+T-20 ===> T=60

Sufficient

felippemed · Answer

Here is my two cents.

I think my approach is for dummies, but without this step-by-step, average test takers cannot absorb most of the creative answers

summer127 · Answer

I think this is a  high-quality  question and I agree with explanation.

SpecterLitt · Answer

Very High Quality Question. Have bookmarked it for later too

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Anonymoux · Answer

The faster approach to statment (2):
If the player won 75% of all the games he played, he lost 25%. We need to find the ratio of the games he won to the games he lost, so we have:
75/25 = 3/1
Sufficient.

Posted from my mobile device

saibharatmba · Answer

The explanations provided are fine. But, in the question it is given that he wins all the games after the first 20 games. Isn't it contradicting the statement -1 stating that 30 more loses?

Any help is appreciated. Thanks

Bunuel · Answer

The key point in Statement 1 is a  hypothetical scenario . The statement says that  if  the player had won 25% of all games, he would have lost 30 more games than he actually lost. This does not contradict the information given in the question.

The actual scenario is that the player won all his games after the first 20. Statement 1 is simply setting up a comparison to calculate the number of games he played. The "30 more losses" refers to the difference in losses between the actual scenario and the hypothetical one described in Statement 1.

Unknown5612 · Answer

Statement 1: If player had won 25% of all his games, why are we assuming the losses are only from his remaining games. Why can't the the win ratio beccome less in the first 20 games as well?

Bunuel · Answer

You're missing the key word  "more"  in the statement. It says the player  would have lost 30  more  games than he actually lost , meaning the 30 extra losses come in addition to the losses he already had in the first 20 games. So only the remaining games are adjusted in the hypothetical. The first 20 stay the same.

alrightalright · Answer

I like the solution - it’s helpful.

M09-23

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