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I think this is a poor-quality question. I think the wording is unclear. "....and all of his remaining games." is confusing. Did he win 25% of his remaining games or did he win ALL of his remaining games? I know it seems silly once you know what the question is asking, but I had to waste time unnecessarily trying to figure out whether I read the question wrong or if there was a catch somewhere that i missed. A small updated to the wording would help.

Per statement 2 - "The player won 75 percent of the games he played." Doesn't this directly answer the question 'the ratio of the number of games he won to the number of the games he lost' to be 3:1 since if he won 75% he lost 25%? What am I missing?

Per statement 2 - "The player won 75 percent of the games he played." Doesn't this directly answer the question 'the ratio of the number of games he won to the number of the games he lost' to be 3:1 since if he won 75% he lost 25%? What am I missing?

Will appreciate a response.

Thanks!

Yes, it does. The solution just solves the statement similarly to statement (1) to illustrate the way of finding the number of remaining games.
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I think this is a poor-quality question. I think the wording is unclear. "....and all of his remaining games." is confusing. Did he win 25% of his remaining games or did he win ALL of his remaining games? I know it seems silly once you know what the question is asking, but I had to waste time unnecessarily trying to figure out whether I read the question wrong or if there was a catch somewhere that i missed. A small updated to the wording would help.

I don;t think it's confusing at all.

The player won 25 percent of the first 20 games he played and all of his remaining games. So, 25% of the first 20 games and 100% of the remaining games.
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Given conditions: Player won 25% of the first 20 games 20*1/4= 5 games won or 15 lost in first 20 matches. Player also won remaining of his matches. so the number of games he lost is 15. we have to find number of matches he won/ number of matches he lost = (5+remaining matches)/15

1) If the player had won 25 percent of the total games he played, he would have lost 30 more games than he actually did.

let the total number of games he played is X then he won X/4 games(25%) or lost 3X/4(75%) games Given 3X/4 = 15 +30(as he already lost 15 in First 20 matches) 3X/4=45 X =60 matches so remaining matches are 40 Required ratio is (5+40)/15=45/15 Sufficient 2) The player won 75 percent of the games he played. Let the total games he played is X 3X/4 he won and X/4 he lost. X/4 =15 (As he won remaining of his matches after first 20 matches) X=60 so remaining matches are 40 Required ratio is (5+40)/15=45/15 Sufficient