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11 May 2013, 00:48
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D
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66% (02:02) correct
34%
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wrong
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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.
(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.
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11 May 2013, 03:35
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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.
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Hope it helps.
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.
Similar questions to practice:
https://gmatclub.com/forum/after-winnin ... 29062.html
https://gmatclub.com/forum/after-winnin ... 29132.html
https://gmatclub.com/forum/after-winnin ... 29338.html
https://gmatclub.com/forum/after-winnin ... 49675.html
Hope it helps.
11 May 2013, 00:59
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A chess player won 25 percent of the first 20 games he played and all of his remaining games. What is the ratio of the number of games he won to the number of the games he lost?
In the first 20 games, 5 W and 15 L. Overall he won \(5+R\) games and lost \(15\). We need to find R
(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.
"If the player had won 25 percent of the total games he played" = lost 75%
\((20+R)*75%=30+15\) the first part is the total losses, the second part is the is 30 more games than he actually did lose (15)
\(0.75R=30\)
\(R=40\)
Suffcient
(2) The player won 75 percent of the games he played.
\(5+R=75%(20+R)\) the first part is the number of games he won, the second part is the transaltion of "won 75 percent of the games he played"
\(R=40\)
Sufficient
D
In the first 20 games, 5 W and 15 L. Overall he won \(5+R\) games and lost \(15\). We need to find R
(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.
"If the player had won 25 percent of the total games he played" = lost 75%
\((20+R)*75%=30+15\) the first part is the total losses, the second part is the is 30 more games than he actually did lose (15)
\(0.75R=30\)
\(R=40\)
Suffcient
(2) The player won 75 percent of the games he played.
\(5+R=75%(20+R)\) the first part is the number of games he won, the second part is the transaltion of "won 75 percent of the games he played"
\(R=40\)
Sufficient
D
