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# M09-23

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:40
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Difficulty:

55% (hard)

Question Stats:

66% (01:25) correct 34% (01:24) wrong based on 188 sessions

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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? (Assume there cannot be a draw in the game.)

(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.

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

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15 Sep 2014, 23:40
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5
Official Solution:

(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. The player won 25% of his first 20 games and 100% of the remaining games, in order to win 25% of total matches he should have won 25% of the remaining games (instead of 100%, so 75% less). So 75% losses in the remaining games 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 information needed to get the ratio. Sufficient.

(2) The player won 75 percent of the games he played. So, $$0.25*20+1*R=0.75*(20+R)$$. The same here: we have only one unknown $$R$$, hence we can solve for it and thus we'll have all information needed to get the ratio. Sufficient.

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09 Dec 2014, 07:23
1
Hi Bunuel,

Dont you think the question should be re framed as the ratio of the games he won to the number of games he DID NOT WIN.
A chess game can also be a draw, I got confused and marked E, since no where do we know how many draws were there ?

Bunuel wrote:
Official Solution:

(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. The player won 25% of his first 20 games and 100% of the remaining games, in order to win 25% of total matches he should have won 25% of the remaining games (instead of 100%, so 75% less). So 75% losses in the remaining games 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 information needed to get the ratio. Sufficient.

(2) The player won 75 percent of the games he played. So, $$0.25*20+1*R=0.75*(20+R)$$. The same here: we have only one unknown $$R$$, hence we can solve for it and thus we'll have all information needed to get the ratio. Sufficient.

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12 Aug 2015, 18:36
1
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.
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17 Aug 2015, 02:41
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davesinger786 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.

There is nothing wrong with the question. Please check alternative approaches here: a-chess-player-won-25-percent-of-the-first-20-games-152608.html

Similar questions to practice:
after-winning-80-of-his-first-40-matches-igby-won-129062.html
after-winning-50-percent-of-the-first-30-matches-she-played-129132.html
after-winning-80-percent-of-the-fi-rst-40-games-it-played-129338.html
after-winning-50-percent-of-the-first-x-games-it-played-149675.html

Hope it helps.
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26 Aug 2015, 03:42
2
I think this is a high-quality question and I don't agree with the explanation. THE QUESTION NEEDS TO CLEARLY MENTION THAT A PLAYER CAN ONLY WIN OR LOSE A GAME AND THAT NO GAME CAN BE DRAWN - NOW THE SOLUTION PROVIDED IS VALID, ELSE THE ANSWER CHOICE IS E ( AS NO. OF DRAWN GAMES IS AN UNKNOWN EVEN AFTER COMBINING BOTH STATEMENTS).
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05 Sep 2015, 20:10
As far as explanation for 2nd option is considered "The player won 75 percent of the games he played", I applied very simple approach as follows:
What is the question looking for?
- What is the ratio of the number of games he won to the number of the games he lost?
- say number of games he won be 'x' and number of games he lost be 'y'
- hence, x/(x+y) = 75%
- question - what is x/y?
- if x/(x+y) = 75/100, (x+y)/x = 100/75
- hence 1 + y/x = 4/3
-hence y/x = 4/3 - 1 = 1/3
- thus x/y = 3
- basically, at step - if x/(x+y) = 75/100, (x+y)/x = 100/75 - you can conclude that you can find value of x/y. You need not actually solve it.

Do I make any sense?
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12 Sep 2015, 06:09
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. one of the possibilities in a chess match is a draw, this aspect is not counted for in the explanation, why?
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14 Sep 2015, 21:22
the q needs to be improved to take account of draws. the similar logics applies here as to the questions with triple overlapping sets - when m08-183778.html - the stimulus says people like both strawberry and apple but the quesiton does not specifically note that they cannot like raspberry as well. same here. unfair
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14 Sep 2015, 21:22
I think this is a poor-quality question and I don't agree with the explanation. the q needs to be improved to take account of draws. the similar logics applies here as to the questions with triple overlapping sets - when m08-183778.html - the stimulus says people like both strawberry and apple but the quesiton does not specifically note that they cannot like raspberry as well. same here. unfair
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20 Sep 2015, 15:35
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.
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23 Nov 2015, 15:13
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. The question does not take into account any other possibility other than a win and a loss.But there are three possibilities that result from a chess game:Win,Lose,Draw.
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26 Nov 2015, 14:02
I think this is a poor-quality question and I don't agree with the explanation. This question does not clearly talk about what happens if the game is drawn. The question should have clearly mentioned 'none of the games were a draw'.
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18 Dec 2015, 07:11
Bunuel wrote:
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?

(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.

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

This is how I went about the question, not sure if its good enough!

[Edited: My mistake was that I read all of the remaining games as 'lost' all of the remaining games]

Player won 25% of first 20 matches = 5 matches.
Let total matches be x. He lost x-5 matches.

We need to find 5/x-5. To find this we need total number of matches.
A) If the player had won 25 percent of the total games he played, he would have lost 30 more games than he actually did.
games won + games lost = total games
x/4 + 5+30 = x. We can solve for x. Sufficient.

B) The player won 75 percent of the games he played.
Something is wrong with my understanding coz he played atleast 20 matches and won 25%. But for the sake of solving the question, I assumed 0.75x = 5. x can be solved. Sufficient.
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19 Jan 2016, 09:12
Updated the question.
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28 Mar 2016, 06:16
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davesinger786 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.

I think it is a good question. I agree that explanation can be clearer. Here is my explanation:
First analyse the information given in the question. He won =5+x. Win/loss=(5+x)/15. Now explore x from (1) and/or (2) to check data sufficiency.
(1) 25% of the total games won=(20+x)/4. So,lost(total)=(20+x)*3/4
From the first 20 games, he lost 15. 30 games more means =15+30=45.
So, total lost=45=(20+x)*3/4. Since x can be found from this equation,sufficient
(2)Similarly, we can say, (20+x)*3/4=5+x. Sufficient
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03 Aug 2016, 05:10
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
>> !!!

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03 Aug 2016, 05:14
rezaulnsu wrote:
davesinger786 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.

I think it is a good question. I agree that explanation can be clearer. Here is my explanation:
First analyse the information given in the question. He won =5+x. Win/loss=(5+x)/15. Now explore x from (1) and/or (2) to check data sufficiency.
(1) 25% of the total games won=(20+x)/4. So,lost(total)=(20+x)*3/4
From the first 20 games, he lost 15. 30 games more means =15+30=45.
So, total lost=45=(20+x)*3/4. Since x can be found from this equation,sufficient
(2)Similarly, we can say, (20+x)*3/4=5+x. Sufficient

I always ask myself whether the moderator, who I am truly fan of, provides a l holistic approach to questions on purpose to stretch our ways to answer questions.
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06 Jan 2017, 23:19
I think this is a high-quality question and I agree with explanation.
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09 Apr 2017, 18:27
1
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
Re: M09-23 &nbs [#permalink] 09 Apr 2017, 18:27

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# M09-23

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