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# After winning 50 percent of the first 20 games it played, Te

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After winning 50 percent of the first 20 games it played, Te [#permalink]

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04 Feb 2014, 01:54
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

After winning 50 percent of the first 20 games it played, Team A won all of the remaining games it played. What was the total number of games that Team A won?

(1) Team A played 25 games altogether.
(2) Team A won 60 percent of all the games it played.

Data Sufficiency
Question: 75
Category: Arithmetic Percents
Page: 158
Difficulty: 600

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Re: After winning 50 percent of the first 20 games it played, Te [#permalink]

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04 Feb 2014, 01:55
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SOLUTION

After winning 50 percent of the first 20 games it played, Team A won all of the remaining games it played. What was the total number of games that Team A won?

The team won 50 percent of the first 20 games --> the team won 10 out of 20 games.

(1) Team A played 25 games altogether. Team A won (25 - 20) + 10 = 15 games. Sufficient.

(2) Team A won 60 percent of all the games it played --> 0.6*(20 + x) = 10 + x --> x= 5 --> the total number of games the team won is 10 + 5 = 15. Sufficient.

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Re: After winning 50 percent of the first 20 games it played, Te [#permalink]

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04 Feb 2014, 04:12
Ans D.

From S1: if team A won 10 games out of first 20 and all the remaining games and we're given the no of games it played in total,we can find out the no. of games it won ie 10+ 5=15.Sufficient.

From S2: let total no. of games = x
we're given: 0.6x = 10 +(x-20)
we can find out x to find out how many did A win. Sufficient.

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Re: After winning 50 percent of the first 20 games it played, Te [#permalink]

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05 Feb 2014, 00:05
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For the first 20 games, the no. of games won = 50% of 20 = (1/2)*20 = 10;
Let us assume the remaining no. of games played = x, as the no. of games played is the same as the no. of games won.

We need to find the total no. of games Team A won: 10 + x

We can rephrase the question further: what is the total no. of games played? or what is the remaining no. of games played?

Statement (1): Sufficient, since we know the total no. of games played: 10 + 5 = 15;

Statement (2): 60% of all games: 60% of (20 + x)
Also, we can arrive at the following equation: 10 + x = 60% of (20 + x);
10 + x = 12 + 0.6x;
0.4x = 2;
x = 5;

So, the total no. of games won = 10 + x = 10 + 5 =15;

Ans is (D).

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Re: After winning 50 percent of the first 20 games it played, Te [#permalink]

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10 Sep 2015, 07:01
[quote="Bunuel"]SOLUTION

After winning 50 percent of the first 20 games it played, Team A won all of the remaining games it played. What was the total number of games that Team A won?

The team won 50 percent of the first 20 games --> the team won 10 out of 20 games.

(1) Team A played 25 games altogether. Team A won (25 - 20) + 10 = 15 games. Sufficient.

(2) Team A won 60 percent of all the games it played --> 0.6*(20 + x) = 10 + x --> x= 5 --> the total number of games the team won is 10 + 5 = 15. Sufficient.

A Little explanation:

After 20 games:
Team A has won 10 games

After 25 games:
Suppose team A won 15 games in total, which is possibly sufficed by (1) Team A played 25 games altogether.

Now coming to (2), to win 60% of all the games, there are multiple possible answers
For total 30 games, team A may win 18 games, which is 60% of total games played,
For total 35 games, team A may win 21 games, which is also 60% of total games played,
For total 40 games, team A may win 24 games, which is also 60% of total games played.

It doesn't give the exact number of games that team A could have won.
Hence option (2) is not sufficient.

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Re: After winning 50 percent of the first 20 games it played, Te [#permalink]

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08 May 2016, 08:21
After winning 50% of the 20 games
or we can say , after winning 10 games out of first 20
team A won all the remaining games
suppose R games are remaining to play.
then total games T = 20 + R ...............................................................................(i)
and total wins W = 10 +R (because team A won all the remaining games) .................(ii)

From statement (1) -
T = 25
putting the value in equation (i) will give us
25 = 20 +R
R = 5
then W = 10 + 5 = 15 ( from equation (ii) )

From Statement (2) -
W = 60 % of T
W = (60/100)T
W = (3/5)T
from equation (i) and (ii)
10+R = 3/5 (20 + R )
by solving we can get R = 5; and W = 15.

Correct option D

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Re: After winning 50 percent of the first 20 games it played, Te [#permalink]

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10 Oct 2017, 22:10
statement I is very straight to understand.
Statement II states winning percent is 60 % over all, and team is winning all of its remaining games i.e. 100%. Now using concept of mixture, we know
first case win %- 50%
Second case win% - 100%
Over all win% - 60%
we also know number of games won in first case thus we can easily find number of games won in second case and total number of games team played
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Re: After winning 50 percent of the first 20 games it played, Te   [#permalink] 10 Oct 2017, 22:10
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