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# After winning 50 percent of the first 20 games it played, Team A won

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Re: After winning 50 percent of the first 20 games it played, Team A won [#permalink]
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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, Team A won [#permalink]
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[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, Team A won [#permalink]
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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, Team A won [#permalink]
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, Team A won [#permalink]
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Games played won
20 10
x x

To find out: (10+x)

1) (10+x)=25
suff

2)60/100 (20+x)=10+x
suff
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Re: After winning 50 percent of the first 20 games it played, Team A won [#permalink]
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After winning 50 percent of the first 20 games it played, Team Red won all of the remaining games it played. What was the total number of games that Team Red won?

(1) Team Red played 25 games altogether

Team Red won 50% of the first 20 games played = 10 games won.
Team Red won all the remaining games = 5 games won

10 + 5 = 15. SUFFICIENT.

(2) Team Red won 60 percent of all the games it played

Statement 1 gives us a clue to statement 2; since we know Team Red won half the first 20 games, we can conclude Team Red won 15 out of 25 games.

15/25 = 60%

SUFFICIENT.

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Re: After winning 50 percent of the first 20 games it played, Team A won [#permalink]
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After winning 50 percent of the first 20 games it played, Team A won [#permalink]
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Statement 1

25 games played altogether

They won 50% of 20 games already played (10) + remaining games (25-20 = 5) so 15 games won. Suff.

Statement 2:

Set up and equation

Games won / Games Played

Team A won 60 percent of all the games it played.

So.... (10 + x)/(20 + x) =.6 Solve and it works. Suff.

Why can we use x as a constant in the Numerator and Denominator????

Because the team won the rest of its games so the additional games played (Variable x) we add on can be added to both the Wins and Total Games played as its the same number.
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Re: After winning 50 percent of the first 20 games it played, Team A won [#permalink]
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, Team A won [#permalink]
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Re: After winning 50 percent of the first 20 games it played, Team A won [#permalink]
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