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games during a season

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by grandh01 » Wed Aug 15, 2012 12:57 pm
During a certain season, a team won
80 percent of its first 100 games and
50 percent of its remaining games. If
the team won 70 percent of its games
for the entire season, what was the
total number of games that the team
played?
(A) 180
(B) 170
(C) 156
(D) 150
(E) 105
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Source: — Problem Solving |

by rijul007 » Wed Aug 15, 2012 1:13 pm
Total number of games = 100+x
Number of games won = 80+50x/100 = 80 + x/2
the team won 70 percent of its games
for the entire season

70/100 = (80+x/2)/(100+x)
Solve for x

x = 50
Total number of games = 100+50 = 150

Option D
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by GMATGuruNY » Wed Aug 15, 2012 1:53 pm
grandh01 wrote:During a certain season, a team won
80 percent of its first 100 games and
50 percent of its remaining games. If
the team won 70 percent of its games
for the entire season, what was the
total number of games that the team
played?
(A) 180
(B) 170
(C) 156
(D) 150
(E) 105
The team won 80 of its first 100 games.

We can plug in the answers, which represent the total number of games.
Since 7/10 of the games are won, the total number games must be a multiple of 10.
Eliminate C and E.

7/10 of A, B and D imply the following options for the number of games won:
A: Total won = (7/10)180 = 126.
B: Total won = (7/10)170 = 119.
D: Total won = (7/10)150 = 105.

Since all of the values in the problem are multiples of 10, it is VERY likely that the correct answer is D, which implies that the total number of games won is a multiple of 5.

Answer choice D: 150
Number of games won after the first 100 = .5(50) = 25.
Total won = 80+25 = 105.
Success!

The correct answer is D.
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by truplayer256 » Fri Aug 17, 2012 4:47 pm
Let the remaining games be x.
(80 + x/2)/(100 + x) = 7/10

800 + 5x = 700 + 7x

100 = 2x => x = 50

Total games played = 100 + 50 = 150 games

Choose D.
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by LalaB » Sat Aug 18, 2012 8:32 am
0.8*100+0.5(x-100)=0.7x
x=150
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