During a certain season

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

During a certain season

by BTGmoderatorDC » Tue Nov 21, 2017 2:39 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

Can some Experts explain the computation of this problem?

OA D

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Source: Beat The GMAT — Problem Solving | Tue Nov 21, 2017 2:39 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Nov 21, 2017 3:56 pm

lheiannie07 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

If we let G = the TOTAL number of games played in the ENTIRE SEASON, then ...
G - 100 = the number of games REMAINING after the first 100 have been played

We can now start with a "word equation":
(# of wins in 1st 100 games) + (# of wins in remaining games) = (# of wins in ENTIRE season)
We get: (80% of 100) + (50% of G-100) = 70% of G
Rewrite as 80 + 0.5(G - 100) = 0.7G
Expand: 80 + 0.5G - 50 = 0.7G
Simplify: 30 = 0.2G
Solve: G = 150

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

by BTGmoderatorDC » Wed Jan 17, 2018 9:21 pm

Brent@GMATPrepNow wrote:
lheiannie07 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
If we let G = the TOTAL number of games played in the ENTIRE SEASON, then ...
G - 100 = the number of games REMAINING after the first 100 have been played

We can now start with a "word equation":
(# of wins in 1st 100 games) + (# of wins in remaining games) = (# of wins in ENTIRE season)
We get: (80% of 100) + (50% of G-100) = 70% of G
Rewrite as 80 + 0.5(G - 100) = 0.7G
Expand: 80 + 0.5G - 50 = 0.7G
Simplify: 30 = 0.2G
Solve: G = 150

Answer: D

Cheers,
Brent

Thanks a lot!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Jan 20, 2018 6:25 am

lheiannie07 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

We are first given that a team won 80 percent of its first 100 games. This means the team won 0.8 x 100 = 80 games out of its first 100 games.

We are next given that the team won 50 percent of its remaining games. If we use variable T to represent the total number of games in the season, then we can say T - 100 equals the number of remaining games in the season. Thus we can say:

0.5(T - 100) = number of wins for remaining games

0.5T - 50 = number of wins for remaining games

Lastly, we are given that team won 70 percent of all games played in the season. That is, they won 0.7T games in the entire season. With this we can set up the equation:
Number of first 100 games won + Number of games won for remaining games = Total Number of games won in the entire season

80 + 0.5T - 50 = 0.7T

30 = 0.2T

300 = 2T

150 = T

Answer: D

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