BTGModeratorVI wrote: ↑

Tue May 12, 2020 2:21 pm

A team won 50 percent of its first 60 games in a particular season, and 80 percent of its remaining games. If the team won a total of 60 percent of its games that season, what was the total number of games that the team played?

(A) 180
(B) 120
(C) 90
(D) 85
(E) 30

Answer: C
Source: Kaplan

We can treat this question as a WEIGHTED AVERAGES question.

First 60 games: 50% win percentage
Let K = number of remaining games it played (with a win percentage of 80%)

KEY CONCEPT: IF K = 60 (for a total of 120 games), then the team played 60 games with a 50% win percentage and the remaining 60 games with an 80% win percentage. This would make the TOTAL win percentage = (50 + 80)/2 = 65%

We're told that the TOTAL win percentage is actually 60%. Since 60% is closer to 50% than it is to 80%, we can conclude that MORE games were played with a 50% win percentage than were played with an 80% win percentage.
In other words, K < 60.
If K is less than 60, then the TOTAL number of games played all year must be LESS THAN 120.
So, we can ELIMINATE answer choices A and B.

We can also ELIMINATE answer choice E, since it's impossible for the total to be less than 60.

This leaves C and D.
We're going to test ONE answer choice. If it works, we're done. If it doesn't work, then the OTHER answer choice must be correct.

Try C: 90 games in total.
So 60 were played with a 50% win percentage (= 30 wins), and the remaining 30 were played with an 80% win percentage (= 24 wins)
Total wins = 30 + 24 = 54
54 wins out of 90 games = 54/90 = 6/10 = 60% win percentage.
This matches our information, so the answer is C

For more information about weighted averages, see this free video: https://www.gmatprepnow.com/module/gmat- ... /video/805

Cheers,
Brent

BTGModeratorVI wrote: ↑

Tue May 12, 2020 2:21 pm

A team won 50 percent of its first 60 games in a particular season, and 80 percent of its remaining games. If the team won a total of 60 percent of its games that season, what was the total number of games that the team played?

(A) 180
(B) 120
(C) 90
(D) 85
(E) 30

Answer: C

Solution:

The team won 30 of its first 60 games. If we let n = the total number of games in the season, then they won 0.8(n - 60) = 0.8n - 48 of the remaining games. Since they won 60% of all the games:

(30 + 0.8n - 48)/n = 6/10

(0.8n - 18)/n = 3/5

5(0.8n - 18) = 3n

4n - 90 = 3n

n = 90

Answer: C