A team won 50 percent of its first 60 games in a particular season, an

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 our free video: https://www.gmatprepnow.com/module/gmat- ... /video/805

Cheers,
Brent

KAPLAN OFFICIAL SOLUTION:

Since we want to work backwards to solve this problem, let’s start by considering our answer choices. Option (E) can be eliminated right away. Since we know that the team has already played 60 games, it is impossible for the team to play 30 games in total.

Next we need to decide which answer choice to assess first. Your best bet is to start with either choice (B) or (C), because, for example, if we test (B) and find it is too small, we know (A) is the answer without any additional work. Similarly, if we test (C) and it is too big, (D) must be the answer. When deciding between (B) and (C), we should go with the option that looks as if it will be easier, in this case that is (C), because it is smaller.

From the question stem, we know that the team won 50% of its first 60 games, which is 30 games. Choice (C) tells us that the team played 90 games, 60% of which it won. That means that the team won 54 games. To find this quickly, determine 10% of 90, which is 9, and multiply by 6.

In order to find how many of those 54 games were won after the first 60 games, subtract 30 from 54, which gives us 24. Thus, we know that during its remaining games, the team won 24 games. Additionally, we know that after the first 60 games, the team played 30 more games, which we found by subtracting 60 from 90.

Now we need to see if the team won 80% of its final 30 games. To determine this set up the fraction of games won over games played, which is 24/30. Simplify this to 4/5 and convert to a percent. 4/5 = 80/100 = 80%. Since this is the percent of remaining games won the question stem wants us to reach, we know that (C) must be the correct answer.

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

No fuss, I have use two equations:

3/5 X = 30 + 4/5 Y

X = 60 + Y, then solve for X, X = 90 games

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