Percent Problem

[bmcshane]

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?

180

170

156

150

105

[abramson]

I arrived at (D) 150 as my answer. This is how:

80% of 1st 100 games is 80 games won. They then won 50% of remaining games.

Total games won can be represented as: 80 + (0.5)x where 'x' is the remaining games they play.
Total games played = 100 + x

Therefore, (80 + 0.5x) / (100+x) is proportion of games won out of total games played.

Since we know this is 70%, equate the above with 0.7 or 7/10 (easier to cross-multiply), and arrive at x = 50.

Therefore, total games played = 100+x = 100+50 = 150.

Hope this helps!

[GMAT 2007]

Assume total no. of games be 'x'

(80% of 100) + 50% of remaning = 70% of all

0.8*100 + 0.5(x-100) = 0.7x

Solve for x, x = 150

GMAT 2007

[bmshane]

That helps, thank you.