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Min/Max Problems, Word Problems

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by swerve » Thu Jul 02, 2020 5:41 am
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A certain basketball team that has played 2/3 of its games has a record of 17 wins and 3 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 all of its games?

A. 7
B. 6
C. 5
D. 4
E. 3

The OA is D

Source: Manhattan Prep
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Re: Min/Max Problems, Word Problems

by Brent@GMATPrepNow » Thu Jul 02, 2020 10:09 am
swerve wrote: ↑
Thu Jul 02, 2020 5:41 am
 A certain basketball team that has played 2/3 of its games has a record of 17 wins and 3 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 all of its games?

A. 7
B. 6
C. 5
D. 4
E. 3

The OA is D

Source: Manhattan Prep
Given:
The team has played 2/3 of its games. The team has played 20 games.
If 2/3 of the total number of games = 20, then the total number of games = 30.
This means that there are 10 games remaining.


We want the team to win at least 3/4 of its games.
3/4 of 30 = 22.5
So, in order to win at least 3/4 of the games, the team must win a total of 23 games or more.

The team has already won 17 games, so it needs to win at least 6 of the remaining 10 games.
Or we can say that the team can lose 4 games at most.

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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