In a football club, \(\frac{1}{4} \text{th}\) of the players

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

In a football club, \(\frac{1}{4} \text{th}\) of the players

by swerve » Mon Dec 16, 2019 5:22 pm

In a football club, \(\frac{1}{4} \text{th}\) of the players are capped players and the remaining are uncapped players. Half of the capped players and all the uncapped players are defenders. If there are 36 players, in the club, who are uncapped, then what is the number of players, in the club, who are not defenders?

A. 3
B. 6
C. 9
D. 12
E. 18

The OA is B

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Mon Dec 16, 2019 5:22 pm

dsan6422: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Dec 12, 2019 4:55 pm

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by dsan6422 » Mon Dec 16, 2019 5:37 pm

Assuming that the total number of players = x
then (1/4) x are capped
and the remaining (3/4)x are uncapped

half of the capped & all the uncapped are defenders. --> 1/2(1/4)x + 3/4x = Defenders
----> Number of Defenders = (1/8+3/4)x = 7/8 x

IF number of uncapped = 3/4 x = 36 --> x=48
therefore, the number of defenders = 7/8 x = 7/8 (48) = 42
And the number of players who are not defenders = x -42= 48-42= 6

Answer: B

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by Scott@TargetTestPrep » Sat Dec 21, 2019 7:21 pm

swerve wrote:In a football club, \(\frac{1}{4} \text{th}\) of the players are capped players and the remaining are uncapped players. Half of the capped players and all the uncapped players are defenders. If there are 36 players, in the club, who are uncapped, then what is the number of players, in the club, who are not defenders?

A. 3
B. 6
C. 9
D. 12
E. 18

The OA is B

Source: e-GMAT

We see that the uncapped players comprise 3/4 of the total number of players in the club. Since there are 36 playes, the total number of players in the club is 36 / (3/4) = 36 x 4/3 = 12 x 4 = 48. That means 1/4 x 48 = 12 players are capped players. Since 1/2 x 12 = 6 of these 12 capped players (and all the uncapped players) are defenders, the remaining 6 capped players are not defenders.

Answer: B

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