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30 Nov 2021, 09:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (01:51) correct
34%
(01:50)
wrong
based on 137
sessions
History
Date
Time
Result
Not Attempted Yet
In a certain football league of 240 players, 100 players are right-footed, and 150 players are male. If at least 25 female players are left-footed, what is the maximum number of right-footed male players?
(A) 35
(B) 50
(C) 85
(D) 100
(E) 115
(A) 35
(B) 50
(C) 85
(D) 100
(E) 115
30 Nov 2021, 10:56
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Bunuel
One approach is to use the Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of football players, and the two characteristics are:
- male or female
- left-footed or right-footed
So we can set up our matrix as follows:
Notice that I used 25+ to represent the fact that there are AT LEAST 25 left-footed female players.
First recognize that we have a total of 100 right-footed players (male and female)
In order to maximize the number of right-footed male players, we must minimize the number of right-footed female players.
Since 0 is the minimum possible number of right-footed female players, we can let 0 equal the number of right-footed female players, which means there are 90 left-footed female players:
When we complete the matrix, we get:
This means there can be a maximum of 100 right-footed male players
Answer: D
This question type is VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch this video:
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