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# Among 100 students in a college, 50 students play soccer, 40 students

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Manager
Joined: 25 Dec 2018
Posts: 225
Location: India
Concentration: General Management, Finance
GMAT 1: 590 Q48 V23
GPA: 3.4
WE: Engineering (Consulting)
Among 100 students in a college, 50 students play soccer, 40 students  [#permalink]

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14 Apr 2019, 07:43
1
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:33) correct 39% (02:52) wrong based on 23 sessions

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Among 100 students in a college, 50 students play soccer, 40 students play hockey and 60 students play tennis. If each student plays at least 1 sport and the number of students who play exactly 2 sports is not less than 3 times the number of students who play all the 3 sports, what is the maximum number of students who play all the three sports?

A. 8
B. 10
C. 15
D. 25
E. 50
Math Expert
Joined: 02 Aug 2009
Posts: 7560
Among 100 students in a college, 50 students play soccer, 40 students  [#permalink]

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14 Apr 2019, 19:20
mangamma wrote:
Among 100 students in a college, 50 students play soccer, 40 students play hockey and 60 students play tennis. If each student plays at least 1 sport and the number of students who play exactly 2 sports is not less than 3 times the number of students who play all the 3 sports, what is the maximum number of students who play all the three sports?

A. 8
B. 10
C. 15
D. 25
E. 50

Let the number of students playing exactly 2 and 3 games be x and y...and $$x\geq{3y}$$..
The formula would give us the equation..
100=50+60+40-x-2y....x+2y=50.......We have added two times twice and three times thrice when we add all three 50+60+40, so we subtract X once and y twice
We are trying to maximize y, so take least value of x, that is 3y..
So 3y+2y=50....y=10

B
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Among 100 students in a college, 50 students play soccer, 40 students   [#permalink] 14 Apr 2019, 19:20
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