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In a school of 150 students, 100 play cricket, 90 play football, 80 pl

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In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   20 May 2018, 02:20
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In a school of 150 students, 100 play cricket, 90 play football, 80 play hockey. Every student plays at least one sport. If 20 students play only football, what is the maximum number of students who play both cricket and hockey but not football?
A) 30
B) 40
C) 50
D) 60
E) 70
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C
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   20 May 2018, 11:35
I could pick up numbers, and the max = 50. Can someone elaborate the solution, thanks.
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   20 May 2018, 18:58
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As Every student plays at least one sport, that means union of students playing Football, Cricket & Hockey = 150.
Conventional Approach : Using Venn diagram
Attachment:
WhatsApp Image 2018-05-21 at 07.24.09.jpeg
WhatsApp Image 2018-05-21 at 07.24.09.jpeg [ 119.21 KiB | Viewed 13498 times ]
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   20 May 2018, 19:05
Expert Reply
This Question can be done easily using Line diagram approach:
1) First we need to restrict the two parallel lines indicating the union of students.
2) Mark the Students who play Cricket.
3) Mark the students who play Football.
4) This is the most crucial step, mark the students who play Hockey such that the condition that students playing only Football is 20.
Try to get the maximum overlap of Cricket & Hockey only (no overlap of Football).
Attachment:
WhatsApp Image 2018-05-21 at 07.25.01.jpeg
WhatsApp Image 2018-05-21 at 07.25.01.jpeg [ 61.53 KiB | Viewed 13058 times ]

With some practice this method will be much easier than the conventional approach.
Happy Learning. :angel:
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   29 May 2018, 04:21
gmatbusters wrote:
As Every student plays at least one sport, that means union of students playing Football, Cricket & Hockey = 150.
Conventional Approach : Using Venn diagram
Attachment:
https://gmatclub.com/chat Image 2018-05-21 at 07.24.09.jpeg



Hi,

Can you please explain how did you arrive at "100+20+80-b-d=150"

Thanks!
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   29 May 2018, 06:22
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Hi
As we know the union means students playing at least one of the game = 150.
Add all the terms in the Venn diagram will be union = 150
So, 100-(a+b+d)+a+20+b+d+c+80-(b+d+c) =150
Simplifying, we get 100+20+80-b-d=150

Hope it is clear now.

ajtmatch wrote:
gmatbusters wrote:
As Every student plays at least one sport, that means union of students playing Football, Cricket & Hockey = 150.
Conventional Approach : Using Venn diagram
Attachment:
https://gmatclub.com/chat Image 2018-05-21 at 07.24.09.jpeg



Hi,

Can you please explain how did you arrive at "100+20+80-b-d=150"

Thanks!
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   10 Jun 2018, 05:50
Why isn't the answer 60? Why have we only given 50 at the start in Hockey, instead of 60?
Bunuel Can you please clarify?

gmatbusters wrote:
This Question can be done easily using Line diagram approach:
1) First we need to restrict the two parallel lines indicating the union of students.
2) Mark the Students who play Cricket.
3) Mark the students who play Football.
4) This is the most crucial step, mark the students who play Hockey such that the condition that students playing only Football is 20.
Try to get the maximum overlap of Cricket & Hockey only (no overlap of Football).
Attachment:
https://gmatclub.com/chat Image 2018-05-21 at 07.25.01.jpeg

With some practice this method will be much easier than the conventional approach.
Happy Learning. :angel:
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GMATBusters
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   10 Jun 2018, 06:08
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Hi vikassriv14

If u see the line diagram , you can see if we extend 60 for overlap of Cricket and Hockey, we can't achieve 20 students for on;y Football. This is the constraint for this problem.
for meeting all the conditions of the problem, 50 is the maximum numbers of students who play Cricket & hockey but not football.
Attachment:
Screenshot002.jpg
Screenshot002.jpg [ 53.79 KiB | Viewed 12013 times ]

vikassriv14 wrote:
Why isn't the answer 60? Why have we only given 50 at the start in Hockey, instead of 60?
Bunuel Can you please clarify?

gmatbusters wrote:
This Question can be done easily using Line diagram approach:
1) First we need to restrict the two parallel lines indicating the union of students.
2) Mark the Students who play Cricket.
3) Mark the students who play Football.
4) This is the most crucial step, mark the students who play Hockey such that the condition that students playing only Football is 20.
Try to get the maximum overlap of Cricket & Hockey only (no overlap of Football).
Attachment:
The attachment https://gmatclub.com/chat Image 2018-05-21 at 07.25.01.jpeg is no longer available

With some practice this method will be much easier than the conventional approach.
Happy Learning. :angel:
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In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   27 Aug 2020, 23:09
Given: In a school of 150 students, 100 play cricket, 90 play football, 80 play hockey. Every student plays at least one sport.
Asked: If 20 students play only football, what is the maximum number of students who play both cricket and hockey but not football?

Cricket ----------100---------------|No cricket -------50----------|
No Football------60----------|Football------------90--------------|
Hockey ------50--------|--------|Hockey----30--|No Hockey 20-|

IMO C
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   28 Aug 2020, 10:18
Kinshook wrote:
Given: In a school of 150 students, 100 play cricket, 90 play football, 80 play hockey. Every student plays at least one sport.
Asked: If 20 students play only football, what is the maximum number of students who play both cricket and hockey but not football?

Cricket ----------100---------------|No cricket -------50----------|
No Football------60----------|Football------------90--------------|
Hockey ------50--------|--------|Hockey----30--|No Hockey 20-|

IMO C


Hello sir,
I understood till no football ... football. But I didn't get how you calculated the hockey part. Can you please elaborate it ?
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   28 Aug 2020, 10:20
This is the approach.

GMATBusters wrote:
This Question can be done easily using Line diagram approach:
1) First we need to restrict the two parallel lines indicating the union of students.
2) Mark the Students who play Cricket.
3) Mark the students who play Football.
4) This is the most crucial step, mark the students who play Hockey such that the condition that students playing only Football is 20.
Try to get the maximum overlap of Cricket & Hockey only (no overlap of Football).
Attachment:
https://gmatclub.com/chat Image 2018-05-21 at 07.25.01.jpeg

With some practice this method will be much easier than the conventional approach.
Happy Learning. :angel:
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gmatter923
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink] New post   29 Aug 2020, 11:50
GMATBusters wrote:
In a school of 150 students, 100 play cricket, 90 play football, 80 play hockey. Every student plays at least one sport. If 20 students play only football, what is the maximum number of students who play both cricket and hockey but not football?
A) 30
B) 40
C) 50
D) 60
E) 70


Okay, So I approached it with the conventional set theory.

I reached at the final equation, which was :

(student who plays all [common to all 3 sets] + plays both cricket & hockey but not football [we have to find max of this value] ) = 50

So, my question is, in order to find the max number , should we assume that none of the students play all the games?
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl [#permalink]
29 Aug 2020, 11:50
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