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

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Senior DS Moderator
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In a school of 150 students, 100 play cricket, 90 play football, 80 pl  [#permalink]

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20 May 2018, 01:20
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5
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Difficulty:

95% (hard)

Question Stats:

44% (03:12) correct 56% (02:41) wrong based on 69 sessions

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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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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl  [#permalink]

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20 May 2018, 10:35
I could pick up numbers, and the max = 50. Can someone elaborate the solution, thanks.
Senior DS Moderator
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl  [#permalink]

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20 May 2018, 17:58
1
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 [ 119.21 KiB | Viewed 1470 times ]

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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl  [#permalink]

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20 May 2018, 18:05
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 [ 61.53 KiB | Viewed 1451 times ]

With some practice this method will be much easier than the conventional approach.
Happy Learning.
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl  [#permalink]

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29 May 2018, 03:21
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:
WhatsApp 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!
Senior DS Moderator
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Posts: 1118
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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl  [#permalink]

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29 May 2018, 05:22
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:
WhatsApp 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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Posts: 2
Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl  [#permalink]

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10 Jun 2018, 04:50
Why isn't the answer 60? Why have we only given 50 at the start in Hockey, instead of 60?

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:
WhatsApp Image 2018-05-21 at 07.25.01.jpeg

With some practice this method will be much easier than the conventional approach.
Happy Learning.
Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1118
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl  [#permalink]

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10 Jun 2018, 05:08
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 [ 53.79 KiB | Viewed 1143 times ]

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

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 WhatsApp 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.

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Re: In a school of 150 students, 100 play cricket, 90 play football, 80 pl &nbs [#permalink] 10 Jun 2018, 05:08
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