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There are 150 students at Seward High School. 66 students

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There are 150 students at Seward High School. 66 students  [#permalink]

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New post 14 Dec 2010, 07:23
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There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?

A. 0
B. 27
C. 30
D. 99
E. 78
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Re: Venn Diagram  [#permalink]

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New post 14 Dec 2010, 07:58
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saurabhgoel wrote:
There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?
A) 0
B) 27
C) 30
D) 99
E) 78


Please help to understand the approach to tackle the venn diagram problems !!!


150 = {baseball} + {basketball} + {soccer} - {exactly 2 sports} - 2*{exactly 3 sports} + {none of the ports}:

150 = 66 + 45 + 42 - 27 - 2*3 + {none of the ports} --> {none of the ports}=30

Answer: C.

Look at the diagram:
Attachment:
untitled.PNG
untitled.PNG [ 9.43 KiB | Viewed 12508 times ]
When we sum {baseball} + {basketball} + {soccer} we count students who play exactly 2 ports (yellow section) twice, so to get rid of double counting we are subtracting {exactly 2 sports} once.

Similarly when we sum {baseball} + {basketball} + {soccer} we count students who play exactly 3 ports (blue section) thrice (as it is the portion of all three groups), so to count this group only once we are subtracting 2*{exactly 3 sports}.

For more on this check: formulae-for-3-overlapping-sets-69014.html#p729340

Hope it helps.
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Re: Venn Diagram  [#permalink]

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New post 15 Dec 2010, 10:22
great explanation using venn diagram +1
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Re: Venn Diagram  [#permalink]

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New post 16 Dec 2010, 01:49
Bunuel can we expect 3 overlapping set question on GMAT and are we supposed to know the formula.
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Re: Venn Diagram  [#permalink]

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New post 16 Dec 2010, 05:24
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Re: There are 150 students at Seward High School. 66 students  [#permalink]

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New post 11 Jun 2013, 08:24
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65

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Re: There are 150 students at Seward High School. 66 students  [#permalink]

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New post 25 Jul 2017, 01:25
Hi you try doing question 203 in OG 17 the same way? there the 2*aandband c is not working Bunuel
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Re: There are 150 students at Seward High School. 66 students  [#permalink]

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New post 25 Jul 2017, 01:32
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Re: There are 150 students at Seward High School. 66 students  [#permalink]

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New post 25 Jul 2017, 01:38
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saurabhgoel wrote:
There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?

A. 0
B. 27
C. 30
D. 99
E. 78


150 = 66+45+42 - 27 - 6 + x
x= 30

C
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Re: There are 150 students at Seward High School. 66 students  [#permalink]

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New post 25 Jul 2017, 01:52
Hi Bunuel thanks a lot can question 132 be tackled the same way?
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Re: There are 150 students at Seward High School. 66 students  [#permalink]

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New post 25 Jul 2017, 01:56
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Re: There are 150 students at Seward High School. 66 students  [#permalink]

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New post 26 Jul 2017, 16:33
saurabhgoel wrote:
There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?

A. 0
B. 27
C. 30
D. 99
E. 78


We can create the following equation:

Total students = # who play baseball + # who play basketball + # who play soccer - # who play exactly two - 2(# who play all 3) + # who play neither

150 = 66 + 45 + 42 - 27 - 2(3) + n

150 = 120 + n

n = 30

Answer: C
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Re: There are 150 students at Seward High School. 66 students  [#permalink]

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New post 11 Aug 2017, 19:28
Bunuel wrote:
saurabhgoel wrote:
There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 27 students play exactly two sports, and three students play all three of the sports. How many of the 150 students play none of the three sports?
A) 0
B) 27
C) 30
D) 99
E) 78


Please help to understand the approach to tackle the venn diagram problems !!!


150 = {baseball} + {basketball} + {soccer} - {exactly 2 sports} - 2*{exactly 3 sports} + {none of the ports}:

150 = 66 + 45 + 42 - 27 - 2*3 + {none of the ports} --> {none of the ports}=30

Answer: C.

Look at the diagram:
Attachment:
untitled.PNG
When we sum {baseball} + {basketball} + {soccer} we count students who play exactly 2 ports (yellow section) twice, so to get rid of double counting we are subtracting {exactly 2 sports} once.

Similarly when we sum {baseball} + {basketball} + {soccer} we count students who play exactly 3 ports (blue section) thrice (as it is the portion of all three groups), so to count this group only once we are subtracting 2*{exactly 3 sports}.


Hope it helps.


Why it is necessary to subtract the 3 twice?
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Re: There are 150 students at Seward High School. 66 students  [#permalink]

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New post 21 Sep 2018, 05:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: There are 150 students at Seward High School. 66 students   [#permalink] 21 Sep 2018, 05:28
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