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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
[Reveal] Spoiler: OA

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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 9628 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
prashantbacchewar wrote:
Bunuel can we expect 3 overlapping set question on GMAT and are we supposed to know the formula.


I've seen several GMAT questions on 3 overlapping sets, so you should understand the concept behind such kind of problems. Check this for more: formulae-for-3-overlapping-sets-69014.html#p729340
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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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 12 May 2017, 08:57
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] 12 May 2017, 08:57
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