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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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14 Dec 2010, 06:23
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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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Kudos if any of my post helps you !!!

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14 Dec 2010, 06:58
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Expert's post
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 = {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

Look at the diagram:
Attachment:

untitled.PNG [ 9.43 KiB | Viewed 9323 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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15 Dec 2010, 09:22
great explanation using venn diagram +1
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16 Dec 2010, 00:49
Bunuel can we expect 3 overlapping set question on GMAT and are we supposed to know the formula.
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16 Dec 2010, 04:24
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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11 Jun 2013, 07:24
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:
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] 11 Jun 2013, 07:24
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# There are 150 students at Seward High School. 66 students

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