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

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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?

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 [ 9.43 KiB | Viewed 10576 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}.

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 _________________

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

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12 May 2017, 08:57

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

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25 Jul 2017, 01:38

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?

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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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}.