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}=30Answer: 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.