SOLUTION: In a class of 100 students, it is known that 45 study mathematics, 26 study chemistry and 27 study physics. It is known that 19 of the students study both mathematics and chemistry

Question 278348: In a class of 100 students, it is known that 45 study mathematics, 26 study chemistry and 27 study physics. It is known that 19 of the students study both mathematics and chemistry,8 study mathematics and physics , 10 study chemistry and physics, and 3 students study mathematics,chemistry,and physics. How many of these students study only chemistry?
A 0 B 3 C 7 D 16 E not enough information
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Answer should be 0.

Here's why.

a total of 26 study chemistry

out of those 26:

19 also study math so we need to subtract those.
10 also study physics so we need to subtract those.
3 also study math and physics so we need to add those back in because they are being counted twice (once in the math and chemistry group, and once in the chemistry and physics group).

we get a total of:

26 - 19 - 10 + 3 = 29 - 29 = 0

there are 0 people who are just studying chemistry alone.

that would be selection A.

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