1. ## Venn Diagram Question!

In a certain class 12 students are interested in Mathematics, 16 are interested in Chemistry and 21 are interested in Physics. 5 are interested in Mathematics and Chemistry, 8 are interested in mathematics and Physics, 12 in Physics and Chemistry and 3 in all the three subjects. How many are there in the class who show interest either in mathematics or physics or chemistry?

I'm new here and will introduce myself later, but now I'm in a mad rush - TIA!

2. Originally Posted by merenwen
In a certain class 12 students are interested in Mathematics, 16 are interested in Chemistry and 21 are interested in Physics. 5 are interested in Mathematics and Chemistry, 8 are interested in mathematics and Physics, 12 in Physics and Chemistry and 3 in all the three subjects. How many are there in the class who show interest either in mathematics or physics or chemistry?

I'm new here and will introduce myself later, but now I'm in a mad rush - TIA!
Since there are 3 students who are interested in all subjects, there are only 2 (5 - 3)students who are interested in math and chemistry but not physics. Similarly, there are 5 (8 - 3) students who are interested in math and physics but not chemistry, and 9 (12 - 3) students who are interested in physics and chemistry but not math. This means that there are only 2 students who are only interested in math (12 - 3 - 2 - 5), 2 students who are only interested in chemistry (16 - 3 - 2 - 9), and 4 students who are only interested in physics (21 - 3 - 5 - 9). That gives us a total of:

3 all + 2 C&M only + 5 M&P only + 9 C&P only + 2 M only + 2 C only + 4 P only = 27 students.

3. Originally Posted by icemanfan
Since there are 3 students who are interested in all subjects, there are only 2 (5 - 3)students who are interested in math and chemistry but not physics. Similarly, there are 5 (8 - 3) students who are interested in math and physics but not chemistry, and 9 (12 - 3) students who are interested in physics and chemistry but not math. This means that there are only 2 students who are only interested in math (12 - 3 - 2 - 5), 2 students who are only interested in chemistry (16 - 3 - 2 - 9), and 4 students who are only interested in physics (21 - 3 - 5 - 9). That gives us a total of:

3 all + 2 C&M only + 5 M&P only + 9 C&P only + 2 M only + 2 C only + 4 P only = 27 students.
OMG you are AWESOME! It's really mortifying that I couldn't do that on my own - I used to be able to

Why isn't Math like riding a bicycle? I actually DID forget everything I learned!