Expert: Steve Holleran - 12/12/2007

Question
in a local high school, there are 100 students in grade 11.Each student takes at least one of the three sciences: biology,physics, and chemistry. Of the 50 students taking biology, 14 students also take physics and 32 students also take chemistry. Of the 30 students taking physics, 16 also take chemistry. there are 10 students who take all three sciences.



how many students take only chemistry?



how many students take biology or chemistry, but not physics?

Answer
Hi Anna,

Tough to draw venn diagrams, which is what you need to solve this.

If you draw a 3-circle venn diagram, in the center overlap of all three you have a 10.  Then in the part common to the P and B circles you have 4.  Then in the part common to the B and C circles you have 22.  In the part common to the P
and C circles you have 6.  

Okay, then the remaining part of the B circle is 14, the remaining part of P is 10 and the remaining part of C is 34.

So  :   34 take only chemistry

       34+22+14 = 70 take bio or chem but not physics.  This is counting the kids who take both Bio and chem.

Hope this helps
Steve