Thread: Logic Word Problem w/ Ans.

This one is giving me a hard time

In a large high school, some teachers teach only 1 subject, and some teachers teach more than 1 subject. Using the information given in the table below about the math, science, and gym teachers in the school, how many teachers teach math only?

12 taught at least 1 class of math
10 taught at least 1 class of gym
20 taught at least 1 class of science
6 taught both gym and science but not math
5 taught both math and science but not gym
2 taught gym only
1 taught math, gym, and science


The answer is 5 but how??? Can someone help me figure this one out please, is there a way to make a table or something to display what's going on?

Have you tried making a Venn Diagram?

Originally Posted by snowtea

Have you tried making a Venn Diagram?

I have tried it but I seem to be getting mixed up with the overlapping and values

The trick with the Venn Diagram is to go from inside out, and never have overlapping values.

I'll show you how to fill in the parts that intersect with the Gym circle.
The Gym circle is decomposed into 4 parts:
People who teach everything (GSM),
People who teach only gym and science (GS),
People who teach only gym and math (GM),
People who teach only gym (G)

You can fill in 1 for GSM right away.
Similarly you can fill in 6 for GS and 2 for G.

10 people teach gym means GSM + GS + GM + G = 10
from what we have earlier, we can solve GM = 1

And we have filled in all the parts that have to do with gym.

Can you do the rest?

I understand the gym part but I don't know how to relate it to the rest of the problem and what to subtract

Ok, lets do the Science part: S, MS, GS, MGS

From before, we already know
MGS = 1
GS = 6

From the problem we also know MS = 5

20 taught science, so
S + MS + GS + MGS = 20
We can solve S = 8

Now, I have told you
MGS = 1, MS = 5, and MG = 1 (from the previous post)

M + MS + MG + MGS = ? (hint 12 taught at least 1 class of math)

M is the number of people only teaching math