SOLUTION: Out of 500 car owners investigated, 400 owned car A and 200 owned car B, 50 owned both A and B. Is this data correct? Explain.

The red circle represents all the car owners that own car A.
The red circle is made up of region w and region x.

The blue circle represents all the car owners that own car B.
The blue circle is made up of region x and region y.

So you see that region x is part of both circle A and B.
Region w is part of circle A but it is NOT part of circle B.
Region y is part of circle B but it is NOT part of circle A.

Therefore 

Region x represents the 50 car owners that own both cars
A and B.  
Region w represents the car owners that own car A but DO NOT
own car B.
Region y represents the car owners that own car B but DO NOT
own car A.
Region z (the area outside the circles but inside the rectangle.

Region z represents the car owners that DO NOT own car A and
also DO NOT own car B.

Therefore we will put the number 50 for region x, since 50 own
both car A and car B.



We are told that 400 owned car A, and the region that contains 50
is part of circle A, so the remaining 400-50=350 that are in circle
A go in region w, so we put 350 in region w: 



We are told that 200 owned car B, and the region that contains 50
is part of circle B, so the remaining 200-50=150 that are in circle
B go in region y, so we put 150 in region y:


 
Now we see that something is wrong, because we were told that
there were only 500 car owners investigated and we already
have 350+50+150 = 550.  So the data we are given is contradictory.

Edwin