Question 940084
{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,w),locate(1.5,1.7,y),locate(-3.7,-1,z), locate(-3.6,2.5,A), locate(-.1,1.8,x),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,B)
 )}}}
<pre>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.

{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,w),locate(1.5,1.7,y),locate(-3.7,-1,z), locate(-3.6,2.5,A), locate(-.2,1.8,50),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,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: 

{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,350),locate(1.5,1.7,y),locate(-3.7,-1,z), locate(-3.6,2.5,A), locate(-.2,1.8,50),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,B)
 )}}}

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:

{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,350),locate(1.5,1.7,150),locate(-3.7,-1,z), locate(-3.6,2.5,A), locate(-.2,1.8,50),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,B)
 )}}}
 
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</pre>