Problem Solving

Hi all,

Can anyone please explain what to do with the "no condition"(in bold) in the problem? Why three is being subtracted from Radio and power windows union in the venn diagram? (see the attachment). Is it 3 because only 3 cars had all 3 options or this 3 is coming from some where else?

Searched yahoo and this forum, but found no explanation.

Thanks in advance.
Here is the problem.


A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options: air conditioning, radio and power windows were already installed. The survey found:


15 had air conditioning
11 had power windows
12 had radio
3 had all three options.
2 had air conditioning and power windows but no radios
6 had air conditioning and radio but no power windows
4 had radio and power windows


What is the number of cars that had none of the options?
a. 1
b. 2
c. 3
d. 4
e. 5

[spoiler]ans: B[/spoiler]

You need to add all 3 main options and then subtract the overlaps.

Air 25, Radio 12, Power Windows 11 = 38. Now subtract each overlapping option air+radio 6, air+pw 2, pw+radio 4, all options 3 = 38-15=23.

Now the total # of cars is 25-23=2

2 is the answer.

The 3 is from the overlap of all option, which you must use to subtract from the total.