In a community of people, each person owns a dog or a cat or both. If there are dog owners and cat owners, how many of the dog owners own no cat?
A typical time consuming question. Several ways to solve. The one I like uses the Venn-diagram.
On the left there are the dog-only owners (red) on the right are the cat-only owners (yellow) in the middle are those who own both a dog and a cat (orange).
If you add up the dog owners (I have a dog) and the cat owners (I have a cat) you count those who have both a dog and a cat twice (because you count them once when they say “I have a dog” and another time because they will tell you they have a cat). That means the orange population is the sum of dog owners plus cat owners minus the total: (280 +316) – 416 = 316- 416 + 280 = -100+280 = 180
Now – please remember to READ THE QUESTION because we were asked to find how many people own a dog only (red) and not how many own a dog and a cat ! (our X is not the final answer !).
All we have to do is subtract the dog+cat owners from the “have a dog” population: 316-180= 136 people