SAT Question of the day Nov 26 2012

In a community of 416 people, each person owns a dog or a cat or both. If there are 316 dog owners and 280 cat owners, how many of the dog owners own no cat?

A.  click to choose answer A   36

B.  click to choose answer B   100

C.  click to choose answer C   136

D.  click to choose answer D   180

E.  click to choose answer E   316

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


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