A survey of 136 pet owners yielded the following information: 47 own fish; 51 ow

Question

A survey of 136 pet owners yielded the following information: 47 own fish; 51 own a bird; 50 own a cat; 64 own a dog; 2 own all four; 11 own only fish; 14 own only a bird; 10 own fish and a bird; 21 own fish and a cat; 24 own a bird and a dog; 27 own a cat and a dog; 3 own fish, a bird, a cat, and no dog; 1 owns fish, a bird, a dog, and no cat; 9 own fish, a cat, a dog, and no bird; and 10 own a bird, a cat, a dog, and no fish. How many of the surveyed pet owners have no fish, no birds, no cats, and no dogs? (They own other types of pets.)

Explanation / Answer

The hardest part is drawing the diagram! Fortunately, an internet search for venn diagram 4 circles gives you a good option.

The next hard part is order. Always start in the middle and work out.

I started with 2 own all., Then the two that only own ___. Then Filled in the 4 areas for Owns A, B, C but not D.

With the info such as "10 own a fish and a bird" remember that this includes Fish Bird Dog, Fish Bird Cat and Fish Bird Dog Cat. So be sure to subtract out this overlap.

Finally use the total numbers for each animal, eg 47 own fish, to fill in missing holes. Again, 47 is the total for the ENTIRE fish circle, so subtract the overlap.

Finally, once it is all filled in, you sum this and subtract from the total of 136.

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