IMAT 2012 Q29 [Cats and Dogs]

In a street, a survey showed that out of a hundred households 60 had a cat, 40 had a dog, and 20 had neither a cat nor a dog.

How many households had a cat but no dog?

A. 20
B. 50
C. 40
D. 10
E. 30

Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
    Eliminate any non-essential information
  • Draw a picture, graph, or equation
    In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve.

The first thing we want to do is eliminate the households without a cat or dog from the total. We can do this by taking the total number of households minus the number without any cats or dogs.


We want to do this because it leaves us with only houses that have cats, dogs, or both. From this we can calculate cats only.

Cats (60) + Dogs (40) = 100

We have 100 cats and dogs total spread across 80 different households. We can take the difference between the two to find the overlap, meaning which houses have both a cat and a dog.

100 - 80 = 20

So 20 houses have both a cat and a dog.

Finally, we can take this number to find the number of cats only houses.

Total cats - number of cats in a cat and dog home = Households with a cat but no dog


\fcolorbox{red}{grey!30}{Therefore the answer is C, $40$.}