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.

100-20=80

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

60-20=40

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