2001 CEMC Gauss (Grade 8) Problems/Problem 11

Problem

In a class of $25$ students, each student has at most one pet. Three-fifths of the students have cats, $20\%$ have dogs, three have elephants, and the other students have no pets. How many students have no pets?

$\text{ (A) }\ 5 \qquad\text{ (B) }\ 4 \qquad\text{ (C) }\ 3 \qquad\text{ (D) }\ 2 \qquad\text{ (E) }\ 1$

Solution 1

Because each student has at most one pet, we know that there cannot be any students with multiple pets. For example, a student in the class that owns a cat cannot own an elephant or a dog. We can also let $n$ be the number of students that don't own pets.

$\frac{3}{5}$ of the students own cats, so $\frac{3}{5} \times 25 = 15$ own cats.

$20\%$ of the students own dogs, so $20\% \times 25 = \frac{1}{5} \times 25 = 5$ own dogs.

We can now set up an equation involving $n$ and the other values:

$n + 15 + 5 + 3 = 25$

$n + 23 = 25$

$n = \boxed {\textbf {(D) } 2}$

~anabel.disher

2001 CEMC Gauss (Grade 8) (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
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CEMC Gauss (Grade 8)