2012 AMC 10A Problem 5

Question

Last year

100

adult cats, half of whom were female, were brought into the Smallville Animal Shelter. Half of the adult female cats were accompanied by a litter of kittens. The average number of kittens per litter was

4.

What was the total number of cats and kittens received by the shelter last year?

150

200

250

300

400

Answer: B

Concepts:fraction mean

Difficulty rating: 870

Small hint:

Half the adult cats are female, and half of those have litters

Big hint:

Multiply the number of litters by the average litter size

Solution:

We have that there are

100 \div 2 = 50

female cats. We then have that

50 \div 2 = 25

cats that have kittens.

Since the average number of kittens per litter is

4,

the total number of kittens is

4 \cdot 25 = 100.

The total number of cats and kittens is then

100 + 100 = 200.

Thus, B is the correct answer.