2005 AMC 10B Problem 3

Question

A gallon of paint is used to paint a room. One third of the paint is used on the first day. On the second day, one third of the remaining paint is used. What fraction of the original amount of paint is available to use on the third day?

\dfrac{1}{10}

\dfrac{1}{9}

\dfrac{1}{3}

\dfrac{4}{9}

\dfrac{5}{9}

Answer: D

Concepts:fraction ratio and proportion

Difficulty rating: 870

Small hint:

After day one,

\dfrac23

of the paint remains

Big hint:

On day two,

\dfrac13

of that

\dfrac23

is used

Solution:

After the first day,

1 - \dfrac13 = \dfrac23

of the paint remains.

On the second day,

\dfrac13 \cdot \dfrac23 = \dfrac29

of the original amount is used.

The fraction available on the third day is

\dfrac23 - \dfrac29 = \dfrac49.

Thus, D is the correct answer.