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

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.

2005 AMC 10B Problem 3

Answer: D

Difficulty rating: 870

Solution:

Problem 3 in Other Years