Bunuel wrote:
A painter wishes to paint a house turquoise. To make the color, he selects an eggshell primer made up of 70% pure-white color, and combines it with a blue base coat in order to create a turquoise color made up of 75% pure-white. How many quarts from the blue base coat should be mixed to make enough turquoise to paint the house?
(1) It will take 300 quarts of paint to cover the house.
(2) The blue base-coat is made up of 90% pure-white color.
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:The correct response is (C).
To find the amount of quarts of blue base, we need to find the ratio between the two components of the mixture: eggshell primer and blue-base. This is given to us in the second statement. We’ll also need to know how much total paint is needed in quarts to find what percent of that total would come from the blue-base coat. This is provided in the first statement. Since this is a Data Sufficiency problem, we don’t need to waste valuable time actually solving. However, if you wanted to check, here’s how:
Eggshell Primer: 70% white
Turquoise Color: 75% white
Blue Base Coat: 90% white
75%-70% = 5%
90% - 75% = 15%
5%/15 % = 1/3 is the ratio of the parts.
Blue Base Coat = 1/4∗300=75 quarts (67.5 white quarts)
Eggshell Primer = 3/4∗300=225 quarts (157.5 white quarts)
To double-check: 67.5 + 157.5 = 225. 225/300 = 75 % white.
Where did you get 1/4 from? Shouldn't it be 1/3 along with the ratio of the parts?