arghya05 wrote:A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4

We are given that a gray pain is obtained by mixing 3 parts of white paint with 5 parts of black paint. We are also given that the paint can be purchased in one or half gallon cans and that the total mixture is 2 gallons. We must determine the minimum number of gallons of paint needed.

Our given ratio is:

w/b = 3/5 = 1.5/2.5 = 0.75/1.25

As we can see, we need to have 0.75 gallons of white paint and 1.25 gallons of black paint in order to have 2 gallons of the mixed (i.e., gray) paint. However, in order to have the 0.75 gallons of white paint, we need to purchase 1 gallon of white paint, and in order to have the 1.25 gallons of black paint, we need to purchase 1.5 gallons of black paint. Thus, we need to purchase a total of 2.5 gallons of paint.

Answer: B