AbeNeedsAnswers wrote:A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. If exactly 1 gallon of blue paint and 3 gallons of red paint were used, how many gallons of green paint were used?
(1) x = y
(2) z = 60
D
Source: Official Guide 2020
Target question: How many gallons of green paint were used?
Given: A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. 1 gallon of blue paint and 3 gallons of red paint were used.
In other words, we have:
1 gallon of BLUE paint representing x% of the mixture
3 gallons of RED paint representing z% of the mixture
? gallons of GREEN paint representing y% of the mixture
Statement 1: x = y
In other words, BLUE paint and GREEN paint comprise the same PERCENTAGE of volume in the mixture
This means the volume of BLUE paint in the mixture = the volume of GREEN paint in the mixture
Since we know there's 1 gallon of BLUE paint in the mixture,
we must also have 1 gallon of GREEN paint in the mixture
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: z = 60
In other words, RED paint comprises 60% of the mixture
In other words, 3 gallons of RED paint = 60% of the mixture's TOTAL volume
It also means that 1 gallon of BLUE paint = 20% of the mixture's TOTAL volume
This means the REMAINING 20% of the mixture must be GREEN paint.
We already know that 1 gallon = 20% of the mixture
So,
we must also have 1 gallon of GREEN paint in the mixture
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
