A paint mixture was formed by mixing exactly 3 colors of

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

Hi All,

We're told that 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 and exactly 1 gallon of BLUE paint and 3 gallons of RED paint were used. We're asked for the number of gallons of green paint that were used. This question is built around 'System math' and has a great, built-in math shortcut that we can take advantage of....

To start, since there are only 3 colors in the mixture - and each color represents a certain percentage of the total, we can create the following equation:
X + Y + Z = 100.

In addition, we know exactly how much blue paint and red paint were used, so we can create a second equation (based around the percentages) - we used 3 times the amount of RED paint as BLUE paint, so...
Z = 3X

We now have 3 variables and 2 unique equations. If we have a third unique equation, then we'll have a System of equations and can solve for all 3 variables - meaning that we COULD answer the question that's asked (and without actually having to do all of that math).

(1) X = Y

Fact 1 gives us a third unique equation, so COULD determine the amount of green paint.
Fact 1 is SUFFICIENT

(2) Z = 60

Fact 2 also gives us a third unique equation, so COULD determine the amount of green paint.
Fact 2 is SUFFICIENT

Final Answer: D

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