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## OG 2020: Question No. 346

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
 Source OG 2020 Type Data Sufficiency Topic Word Problems Sub-Topic Percents / Mixture Difficulty Medium

### Solution

#### Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are 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.
• Exactly 1 gallon of blue paint and 3 gallons of red paint were used.

We need to determine

• The total amount (gallons) of green paint that were used.

If we assume the total volume of the paint mixture is P, then

• Blue paint = P * x/ 100= 1
• Red paint = P * z/100= 3
• Green paint = P * y/100

Therefore, we can say that

• P * z/100 = 3 * P * x/100

Or, z = 3x

We also know that in the mixture, only blue, green, and red paint was present.

• Therefore, x + y + z = 100

Or, x + y + 3x = 100

Or, 4x + y = 100

With this understanding, let us now analyse the individual statements.

#### Step 3: Analyse Statement 1

As per the information given in statement 1, x = y.

Thus, we can say

• Amount of green paint = P * y/100= P * x/100 = 1

Hence, statement 1 is sufficient to answer the question.

#### Step 4: Analyse Statement 2

As per the information given in statement 2, z = 60

• As z = 3x, we can say x = 20.
• Also, x + y + z = 100, implies y = 20

Now, P *  z/100= 3

Or, P *  60/100= 3

Or, P = 5

Therefore, we know the value of P as well as the value of z – thus, we can determine the amount of green paint.

Hence, statement 2 is sufficient to answer the question.

#### Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer choice is option D.

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