## 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?

- x = y
- 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__

__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__

__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__

__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)__

__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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