A certain bag contains red, blue, and green marbles. What is the ratio

Given: A certain bag contains red, blue, and green marbles.
Let R = # number red marbles in the bag
Let B = # number blue marbles in the bag
Let G = # number green marbles in the bag

Target question: What is the value of G/R?

Statement 1: The number of blue marbles in the bag is two times the number of green marbles in the bag.
In other words, B/G = 2/1
Since we don't have any information about the value of R, we cannot answer the target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: The number of blue marbles in the bag is three times the number of red marbles in the bag.
There are several values of x and y that satisfy statement 2. Here are two:
In other words, B/R = 3/1
Since we don't have any information about the value of G, we cannot answer the target question with certainty.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that B/G = 2/1, which means G/B = 1/2
Statement 2 tells us that B/R = 3/1

From here, we can quickly find the value of G/R if we recognize that (G/B)(B/R) = G/R
Replace each expression with its equivalent value to get: (1/2)(3/1) = G/R
Simplify: 3/2 = G/R
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

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