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

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Re: A certain bag contains red, blue, and green marbles. What is the ratio [#permalink]
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tudelue
A certain bag contains red, blue, and green marbles. What is the ratio of number of green marbles to the number of red marbles in the bag?

(1) The number of blue marbles in the bag is two times the number of green marbles in the bag.
(2) The number of blue marbles in the bag is three times the number of red marbles in the bag.

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

Cheers,
Brent
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Re: A certain bag contains red, blue, and green marbles. What is the ratio [#permalink]
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Re: A certain bag contains red, blue, and green marbles. What is the ratio [#permalink]
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