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

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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:

Approach Solution (1):
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 thetarget questionwith 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 thetarget questionwith certainty.
So, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us thatB/G = 2/1, which meansG/B = 1/2
Statement 2 tells us thatB/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 thetarget questionwith certainty, the combined statements are SUFFICIENT
Correct option: C

Approach Solution (2):
To know the ratio between A and B, we have to have some information that relates A and B
S1 talks about the blue and green which does nothing to help with red and green ratio
S2 does the same by providing information only on relation between blue and red
Combining these two statements, we have a relation for red : blue : green
For examples: if there are x green marbles in the bag, there will be 2x blue and 2x/3 red marbles
Correct option: C

Approach Solution (3):
As for the question, let B, R, G stand for # of blue, red and green balls respectively
You are asked for G/R =?
Per statement 1, B = 2G, clearly not sufficient. Take 2 cases, R = 10, G = 10, B = 20
G/R = 1 but if R = 20, g = 10, b = 20, then G/R = 0.5
Per statement 2, B = 3R
Again, not sufficient
Combining, you get, B = 3R = 2G
3R = 2G
G/R = 1.5
Unique value
Hence both statements together are sufficient
Correct option: C

“A certain bag contains red, blue, and green marbles. What is the ratio of the number of green marbles to the number of red marbles in the bag?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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