Data Sufficiency: Marbles in a Bag

Question

A bag contains marbles of three colours—red, blue and green. There are 8 blue marbles in the bag.

There are two additional statement of facts available:

Statement 1: If we pull out marbles from the bag at random, to guarantee that we have at least 3 green marbles, we need to extract 17 marbles.
Statement 2: If we pull out marbles from the bag at random, to guarantee that we have at least 2 red marbles, we need to extract 19 marbles.

Which of the two statements above, alone or in combination shall be sufficient to answer the question "how many green marbles are there in the bag"?

Accepted Answer

B. Let $R, B, G$ be the count of red, blue (8), and green marbles. Worst case to get 3 green: pull all Red + Blue + 3 = 17 $\Rightarrow R + 8 + 3 = 17 \Rightarrow R = 6$. Statement 1 gives $R = 6$, but doesn't yield $G$. Worst case to get 2 red: pull all Blue + Green + 2 = 19 $\Rightarrow 8 + G + 2 = 19 \Rightarrow G = 9$. Statement 2 alone directly gives $G = 9$. Thus Statement 2 alone is sufficient.

Answer

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.

Answer

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Answer

Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question.

Answer

Each statement alone is sufficient to answer the question.

Answer

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Data Sufficiency: Marbles in a Bag

Explanation

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