Quote:
A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9 of the marbles are removed, how many of the marbles left in the jar are red?
(1) Of the marbles removed, the ratio of the number of red ones to the number of blue ones is 2:1.
(2) Of the first 6 marbles removed, 4 are red.
We are given that a jar contains 30 marbles, of which 20 are red and 10 are blue. We are also given that 9 marbles are removed, and we need to determine the number of red marbles left in the jar.
Statement One Alone:
Of the marbles removed, the ratio of the number of red ones to the number of blue ones is 2:1.
We can re-express the ratio of red to blue marbles removed as 2x : x and solve the equation:
2x + x = 9
3x = 9
x = 3
From this we see that 6 red marbles and 3 blue marbles are removed. Thus there are 14 red marbles left in the jar. Statement one alone is sufficient to answer the question.
Statement Two Alone:
Of the first 6 marbles removed, 4 are red.
From this we know that at least 4 red marbles and 2 blue marbles are removed. However, since we don’t know how many of the last 3 marbles are red (or blue), we can’t determine the number of red marbles left in the jar. For example, if the last 3 marbles removed are all red, then 7 red marbles are removed, and thus there are 13 red marbles left in the jar. However, if none of the last 3 marbles are red, then only 4 red marbles are removed, and thus there are 16 red marbles left in the jar. Statement two alone is not sufficient to answer the question.
Answer: A
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