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marbles left in the jar are red

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by sanju09 » Fri Sep 17, 2010 2:23 am
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.



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by Rahul@gurome » Fri Sep 17, 2010 4:28 am
(1) Number of red marbles : Number of blue marbles = 2:1 implies number of red marbles removed = 2* number of blue marbles removed.
If x blue marbles are removed, then x + 2x = 9 implies x = 3
Since 9 marbles are removed so, number of red marbles removed = 2*3 = 6
Therefore, number of red marbles left in the jar = 20 - 6 = 14
So, (1) is SUFFICIENT.

(2) This statement tells us that out of the first 6 marbles, 4 were red marbles but there is no info on the remaining 3 marbles that were removed.
So, (2) is NOT SUFFICIENT.

The correct answer is [spoiler](A)[/spoiler].
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by Scott@TargetTestPrep » Wed Dec 13, 2017 1:00 pm
sanju09 wrote: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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