A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9

No. of marbles = 30, of which Red, R = 20 & Blue, B = 10;
Removed = 9; No. of marbles that will remain = 30 - 9 = 21;

No. of Red marbles remaining in the jar = ?

(1) Removed Marbles- R:B = 2:1; Therefore, 3x = 9; x = 3; So, since we know the no. of removed red marbles as 6, we can find the no. of remaining red marbles = 14;
Sufficient;

(2) Insufficient, since we do not have information about the remaining 3 marbles that have been removed.

Ans is (A).

Clear A.

B tells nothing about number of Red removed out of 9

Although OG categorises it as Probability , I don't think this question will qualify as probability..

Hi Bunuel, why cannot we use the same logic here: a-department-manager-distributed-a-number-of-pens-pencils-104852.html.

By Statement 1: we can also say that the ratio could be 2/1 or 6/3.....

I think I'm missing some important point here.

Here not only we know the ratio of the marbles removed (red:blue = 2:1) but also that the number of removed marbles (9), so 6 red marbles and 3 blue marbles are removed.

Why is the second statement not sufficient? I set up a proportion like this: 4 Red Removed / 6 Removed = (x) Red Removed / 9 Removed and I got x = 6 which means 6 marbles were red out of the 9 marbles removed. I still dont get why is the second statement is not sufficent?

Look at statement 2 this way.

You are given that total red = 20, total blue = 10. You have removed 9, out of which 4 are definitely red, 2 are blue. But you do not know anything about the remaining 3 balls.

If those 3 remaining balls are blue, you get 5 blue balls and 4 red balls removed, giving you the answer to the question asked = number of red balls remaining = 20-4 =16.

BUT, if those 3 remaining balls are red, you get 3 blue balls and 6 red balls removed, giving you the answer to the question asked = number of red balls remaining = 20-6 =14.

Additionally, you can create couple of other combinations for those 3 remaining balls giving you different answers for number of red balls. This makes statement 2 not sufficient.

In your analysis by creating the ratio of red balls to the total balls removed you are assuming that the ONLY case possible is for the proportion of red balls in the first 6 balls to remain the same for the remaining 3 balls. This is a massive assumption that is not supported either by the main question or by statement 2.

Your equation will not hold true if all 3 are blue of if the remaining 3 balls are 2 blue and 1 red or 1 blue and 2 red etc.

Hope this helps.

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

Correct option : A


A jar contains 30 marbles, of which 20 are red and 10 are blue.
Interpretion : R : B = 2:1 ratio before removal of any marble

If 9 of the marbles are removed, how many of the marbles left in the jar are red?
After, 9 Marbles are removed, remaining marble in jar will be 21.
we need to find how many will be Red in jar, after 9 marble removed.

(1) Of the marbles removed, the ratio of the number of red ones to the number of blue ones is 2:1.
before R:B = 2 : 1
after R:B = 2:1
that means, in 21 marble, 14 are Red and 7 are blue - Sufficient

(2) Of the first 6 marbles removed, 4 are red.
here too, out of 6, ratio of red and blue is same 2:1
but, we still have 3 more to remove and left marbles remaining are 24 now,
from statement 2, we dont have ratio or information about the pick to be done - Insufficient
option : B, D and E are out.

makes A winner

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