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Math Expert V
Joined: 02 Sep 2009
Posts: 59674
A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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Difficulty:   5% (low)

Question Stats: 87% (01:09) correct 13% (01:24) wrong based on 618 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

Data Sufficiency
Question: 72
Category: Arithmetic Discrete probability
Page: 158
Difficulty: 600

_________________

Originally posted by Bunuel on 06 Feb 2014, 01:19.
Last edited by Bunuel on 05 Feb 2019, 05:42, edited 1 time in total.
Renamed the topic.
Math Expert V
Joined: 02 Sep 2009
Posts: 59674
Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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2
SOLUTION

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 --> since the total of 9 marbles are removed, then 6 red marbles and 3 blue marbles are removed, thus 20 - 6 = 14 red marbles are left in the jar. Sufficient.

(2) Of the first 6 marbles removed, 4 are red --> we don't know how many of the other 3 marbles removed were red. Not sufficient.

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Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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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.

Using st1, we can say that total no of marbles removed= sum of individuals marble removed which is equal to 2x:x for red : blue marble
So we have 3x=9 or x=3 and thus remainig red marbles can be calculated
A is sufficient
St 2 says only for first 6 marbles in which 4 are red and the remaining 3 can be any ie all blue or all red or 1 red and 2 blue etc

So A alone is sufficient
600 level is okay

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GMAT 1: 590 Q45 V27 Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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1
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).
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Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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Clear A.

B tells nothing about number of Red removed out of 9
Math Expert V
Joined: 02 Sep 2009
Posts: 59674
Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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SOLUTION

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 --> since the total of 9 marbles are removed, then 6 red marbles and 3 blue marbles are removed, thus 20 - 6 = 14 red marbles are left in the jar. Sufficient.

(2) Of the first 6 marbles removed, 4 are red --> we don't know how many of the other 3 marbles removed were red. Not sufficient.

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Posts: 191
Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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.

Data Sufficiency
Question: 72
Category: Arithmetic Discrete probability
Page: 158
Difficulty: 600

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Although OG categorises it as Probability , I don't think this question will qualify as probability..
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Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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Bunuel wrote:
SOLUTION

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 --> since the total of 9 marbles are removed, then 6 red marbles and 3 blue marbles are removed, thus 20 - 6 = 14 red marbles are left in the jar. Sufficient.

(2) Of the first 6 marbles removed, 4 are red --> we don't know how many of the other 3 marbles removed were red. Not sufficient.

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 59674
Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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BrainLab wrote:
Bunuel wrote:
SOLUTION

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 --> since the total of 9 marbles are removed, then 6 red marbles and 3 blue marbles are removed, thus 20 - 6 = 14 red marbles are left in the jar. Sufficient.

(2) Of the first 6 marbles removed, 4 are red --> we don't know how many of the other 3 marbles removed were red. Not sufficient.

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.
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Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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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?
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Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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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.
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Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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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.

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Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9  [#permalink]

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_________________ Re: A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9   [#permalink] 16 Jan 2019, 13:39
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