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# A jar contains red and green marbles, available in two sizes- small

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Manager
Joined: 22 Jul 2014
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A jar contains red and green marbles, available in two sizes- small [#permalink]

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04 Sep 2014, 23:43
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45% (medium)

Question Stats:

68% (01:21) correct 32% (01:47) wrong based on 81 sessions

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A jar contains red and green marbles, available in two sizes- small and big. 20% of the marbles are red and 60% of the marbles are small. How many small green marbles does the jar contain?

(1) The total number of green marbles is 80.
(2) 10% of total marbles in the jar are small and red

Source: 4Gmat

I remember the instructor suggesting that such problems with 3 variables can be solved using the table method.
Can someone help me with it.

Also I would like to know the conventional method. I freeze when I see such problems
[Reveal] Spoiler: OA

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Manager
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Re: A jar contains red and green marbles, available in two sizes- small [#permalink]

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05 Sep 2014, 00:18
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alphonsa wrote:
A jar contains red and green marbles, available in two sizes- small and big. 20% of the marbles are red and 60% of the marbles are small. How many small green marbles does the jar contain?
1) The total number of green marbles is 80.
2) 10% of total marbles in the jar are small and red

Let's assume the total number of marbles be $$100x$$. (We can't use just the number 100 here because statement (1) mentions the number of green marbles explicitly)

Let's draw a table as below and fill it with the information we have from the question stem. In the table, all the rows and columns sum up to the total row or column and the two totals will sum up to the big total in the bottom right corner.

P.S. - I don't exactly know how to draw a table here so bear with me. I have used * to indicate blank columns to preserve the table structure (Consecutive spaces get compressed into one )

* | R | G | Total
--|-----|-----|------
S | *** | *** | 60x
--|-----|-----|------
B | *** | *** | 40x
--|-----|-----|------
T |20x|80x|100x

1) The total number of green marbles is $$80$$

So, we know x = 1 and the table becomes

* | R | G | Total
--|-----|-----|------
S | *** | *** | 60
--|-----|-----|------
B | *** | *** | 40
--|-----|-----|------
T | 20 | 80 | 100

But we can't find the answer. ----> Insufficient

2) 10% of total marbles in the jar are small and red

So, small & red = $$10x$$ and the table becomes

* | R | G | Total
--|-----|-----|------
S |10x|50x| 60x
--|-----|-----|------
B |10x|30x| 40x
--|-----|-----|------
T |20x|80x|100x

We know that small & green = $$50x$$ but have no idea about the value of x. ----> Insufficient

1) and 2) We know $$SG = 50x$$ and $$x = 1$$ ----> Sufficient

Hope that helps
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Re: A jar contains red and green marbles, available in two sizes- small [#permalink]

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05 Sep 2014, 10:04
2
KUDOS
Hi,
Nicely explained by eshan429

Given : 20% red and 60% small

Let total be 100x

Red = 20x implies Green = 80x

Small =60x implies not small = 40x

from (1) we have 80x=80 -> x=1
Still,for knowing the distribution of red small ball or green small ball we must know the color distribution among small balls.So insufficient.

from (2) we get 10x = red and small implying 50x = green and small
but here we do not know the value of x.So insufficient.

Combining 1 and 2 we get the answer..C

This method just saves the time of drawing tables,but IMO it generally leads to confusion so it is better to approach these type of questions using tabular method.
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Re: A jar contains red and green marbles, available in two sizes- small [#permalink]

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05 Sep 2014, 23:46
Thanks a ton.. Seems easy now

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Re: A jar contains red and green marbles, available in two sizes- small [#permalink]

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20 Sep 2015, 00:02
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

A jar contains red and green marbles, available in two sizes- small and big. 20% of the marbles are red and 60% of the marbles are small. How many small green marbles does the jar contain?

(1) The total number of green marbles is 80.
(2) 10% of total marbles in the jar are small and red

Transforming the original condition and the question, we have the below 2by2 table that is common in GMAT math test.

Attachment:

GC DS alphonsa A jar contains red and green marbles(20150918).png [ 2.78 KiB | Viewed 682 times ]

there are 4 variables (a,b,c,d) and 2 equations (a+c=20%(a+b+c+d), a+b=60%(a+b+c+d)) therefore we need 2 more equations to match the number of variables and equations. Since there is 1 each in 1) and 2), C has high probability of being the answer and it turns out that C actually is the answer.

Normally for cases where we need 2 more equations, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: A jar contains red and green marbles, available in two sizes- small [#permalink]

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31 Dec 2017, 11:18
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Re: A jar contains red and green marbles, available in two sizes- small   [#permalink] 31 Dec 2017, 11:18
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