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# A green bucket and a blue bucket are each filled to capacity with seve

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Math Expert
Joined: 02 Sep 2009
Posts: 43896
A green bucket and a blue bucket are each filled to capacity with seve [#permalink]

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03 Nov 2014, 07:49
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Question Stats:

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Tough and Tricky questions: Word Problems.

A green bucket and a blue bucket are each filled to capacity with several liquids, none of which combine with one another. Liquid A and liquid B each compose exactly 10% of the total liquid contained in the green bucket. Liquid C composes exactly 10% of the total liquid contained in the blue bucket. The entire contents of the green and blue buckets are poured into an empty red bucket, completely filling it with liquid (and with no liquid overflowing). What percent of the liquid now in the red bucket is not liquids A, B, or C?

(1) The total amount of liquids A, B, and C now in the red bucket is equal to 1.25 times the total amount of liquids A and B initially contained in the green bucket.
(2) The green and blue buckets did not contain any of the same liquids.

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: A green bucket and a blue bucket are each filled to capacity with seve [#permalink]

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03 Nov 2014, 08:39
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Great and tricky question Bunuel! I fell into the trap of over-calculating also. Here's what I think is the solution:

First, the important parts of the premise:
1) It asks you to identify the percentage of non-ABC liquids in the bucket. Therefore, you don't need to be able to have an exact quantity.
2) Since we are adding two buckets and need to know how the two buckets mix, we DO need to know relative size of the two buckets. (e.g., how much bigger is the blue bucket than the green bucket)

The trap here is to start calculating a bunch of hypothetical numbers or assigning tons of variables to get the answer. But, if you remember that you need to have some info on the relative size of the two buckets, you can quickly eliminate this statement as insufficient since it doesn't tell you anything about the size of the blue bucket. For example, the green bucket could be 1 liter, and the blue bucket is 1000 liters (or vis versa). Since we don't know how much C is in the green bucket or how much A or B is in the blue bucket, sizes could be off the charts different.

Eliminate A and D.

On to statement 2:
Remember here that you have to forget about statement 1. Again, this statement doesn't tell you anything about the relative size of the buckets and now you also don't have info about how the proportions of liquids ends up in the red bucket. Therefore this is insufficient.

Eliminate B.

Both statements combined:
Statement 1 tells you the ratio of A+B in Green to A+B+C in Red. Statement 2 tells you that there is no C in Green and no A or B in Blue. Therefore, you know that:
since A+B+C in red = 1.25 (A+B) in green
and C in green = 0
And A+B in blue = 0
then,
C in blue = .25(A+B) in green

Since A and B are equal portions in green,
then A = B
then C in blue = .25 (A+B) = .25 (A+A) = .25 (2A) = 0.5A
If C is half of A, but still constitutes the same percentage of the blue bucket as A of the green bucket, you know that the blue bucket must be half the size of the green bucket. Now you have your relative size.

You also know from the second statement that blue doesn't have any A or B and green doesn't have any C. So now you can find the solution.

Assume the green bucket is 1000 liters and blue bucket is 500 liters (any ratio of 2:1 would work here).
A = 100 liters
B = 100 liters
C = 50 liters
D = (1000 liters +500 liters) - (100 liters + 100 liters + 50 liters) = 1500 - 250 = 1250.

D as a percentage = 1250/1500 = 83.33%

Therefore both statements together are sufficient.
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Re: A green bucket and a blue bucket are each filled to capacity with seve [#permalink]

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03 Nov 2014, 16:19
LighthousePrep

Since A and B are equal portions in green,
then A = B

_________________________________________________________________

The problem states that A + B = 10% of the liquid in the green bucket. How do you know that A&B are equal?
Manager
Joined: 21 Jul 2014
Posts: 127
Re: A green bucket and a blue bucket are each filled to capacity with seve [#permalink]

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03 Nov 2014, 18:02
ferlytate wrote:
LighthousePrep

Since A and B are equal portions in green,
then A = B

_________________________________________________________________

The problem states that A + B = 10% of the liquid in the green bucket. How do you know that A&B are equal?

Maybe I read the problem incorrectly, but my interpretation was that A = 10% and B= 10% because of the word "each" in the problem.

Liquid A and liquid B each compose exactly 10% of the total liquid
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Re: A green bucket and a blue bucket are each filled to capacity with seve [#permalink]

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03 Nov 2014, 18:38
3
KUDOS
A+B is given but A = B is not given. But then also ans is C.
As C= 0.25(A+B)
Let green - 1000
Then A+B = 1000*10/100 = 100
C = 0.25 * 100 = 25
Then blue = 25 * 100/10 as C is 10 percent of blue.
So blue = 250
Now total = blue + green
= 1000+250 = 1250
Non ABC = 1250- (100+25) = 1125
Percentage = 100*1125/1250 = 90 percent

So ans - C

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Re: A green bucket and a blue bucket are each filled to capacity with seve [#permalink]

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03 Nov 2014, 18:47
1
KUDOS
Let 100g and 100b the total vol. of liquid in green bucket and blue bucket respectively.

From statement 1, we can say :
Vol of A+B in green bucket + Vol of C in green bucket + Vol of A+B in blue bucket + Vol of C in blue bucket = 1.25 * Vol of A+B in green bucket

=> 20 g + Vol of C in green bucket + Vol of A+B in blue bucket + 10 b = 1.25 * 20 g

This is clearly insufficient, since we don't know the vol. of liquid A and B in blue bucket and the vol.of C in green bucket.

Statement 2 is clearly insufficient since we don't have the relationship between both the buckets.

But combining 1 and 2, we can say

=> 20 g + 10 b = 1.25 * 20 g
=> g = 2b

The total volume of liquid present is 100 g + 100 b = 200b +100 b = 300b

Volume of A + B = 20 g = 40 b
Volume of C = 10 b

Total volume of A+B+C in red bucket = 50b

Remaining liquid = 250b i.e 250b/300b *100 = 83.3 %

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Re: A green bucket and a blue bucket are each filled to capacity with seve [#permalink]

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11 Jan 2017, 20:50
3
KUDOS
We can think of the liquids in the red bucket as liquids A, B, C and E, where E represents the totality of every other kind of liquid that is not A, B, or C. In order to determine the percentage of E contained in the red bucket, we will need to determine the total amount of A + B + C and the total amount of E.
It is TEMPTING (but incorrect) to use the following logic with the information given in Statement (1).
Statement (1) tells us that the total amount of liquids A, B, and C now in the red bucket is 1.25 times the total amount of liquids A and B initially contained in the green bucket.

Let's begin by assuming that, initially, there are 10 ml of liquid A in the green bucket. Using the percentages given in the problem we can now determine that the composition of the green bucket was as follows:

10% A = 10 ml
10% B = 10 ml
80% E = 80 ml

Since there were 20 total ml of A and B in the green bucket, we know from statement (1) that there must be 25 ml of A + B + C now in the red bucket (since 25 is 1.25 times 20).
From this we can deduce that, there must have been 5 ml of C in the blue bucket. We can use the percentages given in the problem to determine the exact initial composition of the blue bucket:
10% C = 5 ml
90% E = 45 ml
Since the liquid in the red bucket is simply the totality of all the liquids in the green bucket plus all the liquids in the blue bucket, we can use this information to determine the total amount of A + B + C (25 ml) and the total amount of E (80 + 45 = 125 ml) in the red bucket. Thus, the percentage of liquid now in the red bucket that is NOT A, B, or C is equal to 125/150 = 83 1/3 percent.
This ratio (or percentage) will always remain the same no matter what initial amount we choose for liquid A in the green bucket. This is because the relative percentages are fixed.

We can generalize that given an initial amount x for liquid A in the green bucket, we know that the amount of liquid B in the green bucket must also be x and that the amount of E in the green bucket must be 8x. We also know that the amount of liquid C in the blue bucket must be .5x, which means that the amount of E in the blue bucket must be 4.5x.

Thus the total amount of A + B + C in the red bucket is x + x + .5x = 2.5x and the total amount of liquid E in the red bucket is 8x + 4.5x = 12.5x. Thus the percentage of liquid now in the red bucket that is NOT A, B, or C is equal to 12.5x/15x or 83 1/3 percent.
However, the above logic is FLAWED because it assumes that the green bucket does not contain liquid C and that the blue bucket does not contain liquids A or B.
In other words, the above logic assumes that knowing that there are x ml of A in the green bucket implies that there are 8x ml of E in the green bucket. Remember, however, that E is defined as the totality of every liquid that is NOT A, B, or C! While the problem gives us information about the percentages of A and B contained in the green bucket, it does not tell us anything about the percentage of C contained in the green bucket and we cannot just assume that this is 0. If the percentage of C in the green bucket is not 0, then this will change the percentage of E in the green bucket as well as changing the relative amount of liquid C in the blue bucket.
For example, let's say that the green bucket contains 10 ml of liquids A and B but also contains 3 ml of liquid C. Take a look at how this changes the logic:
Green bucket:
10% A = 10 ml
10% B = 10 ml
3% C = 3 ml
77% E = 77 ml
Since there are 20 total ml of A and B in the green bucket, we know from statement (1) that there must be 25 ml of A + B + C in the red bucket (since 25 is 1.25 times 20).
Since the green bucket already contributes 23 ml of this total, we know that there must be 2 total ml of liquids A, B and C in the blue bucket. If the blue bucket does not contain liquids A or B (which we cannot necessarily assume), then the composition of the blue bucket would be the following:
10% C = 2 ml
90% E = 18 ml
Note, however, that if the blue bucket does contain some of liquids A or B, then the composition of the blue bucket might also be the following:
10% C = 1 ml
10% A = 1 ml
80% E = 8 ml
Notice that it is impossible to ascertain the exact amount of E in the red bucket - since this amount will change depending on whether the green bucket contains liquid C and/or the blue bucket contains liquids A or B.
Thus statement (1) by itself is NOT sufficient to answer this question.
Statement (2) tells us that the green and blue buckets did not contain any of the same liquids. As such, we know that the green bucket did not contain liquid C and that the blue bucket did not contain liquids A or B. On its own, this does not help us to answer the question. However, taking Statement (2) together with Statement (1), we can definitively answer the question.

The correct answer is C: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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Thanks & Regards,
Anaira Mitch

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Re: A green bucket and a blue bucket are each filled to capacity with seve [#permalink]

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28 Jun 2017, 05:27
Hello all,

I need help in understanding the question.The question stem says "The entire contents of the green and blue buckets are poured into an empty red bucket, completely filling it with liquid (and with no liquid overflowing)"

Considering 100 Lts in each of the Blue and Green buckets.
A and B is 10 % each of green bucket volume - remaining is 80 % - 80 Lts
C is 10 % of Blue bucket volume - remaining is 90 % - 90 Lts

Total left is 170 Lts
So % = 170/200*100
So just need to know the green and blue buckets do not contain the same liquids to get the answer as mentioned in option (B).

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Re: A green bucket and a blue bucket are each filled to capacity with seve [#permalink]

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21 Jan 2018, 08:42
GouthamNandu wrote:
Hello all,

I need help in understanding the question.The question stem says "The entire contents of the green and blue buckets are poured into an empty red bucket, completely filling it with liquid (and with no liquid overflowing)"

Considering 100 Lts in each of the Blue and Green buckets.
A and B is 10 % each of green bucket volume - remaining is 80 % - 80 Lts
C is 10 % of Blue bucket volume - remaining is 90 % - 90 Lts

Total left is 170 Lts
So % = 170/200*100
So just need to know the green and blue buckets do not contain the same liquids to get the answer as mentioned in option (B).

Hi There,
Please note that it is not given that green and blue buckets contain same quantity of liquids i.e. 100 lts which you have assumed.
It could be same(equal).
It could be less than i.e. quantity of Liquid in Green Bucket < Quantity of Liquid in Blue Bucket.
or it could be more than i.e. quantity of Liquid in Green Bucket > Quantity of Liquid in Blue Bucket.

So, when we assume that, both the buckets contains 100 lts of liquid, this assumption is flawed.
That's why, we must have to know the ratio of liquid in both the buckets to solve the question correctly and then we can plug in some numbers and solve.
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A green bucket and a blue bucket are each filled to capacity with seve [#permalink]

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21 Jan 2018, 12:30
ASK = % of non ( Liq A, B and C) in red bucket

But we do not know by the description in the question itself that
we have any liquid A or liquid B in green bucket ? or we have any liquid C in bucket green ?

Answer to this is given in statement B : alone B can't suffice

Question asks us to find = non liquid ( A , B and C) in red bucket / total liquid in red bucket
= [( x+ y) - $$\frac{x}{10}$$ - $$\frac{x}{10}$$ -$$\frac{y}{10}$$ ] / ( x+ y)

= 1 - $$\frac{(2x+y)}{10(x+y)}$$

statement 1 : $$\frac{x}{10}$$ + $$\frac{x}{10}$$ + $$\frac{y}{10}$$ = 1.25($$\frac{x}{10}$$ + $$\frac{x}{10}$$)

= 2x + y = 2.5x
= y = 0.5x or x = 2y

answer : 1 - 5y/30y = 5/6 or 83.33% = Ans C
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