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A green bucket and a blue bucket are each filled to capacity

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Manager
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A green bucket and a blue bucket are each filled to capacity  [#permalink]

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New post 09 Aug 2004, 11:50
1
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A
B
C
D
E

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83% (00:46) correct 17% (02:25) wrong based on 32 sessions

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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.

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

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New post 09 Aug 2004, 12:39
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I think it is C.

1. Insufficient - unclear if the green bucket has by any chance liquid C and that the blue bucket has liquid A & B.
2. Insufficient - not enough data.

Combining both statement we are clear the green bucket has A & B and no C. Similarly Blue bucket has C but no A& B.

Solving(for reasons of understanding)

Let X be the total capacity of the Blue buket and let Y be the capacity of Green bucket

We have from 1)
0.2X + 0.10Y = 1.25*0.2X
=>0.10Y = 0.20*0.25X
=>2Y=X

so, the Red bucket has X + Y=> 2Y +Y => 3Y litres of the total content from Blue and Green.

of the 3Y, A+B+C= 0.2X+0.10Y => 0.4Y + 0.10 Y => 0.50Y.
so the 'other' liquids' in the red bucket => 3Y - 0.5Y = 2.5Y

So the %age of 'other liquids' = (2.5Y/3.5Y) * 100 = nearly 72%
Joined: 31 Dec 1969
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Concentration: Entrepreneurship, International Business
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New post 09 Aug 2004, 13:30
My bad , I didn't read the question properly
I agree with you even i got the answer as C
CEO
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New post 09 Aug 2004, 18:50
venksune wrote:
I think it is C.

1. Insufficient - unclear if the green bucket has by any chance liquid C and that the blue bucket has liquid A & B.
2. Insufficient - not enough data.

Combining both statement we are clear the green bucket has A & B and no C. Similarly Blue bucket has C but no A& B.

Solving(for reasons of understanding)

Let X be the total capacity of the Blue buket and let Y be the capacity of Green bucket

We have from 1)
0.2X + 0.10Y = 1.25*0.2X
=>0.10Y = 0.20*0.25X
=>2Y=X

so, the Red bucket has X + Y=> 2Y +Y => 3Y litres of the total content from Blue and Green.

of the 3Y, A+B+C= 0.2X+0.10Y => 0.4Y + 0.10 Y => 0.50Y.
so the 'other' liquids' in the red bucket => 3Y - 0.5Y = 2.5Y

So the %age of 'other liquids' = (2.5Y/3.5Y) * 100 = nearly 72%

Venksune, I'm not sure where you took the numbers i bolded in red. A is not sufficient as we don't know if some colors repeat in each bucket.
I got B.
A + B + X = G --> X=.9G
C + Y = BL --> Y=.9BL
Knowing B, we can say that X+Y = .9R
What is the OA?
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New post 09 Aug 2004, 20:58
Paul,
We cant assume that both the blue bucket and the green bucket has equal quantity of liquids in them. Couple of issues in your approach

1. A+B +X = G (this is right), however X is not equal to .9G.Lets take some numbers here. Let the Green bucket have 10 litres of all the liquids. From the statement given, we know that A is 10% and B is 10%...meaning 1 litre of A and 1 litre of B - totalling to 2 litres of A&B together. The 0.2 in my explanation is the 20% of A&B in the Green bucket. So, per your approach X = 0.8G. This would not matter much, we have equation anyway.

2. Now, C+Y = BL (this is right), also Y=0.9 BL (this is fine too). However,

X+Y = 0.9R is wrong. Because, If the total amount of liquids in BL is 5 litres, then liquid C is 0.5litres. Or the 'other liquids' (Y) = 4.5 litres. Which means X + Y = 8 (from my above point 1) + 4.5 = 12.5 litres out of a total of 10 + 5 litres. 12.5/15 is not 0.9R, it is 0.8333R. Now, if you assume BL with some other number or Green with some other number the total %ages will change.

So without knowing the capacity of Green and BL bucket choice 'b' will have issues. We need to have some relationship for the liquids. This relationship is ascertained through statement 1 - which reads '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'.

I assume X= amount of liquid in Green, Y = amount of liquid in Blue
So, I have 0.2X + 0.10 Y =1.25*0.2X.

hope i was logical.
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New post 09 Aug 2004, 21:03
Venksune, thanks for your detailed explanation. This is what I missed in the original question: Liquid A and liquid B each compose exactly 10% of the total liquid contained in the green bucket. Had A + B composed 10% of Green bucket, B would have been sufficient...
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Re: A green bucket and a blue bucket are each filled to capacity  [#permalink]

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Re: A green bucket and a blue bucket are each filled to capacity   [#permalink] 11 Sep 2018, 00:05
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