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Three completely unmarked containers are used for measuring water. Wat

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Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 03 Nov 2014, 09:04
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Tough and Tricky questions: Word Problems.



Three completely unmarked containers are used for measuring water. Water may be poured from one container to another, but no water may be poured outside the containers. Using nothing but the three containers and an unlimited supply of water, is it possible to measure exactly 4 gallons of water?

(1) The capacity of the first container is 2 gallons more than the capacity of the second container.
(2) The capacity of the second container is 2 gallons more than the capacity of the third container.

Kudos for a correct solution.

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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 03 Nov 2014, 12:36
Its Seems to be (D) to me.

The Container no. doesn't matter here.

Please post me with the correct ans.
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 03 Nov 2014, 17:52
By combining both, we can answer.
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 05 Nov 2014, 05:55
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Bunuel wrote:

Tough and Tricky questions: Word Problems.



Three completely unmarked containers are used for measuring water. Water may be poured from one container to another, but no water may be poured outside the containers. Using nothing but the three containers and an unlimited supply of water, is it possible to measure exactly 4 gallons of water?

(1) The capacity of the first container is 2 gallons more than the capacity of the second container.
(2) The capacity of the second container is 2 gallons more than the capacity of the third container.

Kudos for a correct solution.


If we consider - three containers c1,c2 and c3 then
stmnt 2) let c3 has capacity x then c2 has capacity x+2
If we fill c2 completely ( x+2 water ) and transfer water from c2 to c3 till it gets full
what we are left in c2 is x+2- x = 2
Now c2 has 2 gallons
We cant pour it in c1 as we dont know its capacity and also we cant pour this 2 gallons outside as an intermediate step and repeat same procedure to get 2+2 gallons...so I think statmnt2 is insufficient.

stmnt 1) same as statment2

statment1+2 we know
c1 is x+4, c2 is x+2 and c3 is x
so we can completely fill c1 and transfer water from c1 to c3 till it gets completely filled what we are left in c1 is 4 gallons.

IMO C
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 05 Nov 2014, 21:14
I have a bit of confusion here..
Do we want 4 gallons in each container or 4 gallons in any 1 of the containers..
thanks
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 06 Nov 2014, 00:52
2
1
IMO C.
The question basically asks if the combined capacity of the 3 containers is ATLEAST 4 gallons??
ST (1) has no info about 3rd container. And the combined capacity of the first two can be anything e.g 2.5 gallons and 0.5 gallons or 5 gallons and 3 gallons so insufficient.

ST (2) alone is also insufficent due to the same reason.

Combined we have that the 2nd container is atleast 2 gallons and the 1st is atleast 4 gallons. Sufficient.
Answer is C.
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 08 Nov 2014, 09:11
IMO D.

Using plugin method:

Statement 1:
For this example I used real numbers to help visualize. Container A is 10 gallons, Container B is two gallons less which will be 8. First fill up Container A to 10 gallons, take Container A's water and fill the Container B to the top leaving 8 gallons in the Container B and 2 gallons in Container A. Take the remaining two gallons from Container A and put it into the Container C. Take the 8 gallons from container B and put it back into container A. Fill container A to the top again. Repeat the process of filling container B to the top (8 gallons) which leaves 2 gallons in container A, pour the remaining 2 gallons into container C, you now have 4 gallons in Container C. This process works with any numbers.

Statement 2: same idea as statement 1, sufficient
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 08 Nov 2014, 09:34
psullyz92@yahoo.com wrote:
IMO D.

Using plugin method:

Statement 1:
For this example I used real numbers to help visualize. Container A is 10 gallons, Container B is two gallons less which will be 8. First fill up Container A to 10 gallons, take Container A's water and fill the Container B to the top leaving 8 gallons in the Container B and 2 gallons in Container A. Take the remaining two gallons from Container A and put it into the Container C. Take the 8 gallons from container B and put it back into container A. Fill container A to the top again. Repeat the process of filling container B to the top (8 gallons) which leaves 2 gallons in container A, pour the remaining 2 gallons into container C, you now have 4 gallons in Container C. This process works with any numbers.

Statement 2: same idea as statement 1, sufficient


But how can you assume , C has capacity of 4 gallons ? What if, C has capacity of 1 gallon.....
A=10 gallon, B=8 gallon and C=1 gallon
They have not mentioned anything about capacity of C
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 08 Nov 2014, 12:54
At first glance,


If 1) is true:

Fill container one. Then pour out container 1 until container 2 is full. This leaves you with two extra gallons. Pour those two gallons into container 3.

Repeat the process and you have 4 gallons in container 3.

2)Fill container 2. Then pour out container 2 into container 3 until full. This leaves you with two extra gallons. Pour those two gallons into container 1.

Repeat the process and you have 4 gallons in container 1.



But let's think about this. Both of these are predicated on the assumption that the remaining container can hold at least 4 gallons of water. That information is not given in the question itself. so we can't assume that.



Given both 1) and 2), we have something that looks like this: C(1) = C(2) + 2 = C(3) + 2 ----> C(1) = (C3) + 4. So fill container 1, then pour it into 3 until 3 is full. Four gallons wil be remaining.


So you need BOTH.
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 08 Nov 2014, 16:24
[i]Three completely unmarked containers are used for measuring water. Water may be poured from one container to another, but no water may be poured outside the containers. Using nothing but the three containers and an unlimited supply of water, is it possible to measure exactly 4 gallons of water?

(1) The capacity of the first container is 2 gallons more than the capacity of the second container.
(2) The capacity of the second container is 2 gallons more than the capacity of the third container.


1) no information is given for first container. If capacity for 1st container 2 then answer is yes, but if capacity is 1 then answer is no. Insufficient
2) Second container has capacity of +2 then third container. no info on the capcaity for 3rd container, hence insufficient

Combining both, if capacity for C2 is 3, then C1 is 5 and C3 is 1. We want to measure 4 gallons and this is not enough to measure water.
But if C2 is 4 then C1 is 6 and C3 is 2. Then yes we can measure water by transferring all of it into C2.

Therefore answer should be E.
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 09 Nov 2014, 04:00
Bunuel wrote:

Tough and Tricky questions: Word Problems.



Three completely unmarked containers are used for measuring water. Water may be poured from one container to another, but no water may be poured outside the containers. Using nothing but the three containers and an unlimited supply of water, is it possible to measure exactly 4 gallons of water?

(1) The capacity of the first container is 2 gallons more than the capacity of the second container.
(2) The capacity of the second container is 2 gallons more than the capacity of the third container.

Kudos for a correct solution.



S1. We have 2 containers differing 2 gallons and third that can have any capacity. The problem is that they are unmarked, so we may have problem with finding exactly those containers differing 2 gallons. INSUFFICIENT

S2. The same problem, so INSUFFICIENT

S1+S2. We have three containers differing one another. Even without marking we can differ low, middle and high capacity containers. So, they can be

1,3,5
0.01, 2.01, 4.01
3,5,7
7,9,11
etc.

Idea is that first we pour all water to the biggest container (it is anyway> 4 gallons), then pour it to smallest and difference will be exactly 4. But to measure it the volume of water should be equal to or more than capacity of biggest container. For example, if capacity 7 gallons and volume of measuered water is 6 gallons, the difference between 3rd and 1st containers will be only 3 and conclusion will be wrong

So, must be E
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 13 Apr 2015, 22:51
Condition 1 -
C1 C2
X+2 X

Condition 2 -

C2 C3
Y+2 Y

Combining both condition 1 and 2 -
C1 C2 C3
X+4 X+2 X

So with these combinations we can definitely say that either we will be able to measure 4 gallons or we won't be able to measure.
I think, that should be enough to answer the question and we don't need to do any further calculation.

However, to confirm -
when X=1
C1 C2 C3
5 3 1

Fill C3 four times and after filling up each time, put the water in C1. After 4 iterations we will get 4 gallons.

whenn X=2
C1 C2 C3
6 4 2
Very straight forward, fill C2 and we will get 4 gallons.

when X=3, capacity of the containers
C1 C2 C3
7 5 3
Here is the iterations below-

C1 C2 C3
0 5 0 Fill C2 only, and keep C1 and C3 empty.
0 2 3 Put C2 in C3 till C3 is completely filled. So C3 will be 3 and C2 will be 5
7 2 3 Fill C1 completely, let the other container remain as it is.
4 5 3 Put C1 in C2 till C3 is completely filled. After C2 is completely, C2 will have 5 gallon and C1 will have 4 gallon.
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 13 Apr 2015, 23:12
1
1
Bunuel wrote:

Tough and Tricky questions: Word Problems.



Three completely unmarked containers are used for measuring water. Water may be poured from one container to another, but no water may be poured outside the containers. Using nothing but the three containers and an unlimited supply of water, is it possible to measure exactly 4 gallons of water?

(1) The capacity of the first container is 2 gallons more than the capacity of the second container.
(2) The capacity of the second container is 2 gallons more than the capacity of the third container.

Kudos for a correct solution.


If this were a usual puzzle, each statement alone would be sufficient but this is a data sufficiency question and you cannot assume anything so here the answer will be (C). Here is why:

Three containers and unlimited water. How will you measure 4 gallons?

(1) The capacity of the first container is 2 gallons more than the capacity of the second container.
Step 1: Fill the first container to brim.
Step 2: Pour its water into second container till it is full.
Step 3: Now leftover water in first container is 2 gallons. You pour this 2 gallons in third container.
Step 4: Empty second container and repeat steps 1 and 2.
You now have 4 gallons, 2 gallons in third container and 2 gallons in first container.
The problem in a data sufficiency question is that you cannot assume that the third container can hold 2 gallons. What if its capacity is only 1 gallon? Where do you put the 2 gallons of water then? This makes statement 1 alone INSUFFICIENT.


(2) The capacity of the second container is 2 gallons more than the capacity of the third container.
This statement alone is exactly like statement 1 alone. Just that the containers are different but the case is exactly the same. This makes statement 2 alone INSUFFICIENT.

Using both, we now know that capacity of first container is 4 gallons more than the capacity of third container. Now all you have to do is fill first container and pour its water in third container till it fills up. Whatever is left in first container is 4 gallons.

Answer (C)
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 14 Jan 2017, 17:03
Pouring water from the larger container to the smaller container will leave exactly 2 gallons of water in the larger container. Repeating this operation twice will yield 4 gallons of water.

The problem is - where would these 4 gallons of water accumulate? We will need to use one of the containers. However, neither statement alone tells us whether one of the containers will hold 4 gallons of water.

On the other hand, statements (1) and (2) taken together ensure that the first container can hold at least 4 gallons of water. We know this because (from statement 1) the first container holds 2 gallons more than the second container, which (from statement 2) holds 2 gallons more than the third container, which must have a capacity greater than 0.

Since we know that the first container has a capacity of at least 4 gallons, there are several ways of measuring out this exact amount.
Hence C is the answer.
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 12 Jun 2017, 02:47
It might be tempting to think that either statement is sufficient to answer this question. After all, pouring water from the larger container to the smaller container will leave exactly 2 gallons of water in the larger container. Repeating this operation twice will yield 4 gallons of water. The problem is - where would these 4 gallons of water accumulate? We will need to use one of the containers. However, neither statement alone tells us whether one of the containers will hold 4 gallons of water. On the other hand, statements (1) and (2) taken together ensure that the first container can hold at least 4 gallons of water. We know this because (from statement 1) the first container holds 2 gallons
more than the second container, which (from statement 2) holds 2 gallons more than the third container, which must have a capacity greater than 0. Since we know that the first container has a capacity of at least 4 gallons, there are several ways of measuring out this exact amount. One method is as follows: Completely fill the first container with water. Then pour out just enough water from the first container to fill the third container to the brim. Now, 4 gallons of water remain in the first container. Alternatively: Fill the first container to the brim. Pour out just enough water from the first container to fill the second container to the brim. There are now 2 gallons of water in the first container. Now pour water from the second container to fill the third container to the brim. There are now 2 gallons of water in the second container. Finally, pour all the water from the second container into the first container. There are now 4 gallons of water in the first container.
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 12 Jun 2017, 05:07
Bunuel wrote:

Tough and Tricky questions: Word Problems.



Three completely unmarked containers are used for measuring water. Water may be poured from one container to another, but no water may be poured outside the containers. Using nothing but the three containers and an unlimited supply of water, is it possible to measure exactly 4 gallons of water?

(1) The capacity of the first container is 2 gallons more than the capacity of the second container.
(2) The capacity of the second container is 2 gallons more than the capacity of the third container.

Kudos for a correct solution.


Container 1 - A
Container 2 - B
Container 3 - C

S1 -> A = 2 + B ; No info about C so information is not sufficient to distribute water efficiently.
S2 -> B = 2 + C ; No info about A so information is not sufficient to distribute water efficiently.

S1 + S2 -> Combining both we get A has 4 gallons more capacity than C => Pour all the water from A to C ; The water left in container A would be 4 gallons

C is the answer.
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 17 Jun 2017, 05:11
Simple way:

Statement 1 and 2 are insufficient as we don't have information about the third container

Combining we can say
Let X,Y,Z be the three container and let the capacity be a in 3rd container
so
X Y Z
a+4 a+2 a

we can see clearly that the container X if 4 Gallons more than Z so to measure exactly 4, fill container X to full and then use the water in X to fill containder Z the amount left in X will be exactly 4 gallons after filling Z.
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Re: Three completely unmarked containers are used for measuring water. Wat  [#permalink]

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New post 18 Jul 2018, 06:16
A question right out of Die Hard Movie.
Re: Three completely unmarked containers are used for measuring water. Wat &nbs [#permalink] 18 Jul 2018, 06:16
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