Three completely unmarked containers are used for measuring water. Wat

Question

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.

KarishmaB · Accepted Answer

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)

sunaimshadmani · Answer

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.
KUDOS???

anupamadw · Answer

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

anairamitch1804 · Answer

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.

hero_with_1000_faces · Answer

A question right out of Die Hard Movie.

Manick9 · Answer

Container 1 can hold 2L > Container 2
Container 2 can hold 2L > Container 3

Therefore, Container 1 can hold 4L > Container 3.

Fill up Container 1 fully and then transfer the water to Container 3. You would be left with 4L in container 1.

Therefore, C is the right answer.

Engineer1 · Answer

Hi  KarishmaB  ,I don't have problem solving this question. But to me the wording is not clear (if not misleading). It says "is it possible to measure  exactly  4 gallons of water". I have problem with exactly. Yeah it can measure at least 4 gallons, since ultimately we know container 1 can hold > 4 gallons. What is your thought on the wording in the question? Thanks!

Fungano · Answer

if you fill the first container and than you use the water in this container to fill the secondo, in the first container will remain exactly 2 gallons right? If you do this thing 2 times and each time move the remaining water in the third container, we could also use only one of the two statements at a time. So the answer could also be D. Please tell me if it's not right.

Usernamevisible · Answer

Water Jug Concept
Suppose the container capacities are:
8 gallons
5 gallons
3 gallons
What amounts can be measured?
The key idea:
Any measurable quantity must be a multiple of the GCD of the capacities.
gcd(8,5,3) = 1
Since GCD = 1, you can eventually create any whole-number amount up to the largest capacity.
--------------------------------------------------------------------------------------------

Example
Capacities:
10
6
2
gcd(10,6,2) = 2
Only multiples of 2 can be measured:
✓ 2, 4, 6, 8, 10
✗ 1, 3, 5, 7, 9
---------------

Fast GMAT Rule
If the target amount is T:

1. Find the GCD of the capacities.
2. If the GCD does not divide T, the amount is impossible to measure.
3. If the GCD divides T, the amount is usually possible to measure (assuming T is not larger than all container capacities).

---

DS Shortcut for This Question
From both statements:
x, x+2, x+4
Their GCD is:
gcd(x,2)
because the consecutive differences are 2.
So only two possibilities exist.
Case 1: x is odd
gcd = 1
4 is measurable.
Case 2: x is even
gcd = 2
4 is measurable because 2 divides 4.
Therefore every possible case works.
------------------------------------

Extremely Useful Pattern
Whenever capacities look like:
a, a+k, a+2k
their GCD must divide k.
So immediately check:
gcd(a,k)
instead of working with all three numbers.
Examples:
(5,7,9) → GCD = 1
(8,10,12) → GCD = 2
(12,18,24) → GCD = 6
--------------------

What GMAT Usually Tests

1. Can amount T be measured?
2. Is the GCD 1 or 2?
3. Is the target divisible by the GCD?
4. In DS, do the statements guarantee measurability?
 Focus on:
 Water-jug questions = GCD questions disguised as pouring questions.

Three completely unmarked containers are used for measuring water. Wat

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