If Pool Y currently contains more water than Pool X, and if

Question

If Pool Y currently contains more water than Pool X, and if Pool X is currently filled to 2/7 of its capacity, what percent of the water currently in Pool Y needs to be transferred to Pool X if Pool X and Pool Y are to have equal volumes of water?

(1) If all the water currently in Pool Y were transferred to Pool X, Pool X would be filled to 6/7 of its capacity.

(2) Pool X has a capacity of 14,000 gallons.

Hi.

I came across this DS question on my last MgCAT, and while I do understand how to solve it, I fail to see why (according to the Mg explanation) we should consider both pools capacity as equal, when nothing in the text leads to that assumption… (or am I missing something here?) 
 
Therefore I felt for E.

Thanks for the help.

Bunuel · Accepted Answer

If Pool Y currently contains more water than Pool X, and if Pool X is currently filled to 2/7 of its capacity, what percent of the water currently in Pool Y needs to be transferred to Pool X if Pool X and Pool Y are to have equal volumes of water?

We are nowhere told that the capacities of pools X and Y are equal.

(1) If all the water currently in Pool Y were transferred to Pool X, Pool X would be filled to 6/7 of its capacity.

THe above implies that together pools X and Y contain 6/7 of the capacity  of pool X . Now, for pools X and Y to contain an  equal amount  of water, each pool should contain 3/7 of the capacity  of pool X . Thus, from pool Y, which contains 4/7 (6/7 - 2/7 = 4/7) of the capacity  of pool X , we must transfer 1/7 of the capacity of pool X, which is 25% of the water currently in pool Y (1/7)/(4/7) = 1/4. Sufficient.

Or consider the following:

Let the capacity of pool X be 7 gallons. It's 2/7 full, thus there are 2 gallons of water. If all the water currently in Pool Y were transferred to Pool X, Pool X would be filled to 6/7 of its capacity, and thus would contain 6 gallons of water, which means that there are now 6 - 2 = 4 liters of water in pool Y (it doesn't matter what capacity it has). In order for both pools to contain an  equal amount  of water, each pool should contain 3 gallons of water; thus, we should transfer 1 gallon from pool Y to pool X. 1 gallon is 1/4 of the water currently in pool Y.

(2) Pool X has a capacity of 14,000 gallons. No info about pool Y.

Not sufficient.

Answer: A.

Hope it's clear.

itnas · Answer

Thanks, I guess I just got blinded by not knowing the capacity of either pools.

Your explanations just remind me the scene of Die Hard 3 when transferring gallons of water from one “jar” to another in order to disarm the bomb :lol:

Halawi · Answer

Haha! I started reading the question and thought of the same thing... ahhhh the 90s action movies

Spidy001 · Answer

Lets say pool x's total capacity = x
 => Pool x filled capacity = (2/7)x

Lets say pool y's total capacity = y

lets say pool y's filled capacity = py ( where p is some fraction)

Let r be the volume transferred from y to x.

if py - r = (2/7)x+r , r is what percent of py?

1. Sufficient

py- r = (2/7)x+r = (6/7)x

(2/7)x+r = (6/7)x => r = (4/7)x

py - r = (6/7)x => py = (10/7)x

r is what percent of py? i.e is (((4/7)x) / ((10/7)x)) *100

= (4/10)*100

2. Not sufficient
 we dont know anything about pool y or how much removed from pool y.

Answer is A.

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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kpali · Answer

Question:
Let the capacity of X be C
so, X= 2C/7 and Y>X
If n is the quantity of water taken from Y and put into X
Then,
Y-n = X+n
2n = Y-X => n = (Y-X)/2
n is the quantity that needs to be transferred.
The % will (n/Y) * 100 %
(Note, that we already have one equation with X and C, and we just need one more involving Y and C, if we can get it out of any of the statements, it should be enough to solve)
Now lets take a look at the statements :

(1) If all the water currently in Pool Y were transferred to Pool X, Pool X would be filled to 6/7 of its capacity.

Y+X = 6C/7
and we know that X=2C/7

Hence, Y=4C/7

n = (Y-X)/2 = C/7
Therefore, % of water = (C/7)/(4C/7) *100
=100/4
=25%

Sufficient.

(2) Pool X has a capacity of 14,000 gallons.

We need another relation in Y and C or Y and X to be able to solve, not sufficient.

Ans: A

akshitagandhi · Answer

I did this and got the answer A but I think I went wrong somewhere in the steps - please correct  Bunuel   IanStewart

Py> Px
Let Px's total capacity be C
Px = 2/3 C

To get Py = Px
(Py-Px)/2 + Px = Py

Statement 1-
Py + Px = 6/7C
thus, Py = 6/7C - 2/3C = 4C/21

Percentage of Py which has to be transferred = {(Py-Px)/2} / Py
= (4C - 14C)/21 * 1/2 * 21/4C
= -10C/42 * 21/4C
= -5/4

Thus Statement 1 is sufficient

Statement 2 - NS because enough details of Pool Y not given

Please correct and help in Statement 1 steps / logic as to why I got it in negative

Bunuel · Answer

You used the wrong number. Check the stem again. So, iut should be ((6C/7 - 4C/7)/2)/(4C/7) = 1/4.

99pfqsb · Answer

In Data Sufficiency ; the two statements never contradict each other.

Statement B tells that the capacity is 14,000Lts

Take a hint and assume the volume to be 14 for the pool x

It is filled with 2/7 of its capacity ; 2/7*14 = 4Lts

Using 1. 
Current water in Y pool be be WLts

4+W/14 = 6/7
On Solving W will come out to be 8
To have equal amount of water in both X and Y the only qty possible is 6lts; hence X has to take 2Lts from Y
Therefore % of Water transferred from Y is 2/8*1000 = 25% 
Hence, Sufficient

2.) Insufficient

If Pool Y currently contains more water than Pool X, and if

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GMAT Data Sufficiency (DS) Questions

If Pool Y currently contains more water than Pool X, and if

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