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.
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.
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 --> together pools X and Y contain 6/7 of the capacity of pool X
. Now, in order pools X and Y to contain 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 will 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 both pools to contain 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.
Hope it's clear.
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