Pool X and Pool Y

[chipbmk]

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.

OA: A

Please be as detailed as possible, I have already read through the official answer from MGMAT and I am still confused. Pretend you are explaining this to a 5th grader

Thanks!

[djkvakin]

Pool x is filled up to 2/7 of it's capacity. Let's look at condition I:
It tells us that if we add all the water from Y to X, X will get filled up to 6/7 of the capacity. That means that together both pools contain 6/7 of the water to fill pool X. To equalize the amount of water in both pools we need each pool have 3/7 of the water (that is 6/7 divided by 2). Since pool Y contains 4/7 (that we know because 6/7-2/7=4/7). we know that 1/7 of the water from pool Y has to be transfered to pool X. Our answer then will be 1/7*100%.
Condition II tells us nothing about pool Y. Hence, the answer is A.

[chipbmk]

AAAHHH much better explanation than the official MGMAT.

Thanks!

[beatthegmat]

Nice explanation, djkvakin!

[viju9162]

very nice explanation djkvakin.

Thank you.

Regards,
Viju

[asafe]

Pool x is filled up to 2/7 of it's capacity. Let's look at condition I:
It tells us that if we add all the water from Y to X, X will get filled up to 6/7 of the capacity. That means that together both pools contain 6/7 of the water to fill pool X. To equalize the amount of water in both pools we need each pool have 3/7 of the water (that is 6/7 divided by 2). Since pool Y contains 4/7 (that we know because 6/7-2/7=4/7). we know that 1/7 of the water from pool Y has to be transfered to pool X. Our answer then will be 1/7*100%.
Condition II tells us nothing about pool Y. Hence, the answer is A.

I agree with answer A, but shouldn't the amount to be transfered be 1/4 of pool Y ?
Y contains 4/7 of X => tranfering 1/7 of X means a 1/4 of Y.

[djkvakin]

Pool x is filled up to 2/7 of it's capacity. Let's look at condition I:
It tells us that if we add all the water from Y to X, X will get filled up to 6/7 of the capacity. That means that together both pools contain 6/7 of the water to fill pool X. To equalize the amount of water in both pools we need each pool have 3/7 of the water (that is 6/7 divided by 2). Since pool Y contains 4/7 (that we know because 6/7-2/7=4/7). we know that 1/7 of the water from pool Y has to be transfered to pool X. Our answer then will be 1/7*100%.
Condition II tells us nothing about pool Y. Hence, the answer is A.

I agree with answer A, but shouldn't the amount to be transfered be 1/4 of pool Y ?
Y contains 4/7 of X => tranfering 1/7 of X means a 1/4 of Y.

I think you are right. I have been thinking about that. very good.

[bhumika.k.shah]

Any other approaches?

[kstv]

Another approach is to make some strategic assumptions.
Volume of Pool X = Volume of Pool Y = 7 litres/gallons or 7000 litres/gallons makes no diff.
Volume of water in X = 2 ltrs or 2000 ltrs based on full capacity assumed.
(1) water of Pool Y emptied into Pool X
Pool X is 6/7 full so it had 6 ltrs
Assuming capacity of 7 ltrs is fine cos after the water of Pool Y is emptied the denominator of the fraction is still 7. #
Easy to see that 4 ltrs have been added from Pool Y
So pool y was 4/7 full.
Adding one litre from Y to X would be enough fro both to be 3/7 full.
Sufficient
(2) pool X has a capacity of 14,000 gallons. djkvakin says that nothing is said about Pool Y but we know capacity of Pool Y = Pool X. Importantly , it does not say how much water is there in Pool Y. Hence insufficient

# if the question said that after water from Pool y is emptied in Pool x , Pool X is 9/13 full then will making assumption work ?

[Fiver]

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.

OA: A

Please be as detailed as possible, I have already read through the official answer from MGMAT and I am still confused. Pretend you are explaining this to a 5th grader

Thanks!

Assume total capacity of pool x =x and that of pool y =y

Current capacity of pool x = 2x/7 and that of y=a*y ('a' because we do not know what fraction of y is currently filled)

The question is
If ay - n = 2x/7 + n, then n/ay = ?

(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.

This means: ay + 2x/7 = 6x/7
Hence ay = 4x/7
Now 4x/7 - n = 2x/7 + n
Therefore n = x/7
and n/ay = x/7 * 7/4x = 25%