Pooling Resources - Ratios/fractions problem

[superseema]

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

What is the best way to solve this problem and others like it algebraically? When I think about this logically, I can see that using statement one the answer would be 25%, but that statement 2 is insufficient to answer the question. However, answer key for the online test gives a method that seems very confusing and I am not sure if there would be enough time on the actual test to walk through all of what they do. Also, the answer key does not even solve the question -- it just establishes that there is a relationship between x and y.

What is the best way to solve this problem, either logically or algebraically?

[messi10]

Hi,

I am no expert and this area is not one of my strengths but I will have a go.

What are we looking for? - % of water that needs transferring from pool Y to pool X so that water in pool Y = water in pool X.

I will start with Statement 2 as it is the easier statement

2) Pool X has a capacity of 14,000 gallons
Quick calculations show that there is (2/7 x 14000) = 4000 gallons of water in Pool X.
No information is given about the water in Pool Y, therefore this is insufficient to answer the question.

Using the BD/ACE grid, I can cross out BD

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 tells us the amount of water in Pool Y in terms of volume of pool X.

Amount of water in Pool Y = 6/7 - 2/7 = 4/7 the volume of Pool X.

4/7 is twice of 2/7. This means that pool Y has twice the amount of water than pool X.

Now we have the ratio of amount of water Y:X = 2:1 We can stop at this point and say that this statement is sufficient. But if you want to go a step further, lets pick numbers:

Amount of water in Pool Y = 20 litres
Amount of water in Pool X = 10 litres

Therefore, if we transfer 5 litres of water from Pool Y to Pool X, they will both have 15 litres of water.

5 litres is what percentage of 20 litries? 25%

So statement 1 is sufficient. Answer is A. Please verify if this is correct

Thanks

Sunil

[messi10]

Hi,

Sorry, I didn't actually answer your questions. I was too engrossed in getting the question solved. :) Apologies

However, answer key for the online test gives a method that seems very confusing and I am not sure if there would be enough time on the actual test to walk through all of what they do. Also, the answer key does not even solve the question -- it just establishes that there is a relationship between x and y.

I have not seen the answer key explanation so I cannot comment. Please post it if you would like to discuss it.
The reason answer key doesn't solve the question because this is a DS question. We just need to establish that we can answer what has been asked. Once you know that the current water volume in the two pools is in the ratio 2:1, you now know that you can calculate the percentage. Note that if the question had asked "How much water needs to be transferred from Y to X...." then this statement would have been insufficient. Because this is asking for percentage, makes this question easier and you can stop earlier.

What is the best way to solve this problem, either logically or algebraically?

I cannot say with guarantee that any one method is better than the other for these questions. There are many ways in which this question can be manipulated and there are PS versions of this question as well. So my advice is to be familiar with algebraic way and picking numbers. If you master both, you will be more at ease with this type of question and can take decision on which one to use based on what is given and required in the problem.

Hope this helps

Regards

Sunil

[superseema]

Hi Sunil,

Thanks so much for your response. The way you solved the problem makes sense, and clarified the problem for me. There are so many ways of solving this problem, and I think that the mistake that I made was that I was trying to compute an actual amount, but as you've stated the question doesn't ask for an actual value.

I got correct solution too (A), but I did it in a different way from both you and the answer key. I eliminated BD first. Then, I calculated that of water in Pool Y is 4/7 of the amount of water in Pool X. and the amount of water in Pool X is 2/7 of the amount of water in Pool X. If you decrease the ratio of of water in Pool Y by 1/7 and increase the ratio in Pool X by 1/7 you will have the same amount of water in both pools: 3/7. I knew that 1/7 had to be the "transfer amount" from Y to X, and since 1/7 is 25% of 4/7, the percent transferred would be 25%. Therefore, answer choice A is sufficient. This method might be difficult with "harder" numbers or a different setup of the same problem though.

The answer key explanation arrived at the same ratio of 2:1 of the amount of water in Pool Y as compared to amount of water in Pool X. However, it went about it in a much longer way than you did in your explanation. Here is the explanation from the answer key:

(water currently in Pool X) + (water transferred) = (water currently in Pool Y) - (water transferred)
x + zy = y - zy
x + 2zy = y
2zy = y - x
z = y/2y - x/2y
z = 1/2 (1-x/y)

The rephrased question is: "What is x/y"?

(now the answer key goes on to the method you used....)

(1) SUFFICIENT: if we let X represent the capacity of Pool X, then the amount of water in Pool X is (2/7)X. So, x = (2/7)X. We can calculate the total amount of water in Pool Y, or y, as follows: y = (6/7)X - (2/7)X = (4/7)X. We can see that Pool Y has twice as much water

as Pool X, or 2x = y, or
x/y= 1/2.

(2) INSUFFICIENT: This gives no information about the amount of water in Pool Y.

The correct answer is A.

[jnelson0612]

Let me just add one more thought. As you all have mentioned, statement 2 is unhelpful because it gives us no information about Pool Y. Eliminate BD.

At this point, statement 1 and the question stem involve only fractions and percents. I would plug in actual numbers to make this easier.

I would decide that Pool X's capacity is 7 gallons, so it currently has 2 gallons (according to the stem). If X will be filled to 6/7 of capacity once Pool X receives Pool Y's water, Pool Y must have 4 gallons. Thus, Pool X currently has 2 gallons and Y has 4 gallons. To make them equal, Y must give 1 gallon out of its 4 gallons to Pool X (25%), leaving them each with 3 gallons. Statement 1 is sufficient.

I think this is a quick and easy way to handle this problem, and again, it's permissible since we only have fractions and percents mentioned, NOT real numbers.