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A saltwater solution completely fills a glass cylinder. If the solutio

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A saltwater solution completely fills a glass cylinder. If the solutio  [#permalink]

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New post 05 Sep 2015, 12:47
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A saltwater solution completely fills a glass cylinder. If the solution is then poured into a larger rectangular aquarium, what percent more solution would be needed to completely fill the aquarium?

(1) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: sq rt 2

(2) The height and width of the aquarium are equal to the height and diameter of the cylinder.
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Re: A saltwater solution completely fills a glass cylinder. If the solutio  [#permalink]

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New post 05 Sep 2015, 15:28
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Yash12345 wrote:
A saltwater solution completely fills a glass cylinder. If the solution is then poured into a larger rectangular aquarium, what percent more solution would be needed to completely fill the aquarium?

(1) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: sq rt 2

(2) The height and width of the aquarium are equal to the height and diameter of the cylinder.


A saltwater solution completely fills a glass cylinder. If the solution is then poured into a larger rectangular aquarium, what percent more solution would be needed to completely fill the aquarium?

For these type of problems I normally try and visualize and think if the statements allow for variance in the objects volume. Important to note is that they are asking for the percentage of volume difference, which you can think of a ratio in the volume of one to another.

(1) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: sq rt 2... Before you get bogged down and put pen to paper, just think of the huge variance in size this allows for the rectangular tank. Just assign some arbitrary value "a" to the diameter of the cylinder which will equal some other value "b" you could end up having a base that is a square, which maximizes the area of the base or a base that is almost as long as "b", which will bring the area close to 0. clearly INSUFF

(2) The height and width of the aquarium are equal to the height and diameter of the cylinder... Once again, you don't even need to put pen to paper here, This will allow you to fit the cylinder into the tank however gives no information about the length, meaning it could be a completely maximized fit or the tank might be any number of meters longer in excess of the cylinder... Clearly INSUFF

(1) & (2)... (2) will lock in the height and the width, and (1) will lock in the length by controlling the size of the diagonal SUFFICIENT

Answer: C

Apologies for the wordy answer, and hope it's clear. I ALWAYS make mistakes in the execution of math problems when there is algebra with a lot of moving parts so whenever possible I try and solve the problems visually with logic... This is often a helpful in DS problems which don't require you to actually "calculate" anything. :)
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Re: A saltwater solution completely fills a glass cylinder. If the solutio  [#permalink]

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New post 31 Mar 2018, 01:06
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Bunuel
There seems to be a flaw in this question.

As per statement 1,
Diagonal of Aquarium / Diameter of cylinder =1: sq rt 2

As per Statement 2,
Width of Aquarium = Diameter of cylinder

Hence Combining, we get
Diagonal of Aquarium / Width of Aquarium =1: sq rt 2

Which is not possible because the diagonal of base = hypotenuse of right triangle which is formed by length & width.
Hence diagonal is always greater than width/length, Hence wording of question is not correct.



Yash12345 wrote:
A saltwater solution completely fills a glass cylinder. If the solution is then poured into a larger rectangular aquarium, what percent more solution would be needed to completely fill the aquarium?

(1) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: sq rt 2

(2) The height and width of the aquarium are equal to the height and diameter of the cylinder.

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A saltwater solution completely fills a glass cylinder  [#permalink]

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New post 01 Mar 2019, 12:51
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A saltwater solution completely fills a glass cylinder. If the solution is then poured into a larger rectangular aquarium, what percent more solution would be needed to completely fill the aquarium?

(1) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: sq rt 2

(2) The height and width of the aquarium are equal to the height and diameter of the cylinder.

Can someone explain me this one?

Thanks in advance
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A saltwater solution completely fills a glass cylinder  [#permalink]

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New post Updated on: 01 Mar 2019, 14:45
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lerogmat wrote:
A saltwater solution completely fills a glass cylinder. If the solution is then poured into a larger rectangular aquarium, what percent more solution would be needed to completely fill the aquarium?

(1) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: sq rt 2

(2) The height and width of the aquarium are equal to the height and diameter of the cylinder.

Can someone explain me this one?

Thanks in advance


IF YOU FIND MY SOLUTION HELPFUL, PLEASE GIVE ME KUDOS

It is necessary to know the formulas for volume of a cylinder and volume of a rectangular solid. They are v = pi*r^2h and v=lwh Also, if we can get the algebraic expressions for volume of the cylinder and volume of the aquarium to contain the same variables, we could pick values for the variables to determine the relative volumes in term of a percentage.

(1) The ratio of the diagonal of the base of the aqarium to the diameter of the cylander is 1:sq rt 2 Ok so our cylinder will have diameter sq rt 2 * x and radius = (xrt2)/2. Lets call the diagonal of the base of the aquarium and the diameter of the cylinder x. Lets call the heights of the cylinder and aquarium h1 and h2. So the volume of our cylinder will be pi*(xrt2/2)^2 *h1. Now, since we have a rectangular aquarium, and we know the diagonal of the base is x, we know that the width of the base is x/2 and the length of the base is x*rt 3/2, since the diagonal of any rectangle forums a 30 - 60- 90 right triangle whose dimensions are in the ratio 1: 1rt3: 2. So, volume of the aquarium is then x*xroot3 * h2. Since the volume of the cylinder and the volume of the aquarium contain different variables, we cannot know their relative volumes. NS

(2) the height and width of the aquarium are equal to the height and diameter of the cylinder. Lets call the height H and the width and diameter of the aquarium x. Then the volume of the cylander is pi*(x/2)^2 * h, and the volume of the aquarium is h*x*L Since the volume of the aquarium contains the variable L for length, we cannot find the volume of the aquarium relative to the cylinder. NS

(1) and (2) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: root2 And the height and width of the aquarium are equal to the height and diameter of the cylinder. Ok, so the radius of the cylinder is xroot2/2, the height of the cylinder we can call H3, and the length, width and height of the aquarium are x/2, (xroot3)/2 and H3 (since the heights of the two shapes are the same).

So, our volumes of the cylinder and aquarium are pi*(xrt2/2)^2*H3 and (x/2)*(xroot3)/2*H3. Since there are now, no variables in the expressions for volume of the cylinder that are not in the expression for the volume of the aquarium ( and vice versa) we could pick values for both x and H3. Since we are only needing the volume of the aquarium in relative terms as a percentage of the cylinder, we are Sufficient.

The answer is C

Originally posted by ocelot22 on 01 Mar 2019, 13:48.
Last edited by ocelot22 on 01 Mar 2019, 14:45, edited 1 time in total.
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Re: A saltwater solution completely fills a glass cylinder  [#permalink]

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New post 01 Mar 2019, 14:22
A saltwater solution completely fills a glass cylinder. If the solution is then poured into a larger rectangular aquarium, what percent more solution would be needed to completely fill the aquarium?

(1) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: sq rt 2

(2) The height and width of the aquarium are equal to the height and diameter of the cylinder.

This is a "Value" DS question, so sufficiency will be achieved if a statement allows for one value and one value only.

This question is about volume. We have a certain volume in a cylinder. Volume of a cylinder = pi*r^2*h (area of the circle/base x the height of the tube). Then we pour that volume into a rectangular prism.

To know what percent more solution would be needed to fill the aquarium, we need to know HOW FULL it currently is. So we need two pieces of info:

-the amount of the original volume (pi*r^2*h)
-the total volume of the prism (Volume = lwh)

To know how full it currently is, is essentially that ratio of (pi*r^2*h)/lwh.
If we ignore pi, we essentially need to understand the ratio between the radius and the length and width, and the ratio of the heights.

Let's look at the statements:

(1) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: sq rt 2

This gives us a relationship between the width and length to the diameter, but not quite enough info. It basically says that:
diameter = 2(w^2 + l^2), once we simplify it down. This is great, since we know radius is half the diameter, but we don't know anything about the heights.

(2) The height and width of the aquarium are equal to the height and diameter of the cylinder.

This gives us the info we need about the heights! They are equal! And also, the diameter is equal to the width of the aquarium. We have the relationships we need to solve.

I would not recommend you actually attempt to solve a question like this. It is definitely going to take way more than 2 minutes, and I think it's a 700+ level "time-waster." If you can't "logic" your way through it, I think making your best guess and moving on is the way to go.
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Re: A saltwater solution completely fills a glass cylinder  [#permalink]

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New post 05 Mar 2019, 08:12
Hi Bunuel,
This question has been discussed in the another thread. Here is the LINK of that thread.
Also, there is no SPOILER in this newly made thread!
Thanks__

lerogmat wrote:
A saltwater solution completely fills a glass cylinder. If the solution is then poured into a larger rectangular aquarium, what percent more solution would be needed to completely fill the aquarium?

(1) The ratio of the diagonal of the base of the aquarium to the diameter of the cylinder is 1: sq rt 2

(2) The height and width of the aquarium are equal to the height and diameter of the cylinder.

Can someone explain me this one?

Thanks in advance

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Re: A saltwater solution completely fills a glass cylinder   [#permalink] 05 Mar 2019, 08:12
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