Yes, your logic is correct. Though, as I mentioned in my solution, this calculation is not required.
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I'm not sure if this is the correct place to ask, but if the depth was let's say 3ft instead of 2. Would statement 2 still be sufficient?

Yes, it would be sufficient. 3 points uniquely define a circle i.e. you can make only one circle with given 3 distinct points. It is the circumcircle of the triangle drawn by connecting the 3 points.
So no matter what the dimensions given to you, the dimensions are uniquely defined.
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As mentioned in the question stem, the cylinder is lying horizontally and depth or height of the is 2 ft( in horizontal position) , actual height of the cylinder is 6 ft.
so, volume of the tank is 3.14* R^2* 6

S1) diameter is 4ft .
so, R= 2ft and as mentioned depth or height of the is 2 ft( in horizontal position) so volume of the fluid can be derived from here. so its sufficient.

S2) upper surface of fluid forms a rectangle of area 24.
as , h = 6 so A*6= 24, A= 4;
A/2 =2 which is depth or height of the is 2 ft( in horizontal position) so volume of the fluid can be derived from here. so its sufficient.

So, answer id D.

Let´s suppose the water filet is on the center of the cylinder.
Than the water´s height (2 feet) would be the radius of the supposed cylinder, consequently the diameter would be be 4 feet.
Which by the way is the only possible value for water filet´s width.

Hi chetan2u

Though i understood the logic i am confused at the first place as how u got 2√3 in the beginning..

Seems like a silly doubt but i am not able to catch it

Thanks..

How did we interpret the fact that depth =2 into dia =4 ? Do you also mind elaborating a bit more on statement 2 ?

Thanks a lot !

Hey Karishma,

Thanks for the explanation. However, I do have one doubt related to your explanation for statement 2. Even if we are to calculate the area of the segment, we would still need the angle the segment makes at the center, right? Right now with the current information, we don't have that.

Is this an OG question? Why is it so poorly written?!?!

Honestly, I did not really get the meaning of statement 2 until I saw the sketch of one of the experts

"The top surface of the gasoline" - I initially assumed "The top surface of the gasoline's (tank)...", so that the cylinder stands on a rectangular platform.

How can a liquid form a surface equal to a rectangle. I don't want to sound too overly correct but especially for non-natives this wording is very poorly.. would have love to calculate that on my own but I just did not get the meaning.
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Why do we need either of the statements? Volume=πr2h
R= 3
H= 2

When we say top surface then does that mean cylinder excluding the filled gasoline?
So, in that case shouldnt the area of rectangle be 6* 2 ( 4 - 2 (filled gasoline))= 12

How to improve my understanding for these type of question?

"tank is filled with gasoline to a depth of exactly 2 feet. The tank is a cylinder resting horizontally on its side, with its circular ends oriented vertically."????? this is completely alien to me

A student asked me to explain why statement 2 is sufficient. So,......

Target question: What is the volume of gasoline in the tank?

Statement 2: The top surface of the gasoline forms a rectangle that has an area of 24 square feet.
We know that the tank is 6 ft long
Let x = the width of the surface
We have the following:



Area of rectangle = (base)(height)
So, we can write: 24 = (6)(x)
Solve get: x = 4
So, the diagram looks like this:


IMPORTANT: For geometry Data Sufficiency questions, we’re typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the following video: https://www.gmatprepnow.com/module/gmat ... /video/884

So we want to determine whether there is exactly one tank size such that when the gasoline is 2 feet deep, the surface of the gasoline is 4 feet wide.

So let's start with some random tank like this...

... and fill it with gasoline to a depth of 2 feet

When we measure the width of the surface, we get 3 feet

So, this particular tank is too small.

Let's try slightly bigger tank. Here's one.

Still too small.

As we can see, if we gradually make the tank bigger and bigger and bigger, there will be EXACTLY ONE tank such that the width of the surface is 4 feet.


Since there is EXACTLY ONE tank that meets the given conditions, we know that statement 2 is SUFFICIENT

Answer: D

ASIDE: Some people might be wondering, "Sure, but what is the actual volume of the gasoline in the tank?"
Fortunately, we don't need to find the actual volume. We need to only demonstrate that we COULD find the volume.
One way to do this would be to use geometric properties and formulas. But we can also find the volume in other ways.
For example, if I had very precise measuring equipment and a way to construct cylindrical tanks of any shape, then I COULD keep testing actual tanks until I find one that meets the given conditions. Then, I'd fill that tank with gasoline to a depth of 2 feet. Then I'd pour that gasoline into a very precise measuring cup. Done!!

Cheers,
Brent
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Hi Brent, thank you for the excellent explanation. BrentGMATPrepNow

One question: if we keep the dimensions of the top layer (6 x 4) the same and gradually make the can larger, the level would drop. Would this change the volume?
For instance, if we look at a can with a diameter of 100, the amount of gas would be very low within that can, but the top layer would still be 6 x 4 with a depth of 2.

Every time we change the diameter of the tank, the width of water (when the tank is 2 in deep) changes.
For example, if we take a tank with diameter 100 and fill it to a depth of 2 feet, the width of the water will be 28 ft (not 4 feet)
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(1) We are given diameter. Then the radius = 2, which is equal to the depth of the gasoline. Now if we figure out the volume of cylinder and divide that by 1/2 then we will get the volume of the gasoline. Sufficient.

(2) If the wrapping part of the cylinder is cut out then it will be a rectangle. We know the length of the rectangle = 6 so the height will be 4 and it will be the diameter of the cylinder and half of it is equal to the depth of gasoline. So can calculate the volume with provided information like option 1.
Sufficient.

Ans. D
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Hi VeritasKarishma

I am confused about the orientation of the figure. Shouldn't "circular ends oriented vertically" tell us that the cylinder would be a verticalle right cylinder? I reached the correct answer by assuming that? Am I missing anything?

razorhell -
"The tank is a cylinder resting horizontally on its side, with its circular ends oriented vertically."

You are given that the cylinder is resting horizontally on its side (it means you can roll it along its side).

The circular ends are the top and bottom circles of a vertically aligned cylinder. The orange and the blue surfaces are circular ends. Here the circular ends are oriented horizontally.



In our question the circular ends are oriented vertically. That means the cylinder is lying down along its edge as shown in figures in previous posts.
If you still got the correct answer, I am surprised. If you show your calculations, I can tell you what happened.
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