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A tank is filled with gasoline to a depth of exactly 2 feet. The tank

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A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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A 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. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?

(1) The inside of the tank is exactly 4 feet in diameter.

(2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

From OG 2016 (question 86 DS)


I get why 1 works, but the main qualm I have about 2 is how we can be sure that the 4 feet resulting from the square is a diameter of the circle ie. how we know that it fills the tank exactly up to halfway.

Originally posted by iamschnaider on 23 Jul 2015, 20:04.
Last edited by Bunuel on 24 Jul 2015, 00:23, edited 1 time in total.
RENAMED THE TOPIC.
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 15 Mar 2018, 05:33
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sadikabid27 wrote:
Bunuel VeritasPrepKarishma could you please give a clearer and easier approach to this problem? Thanks :)


It is a DS question so some imagination can give us the answer without solving at all. This is what the cylinder looks like:
Attachment:
DS2.jpeg
DS2.jpeg [ 14.41 KiB | Viewed 14037 times ]

The question stem tells us that Height = 2 and Length = 6.

Stmnt 1: Diameter = 4

This means the tank is half full. We can find the total volume of the tank using the formula of volume of a cylinder and divide it by 2. We will get the volume of gasoline. Sufficient alone.

Stmnt 2: The area of the rectangle is 24.
We know that the Length is 6 so the other side of the rectangle (as visible in the pic) would be 4. Now imagine this: I have a horizontal line of length 4. If I draw a line from its centre of length 2, I will get a defined arc (which we see is a semi circle but that is irrelevant anyway since it is a DS question).

Attachment:
DS1.jpeg
DS1.jpeg [ 7.62 KiB | Viewed 14022 times ]

If there is only one way in which we can make the arc, it means it has defined dimensions and hence the area of this segment can be calculated. Hence the volume of gasoline will be area of this segment * Length of the cylinder.
Sufficient alone.

Answer (D)
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 24 Jul 2015, 06:30
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reto wrote:
iamschnaider wrote:
A 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. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?

(1) The inside of the tank is exactly 4 feet in diameter.

(2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

From OG 2016 (question 86 DS)


I get why 1 works, but the main qualm I have about 2 is how we can be sure that the 4 feet resulting from the square is a diameter of the circle ie. how we know that it fills the tank exactly up to halfway.


Could someone draw this for Statement 2? I don't get it... :(


Hi reto
here it is
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A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 24 Jul 2015, 06:47
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reto wrote:
iamschnaider wrote:
A 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. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?

(1) The inside of the tank is exactly 4 feet in diameter.

(2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

From OG 2016 (question 86 DS)


I get why 1 works, but the main qualm I have about 2 is how we can be sure that the 4 feet resulting from the square is a diameter of the circle ie. how we know that it fills the tank exactly up to halfway.


Could someone draw this for Statement 2? I don't get it... :(


reto, see the attached picture.

The trick with statement 2 is that H = 0 when you calculate the value of H from the 2 equations:

\(H^2 + 2^2 = R^2\)

and

R = 2+H , you get H =0

This means that the depth of the gasoline in the cylinder = radius of the cylinder.

Thus, it is sufficient to answer the question.

FYI, we need to know about the radius as without the depth of gasoline = radius of the cylinder, it will be difficult to calculate the volume of the gasoline in the tank.

Hope this helps.
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GASOLINE CYLINDER.jpg
GASOLINE CYLINDER.jpg [ 30.15 KiB | Viewed 37106 times ]

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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 23 Jul 2015, 21:17
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iamschnaider wrote:
A 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. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?

1) The inside of the tank is exactly 4 feet in diameter.

2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

From OG 2016 (question 86 DS)


I get why 1 works, but the main qualm I have about 2 is how we can be sure that the 4 feet resulting from the square is a diameter of the circle ie. how we know that it fills the tank exactly up to halfway.


Hi,
i agree with you however we still can find the answer ..
we can find the chord/diameter of the circular end as 4..
now we have depth as 2, length as 6 and width as 4 but the volume will vary depending on what the dia would be..
there could be two scenarios..
1) where the center is below the chord... that is greater than 2\(\sqrt{3}\)..
eq becomes \(2^2+(2\sqrt{3}+r)^2=r^2\)
r comes out negative so not possible.
2) where the center is above the chord... that is greater than 2\(\sqrt{3}\).. r can be found so suff..
eq becomes \(2^2+(2\sqrt{3}-r)^2=r^2\)

.
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 23 Jul 2015, 21:57
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chetan2u wrote:
iamschnaider wrote:
A 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. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?

1) The inside of the tank is exactly 4 feet in diameter.

2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

From OG 2016 (question 86 DS)


I get why 1 works, but the main qualm I have about 2 is how we can be sure that the 4 feet resulting from the square is a diameter of the circle ie. how we know that it fills the tank exactly up to halfway.


Hi,
i agree with you ..
we can find the chord/diameter of the circular end as 4..
now we have depth as 2, length as 6 and width as 4 but the volume will vary depending on what the dia would be..
dia could be anything equal to or greater than 4....
so stat II should not be suff...


Hi, Just check this out....
The line joining the center to the point where the tank rests on the ground would be dividing the chord ( whose lenth is 24 / 6 = 4 ) equally and hence we can write two equations. Say x is the distance between center and chord then, x + 2 = radius ( r), and also r^2 = x ^2 + 2 ^2... so we can find the radius using the two equations and hence..statement II is also suffficient...
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 24 Jul 2015, 05:37
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iamschnaider wrote:
A 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. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?

(1) The inside of the tank is exactly 4 feet in diameter.

(2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

From OG 2016 (question 86 DS)


I get why 1 works, but the main qualm I have about 2 is how we can be sure that the 4 feet resulting from the square is a diameter of the circle ie. how we know that it fills the tank exactly up to halfway.


Could someone draw this for Statement 2? I don't get it... :(
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 21 Aug 2015, 03:10
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Wait, I don't understand how you need any more information at all. Given,that the length of the cylinder is 6ft and height of the water is 2, won't the water take the shape of half of a cylinder with radius 2 ? After that you don't need any more information regarding the volume of water, right ?
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 21 Aug 2015, 04:42
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hb4100 wrote:
Wait, I don't understand how you need any more information at all. Given,that the length of the cylinder is 6ft and height of the water is 2, won't the water take the shape of half of a cylinder with radius 2 ? After that you don't need any more information regarding the volume of water, right ?


You need to know the radius of the cylinder and how the radius stacks up against the depth of the water in the cylinder. Without this information, you will not know if the statements are sufficient or not.

Take a look at: a-tank-is-filled-with-gasoline-to-a-depth-of-exactly-2-feet-the-tank-202262.html#p1553082

Your statement is correct if a statement tells you the radius = height of the water but if radius \(\neq\) height of the water, you will not be able to apply any volume formulae.

Hope this helps.
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 13 Dec 2015, 07:17
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abhimahna wrote:
Looking at the question, do we still think its of 600-700 level?

Also, what could be the quickest way to solve such questions?


Quickest way to do this is to realize that depth cant be equal to half the side-surface length unless side-surface length is diameter of the circular side of the tanker. Anywhere else
the depth will smaller than half of side-surface length. Since st2 gives us enough info to calculate side surface length as 4 and we can see half of it i.e. 2 is equal to the depth we know that 2 is the radius and thus can calculate the volume. SUF
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New post 17 Jan 2016, 00:27
For statement 1 why does the OG Answer Explanation assume that the volume of the gasoline is half the volume of the cylinder? I would have thought the volume of the gasoline is 8π, not 12π. Thanks in advance for your thoughts on what I'm missing.
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 17 Jan 2016, 00:33
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nycsfmba wrote:
For statement 1 why does the OG Answer Explanation assume that the volume of the gasoline is half the volume of the cylinder? I would have thought the volume of the gasoline is 8π, not 12π. Thanks in advance for your thoughts on what I'm missing.


Hi,
the Q stem tells us the folloeinf info..
A tank is filled with gasoline to a depth of exactly 2 feet...
the statement one tells us that the dia is 4 feet..

so when you join the two information, we can say that the cylinder is half filled
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 17 Jan 2016, 00:48
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nycsfmba wrote:
For statement 1 why does the OG Answer Explanation assume that the volume of the gasoline is half the volume of the cylinder? I would have thought the volume of the gasoline is 8π, not 12π. Thanks in advance for your thoughts on what I'm missing.


It is not assumed but rather a deduction from the given question statement and statement 1. Question statement mentions that the water is till a depth of 2 feet while statement 1 mentions that the diameter of the cylinder is 4 feet (or the radius is 2 feet). Thus the cylinder is filled half with water.

Hope this helps.
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 17 Jun 2016, 10:28
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I think this question is worded very poorly but it is actually very easy when you understand what it is asking. Volume = pi*r^2*h...... We know h=6.

Statement 1 gives us d = 4 or r = 2. Since the gasoline is also filled up to r =2, the volume of the gasoline is 1/2 of the volume of the container so it's sufficient.

Statement 2 - if you are seeing through the container from up above, the surface of the water will form a 2-d rectangle. Since we know the length of the rectangle is 6 (i.e. the height), the width of the rectangle (i.e. the diameter) must be 4. So again we know that d = 4 or r = 2 like in statement 1. Sufficient.

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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 27 Jun 2016, 21:16
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iamschnaider wrote:
A 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. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?

(1) The inside of the tank is exactly 4 feet in diameter.

(2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

From OG 2016 (question 86 DS)


1) radius =2
Volume= \(\pi * r^2 * h\)
\(\pi * 4*6\)
\(24\pi\) Sufficient
2) area = L * W = 24
12 * 2= 24
6 * 4= 24 since the length is 6 as given in the question so pick this
we know the area and radius so it's sufficient to find the height.
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 29 Jun 2016, 18:13
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Anytime you have the height of a liquid and the chord that it's surface makes, we can find the radius. In this case, if you understand that statement two gives us a chord, you can confirm it's the radius by using this formula:

(1/2*chord)(1/2*chord) = (height of liquid)(distance from surface to top of cylinder)

In this case 2*2=2*(distance from surface to the top of the cylinder) and we see that the distance from the surface of the gasoline to the top of the cylinder is 2, making the surface of the gasoline right in the middle of the cylinder.

So if the chord were length of 4 and the height of the liquid were 1, you could still use that formula to find the radius of 2.5. I'm not sure what you would do with it, but it's easy to get at should you find it necessary on test day.
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 05 Oct 2016, 02:19
Volume is a 3D thing .
The question itself gives the value of 2 of 3 Dimensions,
and statement 1 and 2 gives 3rd dimension in two different ways so either statement is sufficient .
This is the beauty of DS questions you don't need to find the answers you just need to feel whether you can find it or not.
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 30 Jul 2017, 04:02
I am not clear why statement 2 needs a bigger explanation. We find that the rectangle is of the dimension 6*4.
When viewed from the top the width of the rectangle will be equal to the diameter of the base of the cylinder. Why are the other calculations needed?
Please clarify
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 16 Mar 2018, 10:05
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Hello everyone

Could someone explain to me why statement II is sufficient? If we look at the cut that the rectangle is doing on the cylinder it could happen either under the centre or above it. In both cases it'll respect the premises but have completely different volumes of gasoline in it....

I'm really scratching my head with this!
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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New post 16 Mar 2018, 21:19
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bpegenaute wrote:
Hello everyone

Could someone explain to me why statement II is sufficient? If we look at the cut that the rectangle is doing on the cylinder it could happen either under the centre or above it. In both cases it'll respect the premises but have completely different volumes of gasoline in it....

I'm really scratching my head with this!


No. It will be at the centre only. Note that the height is 2 and diameter is 4 which means the radius is 2. Hence it will be a semi circle only.
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank   [#permalink] 16 Mar 2018, 21:19

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