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A cylinder of height h is 3/4 of water. When all of the water is poure

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Bunuel
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A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   08 Jun 2015, 08:08
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A cylinder of height h is 3/4 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?

(A) 25%
(B) 50%
(C) 60%
(D) 80%
(E) 100%
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D
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Re: A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   08 Jun 2015, 08:39
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Bunuel wrote:
A cylinder of height h is 3/4 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?

(A) 25%
(B) 50%
(C) 60%
(D) 80%
(E) 100%

Kudos for a correct solution.


Volume of the first cylinder equal to \(pi*r^2h\)
Volume of the second cylinder equal to \(pi*(\frac{5}{4}r)^2x\) where x is height of second cylinder

We know that \(\frac{3}{4}\) of volume of first cylinder is equal to \(\frac{3}{5}\) of volume of second cylinder so we can write equation:

\(\frac{3}{4}*pi*r^2h=\frac{3}{5}*pi*(\frac{5}{4}r)^2x\)
By dividing this equation on \(pi*r\) we will receive such equation

\(\frac{3}{4}*h=\frac{3}{5}*(\frac{5}{4})^2x\) --> \(\frac{3}{4}h=\frac{15}{16}x\) --> \(\frac{x}{h}=\frac{4}{5}=80\)%
Answer is D
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Re: A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   08 Jun 2015, 08:28
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Bunuel wrote:
A cylinder of height h is 3/4 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?

(A) 25%
(B) 50%
(C) 60%
(D) 80%
(E) 100%

Kudos for a correct solution.


Since the radius ratio is 1:1.25 or 1*4:1.25*4 or 4:5..
lets take integer values for simplification..
original cylinder --- 4r and height h..
new ----5r and ht H...
so \(\pi*(4r)^2*\frac{3h}{4}=pi*(5r)^2*\frac{3H}{5}.\)..
so \(4h=5H\) or \(H= h*\frac{4}{5}\)... so 80%
ans D
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Re: A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   08 Jun 2015, 11:26
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A cylinder of height h is 3/4 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?

(A) 25%
(B) 50%
(C) 60%
(D) 80%
(E) 100%

Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is because "the new cylinder is 3/5 full" means the same as that it's height is 3/5.
Just to notate;

Original cylinder 3/4 = 0.75
New cylinder 3/5 = 0.60

So 3/5/3/4 = 3/5 * 4/3 = 12/15 = 4/5 = 0.80 or 80%.

Answer D
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Re: A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   08 Jun 2015, 11:39
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Radius of new Cylinder R = (1+1/4) * r -> R = 5/4 * r

3/4*(area of old Cylinder with height h) = 3/5*(area of new Cylinder with height H)

3/4 * (pi*r^2*h) = 3/5 * (PI*R^2*H) ---> H=4/5*h -->Height of new Cylinder = 80% of height of old Cylinder

Ans is D.

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Re: A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   09 Jun 2015, 01:44
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Bunuel wrote:
A cylinder of height h is 3/4 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?

(A) 25%
(B) 50%
(C) 60%
(D) 80%
(E) 100%


Ans: D

soluton: volume formula V = Pi* r^2 * h

now put the values of r1,r2,h1 and h2 in below given equation

3/4 *V1= 4/5 *V2

we will get h2 = 4/5 h1
means 80%
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Re: A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   10 Jun 2015, 02:10
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The volume of a cylinder is \(\pi r^2h\). Plugging in numbers: if the original cylinder has a radius of 4 and a height of 4, then the water has a height of 3 and therefore a volume of \(48\pi\). The new cylinder has a radius of 5 and a height of X and therefore a volume of \(25X\pi\). Because the water is only \(\frac{3}{5}\) the volume of the new cylinder, \(48\pi=\frac{3}{5}25X\pi\) -->
\(48=15X\) ->
\(X=\frac{48}{15}\). The percentage this is of the original height is \(\frac{\frac{48}{15}}{4}=\frac{12}{15}=\frac{4}{5}\) or D
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Re: A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   14 Jun 2015, 04:37
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Ratio of radius = 1:1.25
original cylinder: 4R and height H1
new :5R and ht H2
so PIX(4R)^2X3H1/4=piX(5R)^2X3H2/5!
so 4H1=5H2 or H2= H1*4/5 = 80%
Answer D
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Re: A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   15 Jun 2015, 03:24
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Bunuel wrote:
A cylinder of height h is 3/4 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?

(A) 25%
(B) 50%
(C) 60%
(D) 80%
(E) 100%

Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

First, set up a table:
Attachment:
2015-06-15_1422.png
2015-06-15_1422.png [ 64.31 KiB | Viewed 10997 times ]

If the new cylinder is 3/5 full with this volume of water, we can set up an equation:
Attachment:
2015-06-15_1423.png
2015-06-15_1423.png [ 38.45 KiB | Viewed 10984 times ]

Therefore, x is 80% of h.

The correct answer is D.
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Re: A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   30 Oct 2019, 22:17
let h is height of first cylinder and h' is height of 2nd cylinder.
as per given information-
liquid in cylinder 1 = liquid in cylinder 2 => r^2*h*(3/4)(22/7) =( r*5/4)^2*h'*(3/5)(22/7) ----> h*(3/4) = (25/16)(3/5)*h'---->h = h'*(5/4)---->h'= (4/5)*h-----> 80% of h.

Answer D - 80% is correct
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Re: A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   30 Oct 2019, 23:07
Bunuel wrote:
A cylinder of height h is 3/4 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?

(A) 25%
(B) 50%
(C) 60%
(D) 80%
(E) 100%

Kudos for a correct solution.

Let r be radius and h be height of original cylinder.
It is 3/4th full. So volume of water in it. = (3/4)*pi*r^2*h

Radius of new cylinder = 1.25r. Let H be the height of new cylinder.
It is 3/5th full. So volume of water in it = (3/5)*pi*(1.25r)^2*H

Since volume of water is same
So, (3/4)*pi*r^2*h = (3/5)*pi*(1.25r)^2*H
(5/4)*h = (1.25)^2*H
(5/4)* h = (5/4)^2*H
H = 4/5 h = 80% of h.

Answer D.
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Re: A cylinder of height h is 3/4 of water. When all of the water is poure [#permalink] New post   02 Feb 2024, 08:32
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