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When the oil from a circular cylinder leaked, the formula for the spee

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Bunuel
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When the oil from a circular cylinder leaked, the formula for the spee [#permalink] New post  29 Nov 2015, 09:57
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Math Revolution and GMAT Club Contest Starts!



QUESTION #4:

When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 2, the speed of the leak is V’, When the height of the oil remaining is 4, what was the speed of the leak, in terms of V’?

A. 2V’
B. 4V’
C. V’/2
D. V’/4
E. V’


Check conditions below:


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Math Revolution and GMAT Club Contest

The Contest Starts November 28th in Quant Forum


We are happy to announce a Math Revolution and GMAT Club Contest

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Re: When the oil from a circular cylinder leaked, the formula for the spee [#permalink] New post  29 Nov 2015, 10:03
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As Given
V = kh^2

1. h=2 , V can be calculated as

V = Kh^2
V' =4k

2. h=4 ,

V =16k = 4(4k)= 4V'

Hence answer B !
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Re: When the oil from a circular cylinder leaked, the formula for the spee [#permalink] New post  29 Nov 2015, 10:40
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The answer is B.

We know speed of the leak is V=4kh^2. (k is constant and h is height of oil remaining). Given - when height of the cylinder is 2 speed of leak is V'. Assuming height of oil in the cylinder is 2 = height of oil remaining, V' =K*2^2. or K=V'/4

Find V when height of oil remaining is 4. V=(V'/4)*4^2 = V'*4 or option B.
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Re: When the oil from a circular cylinder leaked, the formula for the spee [#permalink] New post  29 Nov 2015, 11:08
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For a cylinder of height 2, that just starts leaking, h = 2. (Appears to be a typo in the question. 2 should be height of remaining oil)
\(V` = 2^2k\\
V` = 4k\)

For a cylinder with remaining oil 4, h=4
\(V = 4^2k = 16k\)

Thus, \(V` = 4V\)

Answer B
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Re: When the oil from a circular cylinder leaked, the formula for the spee [#permalink] New post  Updated on: 29 Nov 2015, 11:52
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V=Kh^2

at h=2; V'=K(2)^2=4K
=> K=V'/4 .... (I)

at h=4; V"=K(4)^2=16K .... (II)

substituting .. (I) into (II) , we have
V" = 16 (V'/4) = 4V'

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Originally posted by Nightfury14 on 29 Nov 2015, 11:22.
Last edited by Nightfury14 on 29 Nov 2015, 11:52, edited 1 time in total.
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Re: When the oil from a circular cylinder leaked, the formula for the spee [#permalink] New post  01 Dec 2015, 13:15
1
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Formula for the speed of leak is v = k*h^2. Let's write the question in terms of this formula:

"If the height of the cylinder is 2, the speed of the leak is V’" in terms for above formula can be stated as:

v' = k*2^2 (v' is the velocity when the hight is 2 )

v' = 4k

k = v'/4

"When the height of the oil remaining is 4, what was the speed of the leak" in terms of formula can be stated as:

v = k*4^2

v = 16k

v = 16*(v'/4)

v = 4v' (this is the velocity of leak in terms of v', when hight of remaining oil is 4)

Option (B) is correct.
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Bunuel
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Re: When the oil from a circular cylinder leaked, the formula for the spee [#permalink] New post  14 Dec 2015, 09:03
Expert Reply
Bunuel wrote:

Math Revolution and GMAT Club Contest Starts!



QUESTION #4:

When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 2, the speed of the leak is V’, When the height of the oil remaining is 4, what was the speed of the leak, in terms of V’?

A. 2V’
B. 4V’
C. V’/2
D. V’/4
E. V’


Check conditions below:


Show Spoiler

Math Revolution and GMAT Club Contest

The Contest Starts November 28th in Quant Forum


We are happy to announce a Math Revolution and GMAT Club Contest

For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday).

To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific.
Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6-months access to GMAT Club Tests.

PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize:

PS + DS course with 502 videos that is worth $299!



All announcements and winnings are final and no whining :-) GMAT Club reserves the rights to modify the terms of this offer at any time.


NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.

Thank you!



MATH REVOLUTION OFFICIAL SOLUTION:

This type of question appears within a score range of 45 to 48. It is important to first find the value of a constant like this speed question. According to the question, when the height of the cylinder is 2, the speed of the leak is V’. Therefore, the first step would be: V’=k(2)^2=k4, k=V’/4. Because the question asks for the speed of the leak when the height is 4, the calculation would be: V=k(4)^2=(V’/4)(16)=V’/4. So, B is the correct answer.
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Re: When the oil from a circular cylinder leaked, the formula for the spee [#permalink] New post  26 Feb 2024, 08:52
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