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bucket and the boy

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by gmatmachoman » Mon Aug 16, 2010 11:27 am
A cylindrical bucket with height 10 and radius r, is 3/4 filled with water. A boy is dropping marbles with volume r/10 in the bucket at a rate of 12 a minute . how many seconds will it take before the water overflows from the bucket ?

A: 2.1 Pi

B :25 Pi

C: 125 Pi

D: 300 Pi

E: 375 Pi

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by madhukumar_v » Mon Aug 16, 2010 11:45 am
Is the volume of the marble r/10 or r^2/10?

I assume its r^2/10, based on that I get C, 125*PI seconds.

Total Volume = PI*r^2*10

3/4th already full, so 1/4th remaining, which is PI*r^2*10/4 = 2.5*PI*r^2 of volume

if the volume of the marble is r^2/10, then it will take 25*PI Marbles to fill the tank and overflow.

If 12 marbles take 1 min, then 1 marble takes 5 secs, so 25PI Marbles take 125 PI seconds.

so C.
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by chris@veritasprep » Mon Aug 16, 2010 12:40 pm
hi gmatmachoman -

the primary difficulty of this problem lies in its length - there are many individual steps. As with many harder GMAT questions, do not get overwhelmed by the complexity of the problem. Break it down into digestible pieces and attack each one separately.

step 1: determine volume of bucket - v= pi * r^2 * h here that is pi * r^2 * 10 or 10pi r^2

step 2: determine the volume of marbles that will make the bucket overflow - since it is 3/4 full we know that 1/4 of the volume of the bucket is the volume of marbles that will make the bucket overflow. this is the volume of the bucket divided by 4 or (10pi r^2)/4 , which can be simplifed to (5pi r^2)/2

step 3 determine how many marbles it takes to fill a volume of (5pi r^2)/2 This is done by dividing the volume we just calculated by the volume of one marble (r/10). Dividing (5pi r^2)/2 by r/10 you will get 25pi * r as the number of marbles required to fill the bucket.

step 4 use dimensional analysis to figure out the time required to drop 25pi * r marbles at the rate given

25pi * r marbles x 1 minute/12 marbles x 60 seconds/ one min = 125pi * r seconds. If I remember this question properly, I think the r was erroneously left out of the answer choices as posted here by machoman. Or as madhukumar_v said in his excellent explanation, it might have been r^2/10 as the volume. EIther way, answer is C. Hope that helps!
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by beatthegmatinsept » Mon Aug 16, 2010 12:43 pm
C too. Using the same method as described in above post.
Whats the source of this question? And do you know if this falls in the medium or difficult level?
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by chris@veritasprep » Mon Aug 16, 2010 3:12 pm
hi beatthegmatinsept,

that is a question from the Veritas books - may have been an Official question previously as some were licensed from GMAC. in terms of difficulty, my experience working with 100s of students on that question is that it would be classified as difficult. No individual step is that hard but students get lost in the large number of steps so it has a low success rate. hope that helps and let me know if you have any other questions.
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