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Manager  Joined: 11 Aug 2012
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Schools: HBS '16, Stanford '16
A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 47% (03:13) correct 53% (03:28) wrong based on 777 sessions

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A cylindrical water tower with radius 5 m and height 8 m is 3/4 full at noon. Every minute, .08π m3 is drawn from tank, while .03π m3 is added. Additionally, starting at 1pm and continuing each hour on the hour, there is a periodic drain of 4π m3. From noon, how many hours will it take to drain the entire tank?

A. 20 2/7
B. 20 6/7
C. 21
D. 21 3/7
E. 22
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Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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2
danzig wrote:

With 3 m3 remaining, after another 3/7 hours, only 3(0.5) = 1.5 m3 will be drained. So the tank will not actually be empty until 22 hours, when the periodic draw empties the remainder."
I don't understand the OE does this: 3(0.5) = 1.5 m3 :S !

Thanks!

Every minute, .05 m^3 is drawn from the tank. In one hour, water drawn from the tank will be 60*.05 = 3 m^3. Since at the end of 21st hr, 3 m^3 water is left in the tank, at the end of the 22nd hour, the entire 3 m^3 water will be drawn and there will be nothing left to drain out in periodic draining.

Further, in 3/7 hrs,
(3/7)*(60)*(.05) = 9/7 m^3 water is drawn

I do not know why they write 3(0.5) = 1.5
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Intern  Joined: 31 Oct 2012
Posts: 21
Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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1
7
This one got me, it is so hard to pay attention to every detail and think so much. I initially went with D. So D is wrong why why?

Alright so
initial volume = (3/4)×∏×5²×8 = 150∏
Relative Drain/ min = .08∏ - .03∏ = .05∏ m³/min drain
Relative drain / hour = .05∏×60 = 3∏ m³/ hr

Every one hour starting from 1pm, 4∏ m³ of water is drained. It means that only at the hour the water is drained and NOT “in that 1 hour“

So after 1 hr the relative drain would be 3∏ + 4∏ = 7∏m³ of water drain

What i did initially was formed an equation 150∏ = 7∏×n (n is the number of hrs) so ended up with 21 3/7. This wrong

Look at this way
after 21 hrs the amount of water drain will be 21×7∏ = 147∏ m³
Left over water in the tank after 21 hrs = 3∏ m³
From above we know that it take 1 more hour to drain that 3∏ m³.

So ans is 22hrs
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Manager  Joined: 26 Dec 2011
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Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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1
at 12: 3/4 * 200 = 150 pie m3
at 12 - 1: -.08 + .03 = -.05 * 60 = 3pie m3
at 1 - 147 pie m3 ===> 3 pie m3 + 4 pie m3 = 7 pie m3 ==> so in hour effectively 7 so it takes 21 hours for 147.

thus 21 (1- thereon)+ 1 (12-1) = 22 hours.
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Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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Another easy approach to this question is:

Volume to be drained= 150pi
Every minute, the volume that drains is : (0.08pi-0.03pi) metre cube or 0.05pi metre cube.
Every hour 4pi metre cube also drains out, but remember this starts 1 hour later.

We can set up an equation here:
$$0.08*number[m]$$ofminutesinyhours$$+$$4(y-1)=150[/m]
or
$$0.08*60*y + 4y=154$$
or
$$7y=154$$
Therefore y=$$22 hours$$

I found this approach rather easier.
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Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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1
12 noon: 150π m3

For every minute there is a net drain of 0.08π-0.03π=0.05π m3. So for every hour=0.05*60=3π m3/hour
This means at 1pm there is 150π-3π=147π m3

And from 1pm there is an additional drain of 4π m3 so net drain= 3π+4π=7π m3/hour
So the time taken to drain 147π m3 is 147π/7π=21 hours. and lets not forget the 1 hour between 12 and 1pm.

Therefore, total time taken is 21+1=22 hours
Manager  Joined: 07 Apr 2014
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Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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3/4 of 200pi = 150pi.

0.08pi removed & 0.03pi added for each minute. for hours 4.8pi removed & 1.8pi added. consolidated will be 3.0pi removed for each hour. Note: This starts at noon.

147pi.

starting from 1pm for each hour 4 pi is removed from the total. (along with the regular 3.0pi) , it will be 7pi removed from 1 pm .

147pi/7pi = 21 hours.

Adding the hour between 12 to 1 pm - 21+1 = 22 hours.
Manager  Joined: 22 Aug 2014
Posts: 136
Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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Marcab wrote:
Another easy approach to this question is:

Volume to be drained= 150pi
Every minute, the volume that drains is : (0.08pi-0.03pi) metre cube or 0.05pi metre cube.
Every hour 4pi metre cube also drains out, but remember this starts 1 hour later.

We can set up an equation here:
$$0.08*number[m]$$ofminutesinyhours$$+$$4(y-1)=150[/m]
or
$$0.08*60*y + 4y=154$$
or
$$7y=154$$
Therefore y=$$22 hours$$

I found this approach rather easier.

hi,
I have not understood why we have used .08 instead of .05(net drainage)
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Joined: 04 Jan 2015
Posts: 3074
Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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ssriva2 wrote:
Marcab wrote:
Another easy approach to this question is:

Volume to be drained= 150pi
Every minute, the volume that drains is : (0.08pi-0.03pi) metre cube or 0.05pi metre cube.
Every hour 4pi metre cube also drains out, but remember this starts 1 hour later.

We can set up an equation here:
$$0.08*number[m]$$ofminutesinyhours$$+$$4(y-1)=150[/m]
or
$$0.08*60*y + 4y=154$$
or
$$7y=154$$
Therefore y=$$22 hours$$

I found this approach rather easier.

hi,
I have not understood why we have used .08 instead of .05(net drainage)

Hi ssriva2,

You are right, it has to be 0.05, which is net drainage and not 0.08. The equation writes 0.08 but solves using 0.05. Assuming 0.08 in the equation will not give the right answer.

Regards
Harsh
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Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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danzig wrote:
A cylindrical water tower with radius 5 m and height 8 m is 3/4 full at noon. Every minute, .08π m3 is drawn from tank, while .03π m3 is added. Additionally, starting at 1pm and continuing each hour on the hour, there is a periodic drain of 4π m3. From noon, how many hours will it take to drain the entire tank?

A. 20 2/7
B. 20 6/7
C. 21
D. 21 3/7
E. 22

I agree with the OA. After 21 hours, 147π m3 will be drained. So, there are 3π m3 that have not been drained. Because the constant drain draws 3π m3 per hour, we will have to wait until the 22th hour. Probably, the periodic drain will draw little water in the 22th hour. Please, confirm whether my reasoning is Ok.

In this sense, I don't understand this part of the OE:
"Had we divided 150/7, we'd land on , but we have to consider how the 3/7 remainder actually leaves the tank.

Now we have to deal with remainders.

With 3 m3 remaining, after another 3/7 hours, only 3(0.5) = 1.5 m3 will be drained. So the tank will not actually be empty until 22 hours, when the periodic draw empties the remainder."
I don't understand the OE does this: 3(0.5) = 1.5 m3 :S !

Thanks!

Volume of the cylinder is 150pi
At 1 pm the volume is 147pi (the net drain is 3pi)
Then onwards, the net drain is 7pi per hour.
Setting AP we get 21 hours.
Therefore, total time taken is 22 hours.
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GMAT 1: 750 Q49 V43 A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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danzig wrote:
A cylindrical water tower with radius 5 m and height 8 m is 3/4 full at noon. Every minute, .08π m3 is drawn from tank, while .03π m3 is added. Additionally, starting at 1pm and continuing each hour on the hour, there is a periodic drain of 4π m3. From noon, how many hours will it take to drain the entire tank?

A. 20 2/7
B. 20 6/7
C. 21
D. 21 3/7
E. 22

AT 12 O' CLOCK ) Water at the tank =$$π*5^2*8*\frac{3}{4} = 150π$$

Water Removed =$$\frac{0.08π}{min}$$;

Water Added=$$\frac{0.03π}{min}$$

Net change in water volume = $$\frac{0.05π}{min}$$

AT 1 PM ) Water at the tank = 150π -0.05π*60 ==>150π-3π=147π (TIME TAKEN =1 hour)

Now starting at 1 PM , in addition to 3π another 4π of water is removed every hour
so Net Loss of water ever hour = 3π+4π =7π
Let t be the time taken by tank to completely empty

147π-7π*t=0

7π*t=147π

t=$$\frac{147π}{7π}$$=21
TOTAL TIME =21 hours + 1 HOUR (FROM 12 O CLOCK TO 1 O CLOCK) = 22

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Originally posted by LogicGuru1 on 17 Jul 2016, 06:26.
Last edited by LogicGuru1 on 07 Aug 2018, 06:08, edited 2 times in total.
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Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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danzig wrote:
A cylindrical water tower with radius 5 m and height 8 m is 3/4 full at noon. Every minute, .08π m3 is drawn from tank, while .03π m3 is added. Additionally, starting at 1pm and continuing each hour on the hour, there is a periodic drain of 4π m3. From noon, how many hours will it take to drain the entire tank?

A. 20 2/7
B. 20 6/7
C. 21
D. 21 3/7
E. 22

Volume of water present in the tank= 3/4 π r^2h= 3/4π *5*5*8= 150π

Every minute after noon till 1:00 pm the net water that is drained out was= .08π m3- .03π m3 = .05 π cubic meter
In one hr from noon to 1:00 pm, total water loss was = .05 π *60= 3 π cubic meter

At 1:00 pm 150π-3π= 147π water is remaining that has to be drained out.

In addition to 3π, 4π water is also draining out of the tank, making total 7π water draining out after 1:00 pm

147π water will be drained out in 147π/7π= 21 hrs after 1 pm

Add 1 hr to this as water was drained out from noon to 1:00 pm, making total 21+1= 22 hrs

E is the answer
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Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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danzig wrote:
A cylindrical water tower with radius 5 m and height 8 m is 3/4 full at noon. Every minute, .08π m3 is drawn from tank, while .03π m3 is added. Additionally, starting at 1pm and continuing each hour on the hour, there is a periodic drain of 4π m3. From noon, how many hours will it take to drain the entire tank?

A. 20 2/7
B. 20 6/7
C. 21
D. 21 3/7
E. 22

Let, the time taken was 't' hours [ say, if the time is 1.5 hrs the periodic drain would be 1 time. Similarly, if time is 2 hrs periodic drain would be 2 times & for 15.36hrs it would be 15 times & so on.. So, no. of periodic drain is clearly an integer] . Lets assume its 'n'.

Now, pie x 5^2 x (8) x 3/4 + (-0.08pie + 0.03pie) x t x 60 - n x 4 x pie = 0
=>(150 -3t)/4 = n

So, substituting the values in the options, we find only 22 (option E) gives us n=21 (integer) rest all give us decimal no.s .

Hence, Answer is option E.
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GMAT 1: 760 Q50 V44 GMAT 2: 740 Q48 V44 Re: A cylindrical water tower with radius 5 m and height 8 m is  [#permalink]

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"Starting at 1pm and continuing each hour on the hour, there is a periodic drain..."

Guys, is this GMAT wording? It sounds super ambiguous to me.

If 150pi is volume at noon... if at 1pm you start having an extra drain of 4pi... then at 1pm the volume should be 150-3-4 ? But it seems the question assumes that at 1pm the extra 4pi drain has not started... and only kicks in at 2pm.

Why is this? "Starting at 1pm..." seems to imply that at 1pm the extra drain already is taking effect?

I will be grateful if you could help me understand this. Thank you. Re: A cylindrical water tower with radius 5 m and height 8 m is   [#permalink] 19 Oct 2018, 07:29
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