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Flow Rida (m05q09) [#permalink]
 12 Nov 2008, 13:23
Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there? (A) 2.5 (B) 3 (C) 4 (D) 5 (E) 6 Source: GMAT Club Tests - hardest GMAT questions
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bigfernhead wrote: Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there?
2.5
3
4
5
6 so in 1 hour we get 12 liters, 54 liters will take 54/12 =4.5 hours. bu it takes 12 hours to fill up, which means 12-4.5hours=7.5hrs are due to big pipes 7.5/1.5 or 75/15 =15/3 or 5 pipes
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Total Inflow = # of pipes x Time x Flow rate per pipe per hour Substituting we get, Total Inflow = 12 x 12 x 1 = 144 Total Outflow follows the same calculation = # of pipes x Time x Flow rate per pipe per hour So Total Outflow = N x 12 x 1.5 We are told that at the end of 12 hours, the tank is Full. So Total Inflow - Total Outflow = 54 144 - N x 18 = 54, Or N = 90/18 = 5 My pick D
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bigfernhead wrote: Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there?
2.5
3
4
5
6 54= 12*12 - 1.5*N*12 = 144-18N N= 90/18 =5
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Re: Flow Rida (m05q09) [#permalink]
03 Sep 2009, 03:13
Great approach masuhari!! I like the subject of the topic..Flo Rida -Right round anyone?! 
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Re: Flow Rida (m05q09) [#permalink]
16 Feb 2010, 04:14
bigfernhead wrote: Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there? (A) 2.5 (B) 3 (C) 4 (D) 5 (E) 6 Source: GMAT Club Tests - hardest GMAT questions Total inflow in 12 hr = 1*12*12 = 144 Tank limit = 54 Total outflow in 12 hr = 1.5*12*N = 144 - 54 = 90 so N = 5 hence D
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Re: Flow Rida (m05q09) [#permalink]
16 Feb 2010, 11:28
12 ( 12∙1 - x∙1,5 ) = 54
x=5
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Re: Flow Rida (m05q09) [#permalink]
16 Feb 2010, 12:57
N = (12x12-54)/(1,5x12)=90/18 = 5 or
N = (12-54/12)/1,5 = 7.5/1,5 = 5
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Re: Flow Rida (m05q09) [#permalink]
16 Feb 2010, 15:14
12 * 12 *1 - 12* 1.5 *X = 54
So, X=5
Option D
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Re: Flow Rida (m05q09) [#permalink]
16 Feb 2010, 15:40
Thanks! You al make it look so easy!
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Re: Flow Rida (m05q09) [#permalink]
16 Feb 2010, 16:55
Its D
equation is
(12-n*1.5)12=54
=> n= 5
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Re: Flow Rida (m05q09) [#permalink]
17 Feb 2010, 00:59
D
Let X be number of big pipes, then
12*12 =54 + 1.5X*12
solves X = 5
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Re: Flow Rida (m05q09) [#permalink]
18 Feb 2010, 09:58
Answer is D.) 5
If the tank fills up to 54L in 12 hours then it is keeping 4.5L per hour. If the small pipes are putting in 12L per hour that means that 12L - 4.5L = 7.5L being lost out of the big tank per hour. Loss of an individual big pipe per hour is 1.5L so take 7.5 / 1.5 and that gives you 5 big pipes.
Hopefully somebody knows to shut off the water or it's going to make a mess.
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Re: Flow Rida (m05q09) [#permalink]
05 Sep 2010, 10:02
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This can be solved as a combined work rates problem:
1/Total Time = 1/A - 1/B, where
Total Time = 12 hours, A = 4.5 hours to fill tank, & B = 36 hours to empty tank per X pipes
1/12 = 1/4.5 - X/36,
3/36 = 8/36 - x/36,
-5/36 = -x/36,
X = 5
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Re: Flow Rida (m05q09) [#permalink]
21 Feb 2011, 07:41
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Re: Flow Rida (m05q09) [#permalink]
21 Feb 2011, 09:51
12 (12 - 1.5x) = 54 X = 5 . D) Posted from my mobile device 
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Re: Flow Rida (m05q09) [#permalink]
21 Feb 2011, 10:28
easy one...it is 5pipes & ans is d
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Re: Flow Rida (m05q09) [#permalink]
21 Feb 2011, 16:06
I am good with math... except word problems, I always have a hard time setting up the problem. In this particular case, (for my benefit) I drew a little picture that represents the tank, and then drew a line that assumed a rate of 12 liters per hour going in. Then because I started to panic, I just selected C at random and tried it. I found that after 12 hours, it would overflow at 72 liters. So I knew that more material had to exit the tank, meaning I would try adding a pipe. I tried answer D, plugged it in and it worked. Not sure if I was just lucky or what... I ultimately got to the answer, but I wish I knew how to set up the problem automatically like many people here in the forum.
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Re: Flow Rida (m05q09) [#permalink]
22 Feb 2011, 15:34
Nice equation setup. I need to get better at this. I picked numbers to come up with the answer to this problem though and was lucky enough to hit D on the first try.
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Re: Flow Rida (m05q09) [#permalink]
23 Feb 2011, 09:52
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I did this
12pipes 1/lph= 12lhp * 12 hrs = 144.
144-54(tank size)=90
90(gallons out)/12(hourly)=7.5(gallons removed per hour)
7.5/1.5=5.
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Re: Flow Rida (m05q09)
[#permalink]
23 Feb 2011, 09:52
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