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M05-09

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Math Expert
Joined: 02 Sep 2009
Posts: 59712

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16 Sep 2014, 00:24
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75% (01:58) correct 25% (02:16) wrong based on 226 sessions

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Water flows into an empty tank of 54 liters via 12 small pipes. The rate of flow in each pipe is 1 liter per hour. However, water also flows out of the tank via several large pipes at the rate of 1.5 liter per hour. If the tank is completely full after 12 hours, how many large pipes are there?

A. 2.5
B. 3
C. 4
D. 5
E. 6

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Joined: 02 Sep 2009
Posts: 59712

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16 Sep 2014, 00:24
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Official Solution:

Water flows into an empty tank of 54 liters via 12 small pipes. The rate of flow in each pipe is 1 liter per hour. However, water also flows out of the tank via several large pipes at the rate of 1.5 liter per hour. If the tank is completely full after 12 hours, how many large pipes are there?

A. 2.5
B. 3
C. 4
D. 5
E. 6

The tank is full in 12 hours, therefore, the effective inflow has to be $$\frac{54}{12} = 4.5$$ liters per hour. Currently our nominal inflow is 12 liters per hour and outflow is unknown. To find the outflow, we need to subtract effective inflow from the nominal inflow. $$12 - 4.5 = 7.5$$; We know that each of the large, outgoing pipes has a flow rate of 1.5 liters per hour, therefore, $$\frac{7.5}{1.5} = 5$$.

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Joined: 09 Feb 2015
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15 May 2015, 02:04
7
Other solutions:
Let x be large pipes:
=> (1*12 - 1.5*x)*12 = 54
Solving we get x=5.
Is it right!
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Joined: 29 May 2015
Posts: 10

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25 Aug 2015, 22:17
5
1
If I may elaborate above explanation,

A = RT
54 = Final R * T
54 = (Inflow Rate - Outflow Rate) * T
54 = (12-1.5x)*12
x=5
Manager
Joined: 08 Apr 2019
Posts: 157
Location: India
GPA: 4

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17 Jul 2019, 23:18
4
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Here's a simpler solution, in every work rate problem, we know Work = Rate * Time

Hence, Work (Volume to be filled) = Effective Rate (Inflow - Outflow) * Time

54 = (12 - 1.5x) * 12

4.5 = 12 - 1.5x

1.5x = 7.5

and hence, x = 5.

PLEASE HIT KUDOS IF YOU LIKE MY SOLUTION
Manager
Joined: 16 May 2019
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26 Aug 2019, 09:35
1
Bunuel wrote:
Water flows into an empty tank of 54 liters via 12 small pipes. The rate of flow in each pipe is 1 liter per hour. However, water also flows out of the tank via several large pipes at the rate of 1.5 liter per hour. If the tank is completely full after 12 hours, how many large pipes are there?

A. 2.5
B. 3
C. 4
D. 5
E. 6

An alternative approach - As I often like to do on Problem Solving questions, I took a more intuitive, logic-based approach to solving this one. With the answers staring us right in the face, why not reason our way to what must be correct, leaving no room for error? The first step is to eliminate choice (A), on the grounds that there cannot be half a pipe. (What would that mean? Half as long? Sawed in half to leave only a semicircle?) With four choices remaining, we can choose one of those in the middle to use as a gauge. For the sake of illustration, let us assume we chose (C), 4, first.

1) If there were 4 "out" pipes, each flowing at 1.5 L/h, then 4 x 1.5 = 6 L/h of outflow.
2) Since we know the inflow is 12 (pipes) x 1 (L/h), or 12 L/h, we can make quick work of the net inflow by subtracting our calculated outflow from the last step: 12 - 6 = 6 L/h.
3) To fill a 54 L tank, an inflow of 6 L/h would take 9 hours (from 54 divided by 6). This does not corroborate our known information--it should take 12 hours instead--but importantly, we can see that we need to slow the rate of inflow to drag out the total time it will take to fill the tank. Hence, (B) makes no sense, and the answer will have to be (D) or (E).

Since I am not as fond of decimals as I am whole numbers, I might try (E), 6, next. Repeating the same process from before, we get the following:

1) 6 x 1.5 = 9 L/h of outflow.
2) 12 - 9 = 3 L/h of net inflow.
3) 54/3 = 18 h.

We have overshot the target, so one more adjustment is needed, and without doing the math, we know the answer has to be (D), the only sensible choice remaining. If you were curious about proving (D) (even though I would not bother on the actual test):

1) 5 x 1.5 = 7.5 L/h of outflow.
2) 12 - 7.5 = 4.5 L/h of net inflow.
3) 54/4.5 (understanding that 4.5 is half of 9, so the answer will be double that of 54/9) = 12 h, the very number we are given.

Such a Goldilocks approach should not be overlooked or written off if it gets you the correct answer in a time-efficient manner. Better than feeling stuck during the test and fishing around for a formula you are sure you have forgotten.

- Andrew
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Joined: 25 Mar 2013
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Location: United States
Concentration: Entrepreneurship, Marketing
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03 Feb 2017, 09:10
Empowergmat Rich, can you pls explain this simpliest way to solve this problem
What concept am I lacking to think like Bunuel.
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Joined: 19 Jun 2017
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11 Sep 2017, 19:33
I think this is a poor-quality question and I agree with explanation. Question should explicitly note that the outflow rate of 1.5 l/h is "in each large pipe" (to borrow from the language of the preceding sentence).

Otherwise, Q is excellent as always. But the answer wouldn't make sense if one didn't assume 1.5l/h was on a per pipe basis (of course, one would eventually figure it out, but I don't think question wording should be allowed to unnecessarily cost the user time).
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Joined: 04 Feb 2018
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26 Aug 2019, 09:50
Since the rate of flow through each small pipe is 1 litre per hour, the rate for 12 pipes is equal to 12 litres per hour. In 12 hours we should have 144 litres (12 x 12) in the tank. However, because the tank only has a capacity of 54 litres, 90 litres (144-54) would have flowed out of the tank during the 12-hour period. Therefore the rate of outflow is equal to 90/12 = 7.5 litres per hour.

Since the rate of outflow for one large pipe is 1.5 litres per hour, the total number of large pipes is equal to 7.5/1.5 = 5.
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Joined: 09 Nov 2018
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10 Dec 2019, 09:47
I think this is a poor-quality question and I agree with explanation. Question should be clear whether 1.5 lt/ hr is for all or 1 pipe
Re M05-09   [#permalink] 10 Dec 2019, 09:47
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