M05-09

Question

An empty tank with a capacity of 54 liters is filled with water through 12 small pipes, each with a flow rate of 1 liter per hour. The tank also has several large pipes through which water flows out at a rate of 1.5 liters per hour per pipe. If the tank becomes completely full in 12 hours, what is the number of large pipes that are draining water from the tank?

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

Show Answer

Official Answer

D

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

Bunuel · Accepted Answer

Official Solution:

An empty tank with a capacity of 54 liters is filled with water through 12 small pipes, each with a flow rate of 1 liter per hour. The tank also has several large pipes through which water flows out at a rate of 1.5 liters per hour per pipe. If the tank becomes completely full in 12 hours, what is the number of large pipes that are draining water from the tank?

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

Show Answer

Official Answer

D

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

Let the number of large pipes be  x .
 
Since the tank is full in 12 hours, the net inflow is  \frac{54}{12} = 4.5  liters per hour.
 
(Total inflow) - (Total outflow) = (Net inflow)
 
 1*12 - 1.5*x = 4.5 
 
 x=5

Answer: D

Mrtinhnv · Answer

Other solutions:
Let x be large pipes:
=> (1*12 - 1.5*x)*12 = 54
Solving we get x=5.
Is it right!

vityakim · Answer

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

RJ7X0DefiningMyX · Answer

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.

AndrewN · Answer

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

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Bunuel · Answer

Similar questions to practice: https://gmatclub.com/forum/m40-424805.html https://gmatclub.com/forum/m05-183682.html https://gmatclub.com/forum/m04-183659.html

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

M05-09

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards