GMAT Challenge Series (700+): Q4

Water Pipe.jpg

Question:

Pipe A and Pipe B fill water into a tank of capacity 1000 liters at the rate of 100 liters/minute and 25 liters/minute respectively. Pipe C drains water from the same tank at the rate of 50 liters/minute. Pipe A is kept open for a minute and then closed, then pipe B is kept open for a minute and then closed, followed by a drain pipe C for a minute and then closed. This process is repeated until the tank is full. How long will it take to fill the tank?

A. 39 min

B. 40 min

C. 39 min 20 sec

D. 37 min

E. 41 min

MBA Wisdom's Answer:

$$\text{The Cycle Over Time:}$$ $$\textit{0 min: 0L}$$ $$\textit{1 min: 100L (+100L Pipe A)}$$ $$\textit{2 min: 125L (+25L Pipe B)}$$ $$\textit{3 min: 75L (-50L Pipe C)}$$ $$\textit{4 min: 175L (+100L Pipe A)}$$ $$\textit{...}$$ $$$$ $$\text{There is a 3 min cycle whereby the water rises and then falls.}$$ $$\text{At the end of every 3 min cycle the water has increased by 75L.}$$ $$\textit{est. cycles} = \frac{1000}{75} = {13}\frac{1}{3}$$ $$\textit{est. volume after 13 cycles/39 min} = \left({13}\right) \left({75}\right) = 975$$ $$\text{Since the cylce is not constant we need to check before and after this moment.}$$ $$\textit{...}$$ $$\textit{36 min: 900L (-50L Pipe C)}$$ $$\textit{37 min: 1000L (+100L Pipe A)}$$ $$\textit{38 min: 1000L (+25L Pipe B)}$$ $$\textit{39 min: 950L (-50L Pipe C)}$$ $$\textit{40 min: 1000L (+100L Pipe A)}$$ $$\text{First moment the tank is full is at 37 min.}$$

D. 37 min