CAT Pipes and Cisterns – Do-able but atypical

Question
A drain pipe can drain a tank in 12 hours, and a fill pipe can fill the same tank in 6 hours. A total of n pipes – which include a few fill pipes and the remaining drain pipes – can fill the entire tank in 2 hours. How many of the following values could ‘n’ take?
a)      24
b)      16
c)       33
d)      13
e)      9
f)       8
A.      3
B.      4
C.      2
D.      1
Correct Answer: (A)
Explanatory Answer:
Two drain pipes can drain the same volume that one fill pipe fills. This means that a D-D-F combination has to have a net volume effect of 0.
In spite of this, the tank still gets filled. Only the fill pipes can manage to fill the tank. In addition to all the net zero effect pipes, we need three more fill pipes in order to fill the tank in 2 hours.
So, we can have as many D-D-Fs as we want, but we need one F-F-F at the end to ensure that the tank gets filled in 2 hours.
So the number of pipes will be → (D – D – F)…….(D – D – F) + (F – F – F)
The number of pipes has to be a multiple of 3. Only options A, C and E fit the description.
Answer Choice (A)

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