CAT Quantitative Aptitude Questions | CAT Time and Work questions

The question is from Pipes and Cisterns: Fill pipes and Drain Pipes. Again a question on possible values. How many fill and drain pipes required to fill the tank in 'x' hours? Find a complete "Null System". Work on the question after that.

Question 5: A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which of the following are possible values of n (More than one option could be correct)?

1. 32
2. 54
3. 29
4. 40

1. 1 and 2 only
2. 1 and 3 only
3. 2 and 4 only
4. 2 and 3 only

Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: Find a complete "Null System". Work on the question after that.

2 fill pipes cancel out 3 drain pipes. Plus, you need an additional 4 fill pipes fill the tank in 5 hours. so the answer has to be 5k + 4.
Both 54 and 29 are possible.

The question is "which of the following are possible values of n?"

Hence, the answer is "2 and 3 only".

Choice D is the correct answer.