Two pipes can fill a tank in 35 minutes. The larger pipe alone can fil

You can actually eliminate three of the answers right off the bat. If both pipes took 70 minutes, then they would take 35 minutes together. In this problem, the pipes have different rates, so one must take less than 70 minutes and the other must take more than 70 minutes.

> A) Eliminate. Both are less than 70 minutes.
> B) Eliminate. Both are less than 70 minutes.
> C) Keep.
> D) Keep.
> E) Eliminate. Both are greater than or equal to 70 minutes.

Now, it's going to be faster to test C and D. For C, if you say that the tank is 300 liters, then

> Pipe A: Time = 50 mins. Rate = 300/50 = 6.
> Pipe B: Time = 60 mins. Rate = 300/60 = 5.
> Pipe A+B: Combined rate = 11. Total = 11 × 35 = 385 liters. No, the total should be 300.

At this point, you know the answer must be D. You can select it. If you want to see why it works, here is the work using 840 liters.

> Pipe A: Time = 60 mins. Rate = 840/60 = 14.
> Pipe B: Time = 84 mins. Rate = 840/84 = 10.
> Pipe A+B: Combined rate = 24. Total = 24 × 35 = 840 liters. Yes!

For this question, we may plug in the answers to find the combined rate and check if it is \(\frac{1}{35}\).

If the answers are x and y we will try to calculate \(\frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy}\) to see if it is equal to \(\frac{1}{35}\). Comparing \(\frac{x + y}{xy}\) and \(\frac{1}{35}\), we can use number properties to deduct xy must have a factor of 35, hence the answers need to have a multiple of 5 and 7.

Among these numbers only D has a factor of 5 from 50 and a factor of 7 from 84 so D is the answer (and E does not simplify with 94 = 2*47). Let us do a check anyways:

\(\frac{60 + 84}{60*84} = \frac{144}{60*84} = \frac{12 }{ 60 * 7} = 1/35\).

Ans: D

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