Question: A draining pipe can drain a tank in 12 hours, and a filling pipe can fill the same tank in 6 hours. A total of n pipes – which include both types of pipes – can fill the entire tank in 2 hours. Which of the following could be a value of n?

1. 6
2. 7
3. 9

1. I only
2. II only
3. I and II only
4. I and III only
5. I, II, and III

Correct Answer: C
Solution and Explanation:
Approach Solution 1:

Given to us that a tank can be completely drained in 12 hours using a draining pipe, and completely filled in 6 hours using a filling pipe. The full tank can be filled in 2 hours with a total of n pipes, which includes both kinds of pipes. What one of the following could n represent?

Three pipes are needed to fill the tank in 6/3 of a day, or in 2 hours, if one pipe can fill a tank in 6 hours.
Now, in order to eliminate each filling pipe, you need two draining pipes.

The tank will be filled in 2 hours with any combination of 3 filling pipes and x(2 draining, 1 filling).

Consequently, the solution is 3+x(2+1)=3+3x, where x is any positive integer.
Pipes are 3+3=6 when x = 1 and 3+2*3=9 when x=2, respectively.

Approach Solution 2:

We can observe that the inflow rate for a filling pipe is 1/6 tank per hour, and the outflow rate for a draining pipe is 1/12 tank per hour. We can construct the following equation if we allow f to equal the quantity of filled pipes (where f is a positive integer n).

f x 1/6 - (n - f) x 1/12 = 1/2

When we divide the two sides of the equation by 12, we get:

2f - (n - f) = 6

3f - n = 6

Let's now review the options for Roman numerals.

1. When n equals 6, we have:

3f - 6 = 6
3f = 12
f = 4
Since 4 is a positive number that equals 6, it is possible.

2. When n is 7, we get:

3f - 7 = 6
3f = 13
f = 13/3
13/3 is not an integer, hence this is not possible.

3. When n equals 9, we have:

3f - 9 = 6
3f = 15
f = 5
Since 5 is a positive number that equals 9, it is conceivable.

D is the correct answer.

Approach Solution 3:

The tank can be emptied by one pipe in 12 hours, but it takes six pipes to do so in just two. In the same way, if one pipe can fill a tank in six hours, then three pipes are required to fill a tank in two hours.

9 pipes total (six to empty and three to fill).
b.) Six pipes can concurrently fill and empty the tank in 2 hours if one pipe can do so in 1/6 - 1/12 hrs (1/12 hrs).

Thus, D is the correct response.

“A draining pipe can drain a tank in 12 hours, and a filling pipe can f" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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