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Bunuel
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A draining pipe can drain a tank in 12 hours, and a filling pipe can f 21 Apr 2020, 09:22
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D
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75% (hard)

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59% (02:39) correct 41% (02:25) wrong based on 254 sessions

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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?

I. 6
II. 7
III. 9

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


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D
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firas92
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A draining pipe can drain a tank in 12 hours, and a filling pipe can f 21 Apr 2020, 10:49
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Bunuel
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?

I. 6
II. 7
III. 9

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


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Let \(F\) be the rate of the filling pipe (\(F=\frac{1}{6}\)) and \(D\) be the rate of the draining pipe (\(D=\frac{1}{12}\))

Let the number of filling pipes be \(a\) which makes the number of draining pipes \((n-a)\)

We have,

\(Fa-D(n-a)=\frac{1}{2}\)
\(\frac{a}{6}-\frac{n}{12}+\frac{a}{12}=\frac{1}{2}\)
\(\frac{3a-n}{12}=\frac{1}{2}\)

\(n=3(a-2)\)

So \(n\) must be a multiple of \(3\)

Which means n can be I or III

Answer is (D)
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A draining pipe can drain a tank in 12 hours, and a filling pipe can f 21 Apr 2020, 09:33
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Bunuel
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?

I. 6
II. 7
III. 9

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


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If one pipe can fill a tank in 6hrs, we require 3 pipes to fill the tank in 6/3 or 2 hrs.
Now you require 2* draining pipes for each filling pipe to be negated..

Any combination of 3*filling pipe+x(2*draining+1*filling) will fill the tank in 2 hrs...

So answer is 3+x(2+1)=3+3x, where x is any non-negative integer..
when x=1, pipes are 3+3=6
when x=2, pipes are 3+2*3=9

D
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A draining pipe can drain a tank in 12 hours, and a filling pipe can f 21 Apr 2020, 11:13
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Bunuel
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?

I. 6
II. 7
III. 9

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


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On a broad reading of the question, I noticed 3 numbers - 12,6 and 2. Hence even before reading the question properly, I assumed the capacity of the tank to be 12 units. Hence, the rate of work of filling pipes is 2 units per hour of draining pipes is 1 unit per hour. It's important to note here that 2 draining pipes along with 1 filling pipe will give us no inflow/no outflow. Since tike required to fill the tank is 2 hours, every hour net 6 units needs to be filled (12 units/2 hours). Hence, 3 filling pipes will get the job done. As we have already calculated that a set of 3 pipes (2 draining + 1 filling) will result in net 0 inflow, the possible combination of pipes here will be 3 filling pipes + any number of sets of 3 pipes (2 draining +1 filling). Hence the solution would be 3,6,9,12, etc. The answer here would be "D". I have always found that assuming a capacity of the tank in such questions makes it easier and faster to solve the questions. It took me 41 seconds to arrive at this answer using this method. Give kudos if you liked the answer

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A draining pipe can drain a tank in 12 hours, and a filling pipe can f 22 Apr 2020, 23:03
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Let the number of Filler Pipes (FP) and Draining Pipes (DP) be 'x' and 'y respectively.

In 2 hrs, 'x' FPs will fill (2*x)/6 th of the tank and 'y' DPs will drain (2*y)/12 th of the tank. Therefore: x/3 - y/6 = 1...> x = 3 + y/2.
Since 'x' and 'y' are both positive integers, 'y' must be a multiple of 2 i.e. 2,4,6...
When 'y' is 2, x=4 and n=6. When y=4, x=5 and n=9. The value of 'n' becomes higher with progressively higher values of 'y' so 7 cannot be a value of 'n'.
So, among the given options, 6 and 9 are the only possible values of 'n'. ANS: D
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A draining pipe can drain a tank in 12 hours, and a filling pipe can f 22 Apr 2020, 23:36
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Bunuel
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?

I. 6
II. 7
III. 9

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


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X*Rate*T=Work
Where X is the number of pipes with same rate
\(X*(1/6)*2-Y*(1/12)*2=1\)
2X-Y=6
and we have values for X+Y
lets solve for X and Y
from option 1 X+Y=6; 2X+2Y=12 subtract from 2X-Y=6; 3Y=6;Y=2;X=4
from option 2 X+Y=7; 2X+2Y=14 subtract from 2X-Y=6; 3Y=8;Y=8/3 Absurd
from option 3 X+Y=9; 2X+2Y=18 subtract from 2X-Y=6; 3Y=12;Y=4;X=5
D:)
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A draining pipe can drain a tank in 12 hours, and a filling pipe can f 23 Apr 2020, 04:05
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Bunuel
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?

I. 6
II. 7
III. 9

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III


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We see that a filling pipe’s (inflow) rate is 1/6 tank per hour and a draining pipe’s (outflow) rate is 1/12 tank per hour. If we let f = the number of filling pipes (where f is a positive integer < n), we can create the equation:

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

Multiplying both sides of the equation by 12, we have:

2f - (n - f) = 6

3f - n = 6

Now let’s check the choices in the Roman numerals.

I. If n = 6, we have:

3f - 6 = 6

3f = 12

f = 4

This is possible since 4 is a positive integer < 6.

II. If n = 7, we have:

3f - 7 = 6

3f = 13

f = 13/3

This is not possible since 13/3 is not an integer.


I. If n = 9, we have:

3f - 9 = 6

3f = 15

f = 5

This is possible since 5 is a positive integer < 9.

Answer: D
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A draining pipe can drain a tank in 12 hours, and a filling pipe can f 03 Aug 2021, 03:13
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I tried solving this question in the following way, can someone let me know if its correct?

a.) 1 pipe can empty the tank in 12hrs, then we need 6 pipes to empty the tank in 2 hours. Similarly, if 1 pipe can fill a tank in 6 hours, then we need 3 pipes to fill a tank in 2 hrs.

(6 pipes to empty + 3 pipes to fill = 9 pipes)

b.) If one pipe can simultaneously fill and empty the tank in 1/6 - 1/12 hrs = 1/12 hrs then 6 pipes can do the same in 2 hours.

Therefore, the answer is D
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A draining pipe can drain a tank in 12 hours, and a filling pipe can f 28 Feb 2025, 01:06
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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?

Let filling pipes be x & draining pipe by y in numbers.
x + y = n
x/6 - y/12 = 1/2
2x - y = 6; y = 2x-6

x + (2x-6) = n
n = 3x - 6 = 3(x-2)

I. 6; n = 6 = 3(x-2); x = 4; Possible
II. 7; n = 7 = 3(x-2); Not possible since x is an integer
III. 9; n = 9 = 3(x-2); x = 5; Possible

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

IMO D
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