I dint really get whts being asked

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A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?


10:00am


10:45am


12:00pm


12:30pm


1:30pm

[Brent@GMATPrepNow]

A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A) 10:00am
B) 10:45am
C) 12:00pm
D) 12:30pm
E) 1:30pm

I've read the blue sentence several times, and I still have no idea what it is asking. Rest assured that the GMAT would never ask such a convoluted question.

That said, after searching the Internet, I found an interpretation.

The goal here is the have a filled tank at 3:30pm (6 hours from the time the tank was empty and we started filling it). Of course, since it takes only 5 hours to fill the tank, the tank will DEFINITELY be filled after 6 hours (with a lot of water spilling over the edges).

That said, I believe the intent of the question is to open the outlet pipe at some point during the 6-hour period so that, at exactly 3:30pm, the tank becomes completely filled, WITHOUT losing any water spilled over the edges.

So, here it goes...

Given: Inlet pipe FILLS the tank in 5 hours
Outlet pipe EMPTIES the tank in 15 hours

Let's choose a NICE NUMBER for the volume of the tank.
Let's say the tank has a total capacity of 15 gallons.

This means that inlet pipe FILLS the tank at a rate of 3 gallons/hour
And the outlet pipe EMPTIES the tank at a rate of 1 gallon/hour

So, in 6 hours, the inlet pipe (at 3 gallons/hour) will add 18 gallons to the tank. This is 3 gallons MORE than we need. So, we need the outlet pipe to remove those extra 3 gallons.
Since the outlet pipe EMPTIES the tank at a rate of 1 gallon/hour, we need to give the outlet pipe 3 hours to do its job.
So, we need to open the outlet pipe 3 hours BEFORE 3:30pm
In other words, we need to open the outlet pipe at [spoiler]12:30pm [/spoiler]

Answer: D

Cheers,
Brent

[vipulgoyal]

alt plug in approach

fill in 5 hour , in one hour 1/5 th part fill
empty in 15 hour, If both lets are open 1/5-1/15 = 2/15 per hour addition

pick any option let say C

for 2.5 hours only inlet open and for 3.5 hours both are open

1/5*5/2 + 2/15*7/2 == 29/30 No

pick 12:30 option D

for 3 hours inlet is open and for another 3 hours both are open

1/5*3 + 2/15*3 = 3/5 +2/5 = 1 yes

[GMATGuruNY]

A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A)10:00am

B)10:45am

C)12:00pm

D)12:30pm

E)1:30pm

Let the tank = 30 liters.

Rate for the inlet pipe = w/t = 30/5 = 6 liters per hour.
Rate for the outlet pipe = w/t = 30/15 = 2 liters per hour.
When the inlet pipe and the outlet pipe work together, the inlet pipe pumps IN 6 liters per hour, while the outlet pipe pumps OUT 2 liters per hour.
Thus, the NET rate for the 2 pipes working together = 6-2 = 4 liters per hour.

To fill the tank in 6 hours, the required average rate = w/t = 30/6 = 5 liters per hour.
The required average rate (5 liters per hour) is HALFWAY between the rate for the inlet pipe alone (6 liters per hour) and the rate for the 2 pipes working together (4 liters per hour).
Implication:
For 1/2 the time (3 hours) the inlet pipe must work alone.
For 1/2 of the time (the remaining 3 hours) the 2 pipes must work together.
Since the inlet pipe works alone for 3 hours, the outlet pipe is turned on 3 hours after the start time:
9:30am + 3 hours = 12:30pm.

The correct answer is D.

[ceilidh.erickson]

then at what time should the outlet pipe be opened ?

Brent is right; this question makes very little sense. The GMAT will never ask you a question this semantically or conceptually complicated on the Quant.

What is the source of this question? It's certainly not a good question. A good rule of studying is: never study from sources that post un-GMAT-like questions!

[Matt@VeritasPrep]

Just to follow up on the sentence that Brent quoted:

"If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened?"

seems to me to mean

"If we just turn on the pipe at 9:30 AM, then the tank will fill in 5 hours. But we don't want it to fill in 5 hours, we want it to fill in exactly 6 hours! To do so, we'll have to turn on the outlet pipe at some time so that the tank doesn't fill quite as quickly as it would otherwise. At what time should we turn on the outlet so that the tank is full at 3:30 PM?"

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The question is from Veritas question bank!

then at what time should the outlet pipe be opened ?

Brent is right; this question makes very little sense. The GMAT will never ask you a question this semantically or conceptually complicated on the Quant.

What is the source of this question? It's certainly not a good question. A good rule of studying is: never study from sources that post un-GMAT-like questions!

[tanvis1120]

I think that's a good question !

Let's assume the vol of tank to be x lts. (x will be cancelled out eventually)
Inlet pipe:
In 1 hr, fills x/5 lts.
Hence, in 6 hours. fills 6x/5 lts. (which is x/5 more than the actual volume of the tank)
So, Outlet pipe, needs to empty x/5 lts of the tank.
Similarly following the method of inlet pipe, the outlet pipe empties:
x/15 lts of the tank in 1 hr.
Hence, x/5 lts of the tank is emptied in ((1 / (x/15))*(x/5)) hours = 3 hours.
So, outlet should be turned on 3 hours after 9:30 am, that is 12:30 PM.
Here goes the answer as D.

[vipulgoyal]

Mitch's solutionis perfet, here are two alt ways to solve this

1.let for x hours first inlet pipe is opened
x/5 + 2(6-x)/15 = 1 (why 2/15 if both pipes are opened 1/5 - 1/15 = 2/15 paet fill in hour)
x+12 = 15
x= 3 after 3 hours it means 12:30

2.plug in approach
I provided earlier in this post