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
I dint really get whts being asked
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 429
- Joined: Wed Sep 19, 2012 11:38 pm
- Thanked: 6 times
- Followed by:4 members
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
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.[email protected] wrote: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
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
-
- Master | Next Rank: 500 Posts
- Posts: 468
- Joined: Mon Jul 25, 2011 10:20 pm
- Thanked: 29 times
- Followed by:4 members
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
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
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let the tank = 30 liters.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
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
- Followed by:247 members
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.then at what time should the outlet pipe be opened ?
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!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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?"
"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?"
-
- Master | Next Rank: 500 Posts
- Posts: 429
- Joined: Wed Sep 19, 2012 11:38 pm
- Thanked: 6 times
- Followed by:4 members
The question is from Veritas question bank!
ceilidh.erickson wrote: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.then at what time should the outlet pipe be opened ?
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
- Senior | Next Rank: 100 Posts
- Posts: 95
- Joined: Sat Dec 28, 2013 8:53 am
- Location: United States
- Thanked: 2 times
- Followed by:5 members
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.
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.
-
- Master | Next Rank: 500 Posts
- Posts: 468
- Joined: Mon Jul 25, 2011 10:20 pm
- Thanked: 29 times
- Followed by:4 members
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
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