Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Final Lap
Joined: 25 Oct 2012
Posts: 270
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)

Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
10 Feb 2013, 07:11
Question Stats:
73% (02:27) correct 27% (02:15) wrong based on 437 sessions
HideShow timer Statistics
Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ? A) 2hrs, 48mins B) 6hrs, 32mins C) 7hrs, 12mins D) 13hrs, 4mins E) 14hrs, 24mins
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
KUDOS is the good manner to help the entire community.
"If you don't change your life, your life will change you"



Math Expert
Joined: 02 Sep 2009
Posts: 46267

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
10 Feb 2013, 07:32



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
10 Feb 2013, 07:35
Rock750 wrote: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
A) 2hrs, 48mins B) 6hrs, 32mins C) 7hrs, 12mins D) 13hrs, 4mins E) 14hrs, 24mins I'll use letters to label the pumps rather than numbers, because there will be so many numbers elsewhere in the solution. Real GMAT questions would normally compare how long it takes each pump to fill the pool, rather than compare the rates at which each pump fills the pool. That is, a real GMAT question would say that Pump C takes four times as long as Pump A (if A's rate is four times that of C, then C takes four times as long), and that Pump B takes twice as long as Pump A. So, say Pump A fills the pool in t minutes. Then we know: A fills 1 pool in t minutes B fills 1 pool in 2t minutes C fills 1 pool in 4t minutes You could use the rates formula now, or you can just get the same amount of time for each pump  we can use 4t minutes: A fills 4 pools in 4t minutes B fills 2 pools in 4t minutes C fills 1 pool in 4t minutes So if they all work together for 4t minutes, they fill 4+2+1 = 7 pools. If they fill 7 pools in 4t minutes, they fill 1 pool in 4t/7 minutes. This is equal to 56 minutes, from the question, so 4t/7 = 56 4t = 56*7 4t = 392 Notice that 4t is what we wanted to find  that's the time it takes pump C. So the answer is 392 minutes, or 6 hours and 32 minutes.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Intern
Joined: 06 Aug 2012
Posts: 12
Location: Russian Federation
Concentration: International Business, General Management
GMAT Date: 06282013
WE: Sales (Manufacturing)

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
04 Jun 2013, 00:06
My approach is quite similar to Bunuel's. A,B,C  each pump's rate respectively. We know that all 3 pumps fill the pool for 56 min: 1/(A+B+C)=56 We also know that: A=2B=4C; or A= 4C and B=2C
substitute these equalities in first equation: 1/(4C+2C+C)=56 ====> 1/7C=56 ===> C=1/392 meaning that pump C needs 392 minutes or 6 h 32 min to fill the pool alone.



Intern
Joined: 09 Apr 2013
Posts: 40
Location: United States (DC)
Concentration: Strategy, Social Entrepreneurship
GPA: 3.55
WE: General Management (NonProfit and Government)

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
05 Jun 2013, 10:01
I think of the fraction of the pool that each pump fills. If the third pump fills up x, the second pump fills up 2x, and the first pump fills up 4x, so there are seven "parts" (4+2+1) which means First pump fills 4/7 of the pool in 56 mins 2nd pump fills 2/7 of the pool in 56 mins 3rd pump fills 1/7 of the pool in 56 mins
for the 3rd pump to fill the whole pool by itself, it would take 7 times the time. So... 56 x 7 = 392 mins = 6 hours and 32 minutes
Answer is B



Intern
Joined: 17 Jun 2013
Posts: 3

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
19 Jun 2013, 05:36
I am getting the same solution like Bunuel Using the method of The Highest Common Factor Given that x+2x+4x=1/56 x=1/392 = 392 minutes = 6 hours and 32 minutes.



Director
Joined: 23 Jan 2013
Posts: 598

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
26 Oct 2014, 05:28
1/x+1/2x+1/4x=1/56 7/4x=1/56 x=1/98 portion of work per minute does fastest pump. So, slowest does 1/98*4=1/392 portion, i.e in 392 min. 392/60=6.5... or 6h.32 min
B



Intern
Joined: 26 May 2016
Posts: 22

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
01 Oct 2016, 18:40
Bunuel wrote: Rock750 wrote: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
A) 2hrs, 48mins B) 6hrs, 32mins C) 7hrs, 12mins D) 13hrs, 4mins E) 14hrs, 24mins The rate of pump 1 = 4x job/minute. The rate of pump 2 = 2x job/minute. The rate of pump 3 = x job/minute. Given that x+2x+4x=1/56 > x=1/392 > (time) = (reciprocal of rate) = 392 minutes = 6 hours and 32 minutes. Answer: B. How about this approach: Water pumped by pump 1 in 56 mins : 400 lts Water pumped by pump 2 in 56 mins : 200 lts Water pumped by pump 3 in 56 mins : 100 lts total water pumped in 56 mins by all: 700 lts Hence, pump 3 needs to pump 700 lts for pump 3, 100 lts take 56 mins so 700 lts will take 56 * 7 = 350 + 42 = 392mins = 392/60 hours = 6 hours and 32 mins.



SVP
Joined: 08 Jul 2010
Posts: 2114
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
10 Nov 2016, 00:41
Rock750 wrote: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
A) 2hrs, 48mins B) 6hrs, 32mins C) 7hrs, 12mins D) 13hrs, 4mins E) 14hrs, 24mins Answer: Option B Please check attachment
Attachments
File comment: www.GMATinsight.com
3.jpg [ 59.66 KiB  Viewed 3113 times ]
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3511
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
10 Nov 2016, 10:31
Rock750 wrote: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
A) 2hrs, 48mins B) 6hrs, 32mins C) 7hrs, 12mins D) 13hrs, 4mins E) 14hrs, 24mins Ratio of efficiency of the 3 pumps is  Pump  I : Pump  II : Pump  III = 4 : 2 : 1 Total capacity is 56*7 Time taken to fill the tank using only Pump  III = \(\frac{56*7}{60}\) = 6 Hrs 32 minutes... Hence, Answer will be (B) 6hrs, 32mins
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Intern
Joined: 30 May 2017
Posts: 8

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
06 Jul 2017, 14:27
Hey guys,
This is my approach and line of thinking, could you help me figure out where I'm going wrong?
We know that working together the pumps can fill the pool in 56 minutes, so the three pumps collectively fill 1/56 of the pool per minute. (1/56=1/pump1 + 1/pump2 + 1/pump3) or Pump1 + pump2 + pump3 = 56
Next, because pump 1 works 4 times as fast as pump 3, and twice as fast as pump 2,
Let pump 1 = a (Pump 1 can fill the pool in a minutes) Let pump 2 = 2a (Pump 2 can fill the pool in 2a minutes) Let pump 3 = 4a (etc.. etc...)
1/a+ 1/2a+ 1/4a= 56 a= 32 4a= 128 Answer should be 2 hours and 8 minutes.....
It's clear to me that I'm wrong, but I'm not sure which part I've confused.
Thanks guys!



VP
Joined: 07 Dec 2014
Posts: 1019

Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
06 Jul 2017, 17:28
Rock750 wrote: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
A) 2hrs, 48mins B) 6hrs, 32mins C) 7hrs, 12mins D) 13hrs, 4mins E) 14hrs, 24mins because rate of pump 3=1/7 of combined rate, it will take pump 3 seven times as long to fill pool alone 7*56=392 minutes=6 hrs, 32 minutes B



Manager
Joined: 11 Feb 2017
Posts: 202

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
11 Jan 2018, 03:53
Bunuel wrote: Rock750 wrote: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
A) 2hrs, 48mins B) 6hrs, 32mins C) 7hrs, 12mins D) 13hrs, 4mins E) 14hrs, 24mins The rate of pump 1 = 4x job/minute. The rate of pump 2 = 2x job/minute. The rate of pump 3 = x job/minute. Given that x+2x+4x=1/56 > x=1/392 > (time) = (reciprocal of rate) = 392 minutes = 6 hours and 32 minutes. Answer: B. Hi bro, just a query How do we know the rate is given in 4x/minute rather than 4x/hour? Please help



Math Expert
Joined: 02 Sep 2009
Posts: 46267

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
11 Jan 2018, 05:13
rocko911 wrote: Bunuel wrote: Rock750 wrote: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
A) 2hrs, 48mins B) 6hrs, 32mins C) 7hrs, 12mins D) 13hrs, 4mins E) 14hrs, 24mins The rate of pump 1 = 4x job/minute. The rate of pump 2 = 2x job/minute. The rate of pump 3 = x job/minute. Given that x+2x+4x=1/56 > x=1/392 > (time) = (reciprocal of rate) = 392 minutes = 6 hours and 32 minutes. Answer: B. Hi bro, just a query How do we know the rate is given in 4x/minute rather than 4x/hour? Please help The rate is given in minutes (check the highlighted part) and the relative ratio of the three rates would be same for any time interval.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2771
Location: United States (CA)

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
18 Jan 2018, 08:45
Rock750 wrote: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
A) 2hrs, 48mins B) 6hrs, 32mins C) 7hrs, 12mins D) 13hrs, 4mins E) 14hrs, 24mins We can let n = the number of minutes it takes for pump 3 to fill the pool alone. Thus, the rate of pump 3 is 1/n, and that of pump 1 is 4/n and that of pump 2 is 2/n. Since they can fill the pool in 56 minutes when they work together, their combined rates can be equated as follows: 4/n + 2/n + 1/n = 1/56 7/n = 1/56 n = 7 x 56 n = 392 minutes Since 1 hour = 60 minutes, 392 minutes = 360 minutes + 32 minutes = 6 hours 32 minutes. Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Joined: 09 Mar 2016
Posts: 608

Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
18 Jan 2018, 10:53
Bunuel wrote: Rock750 wrote: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
A) 2hrs, 48mins B) 6hrs, 32mins C) 7hrs, 12mins D) 13hrs, 4mins E) 14hrs, 24mins The rate of pump 1 = 4x job/minute. The rate of pump 2 = 2x job/minute. The rate of pump 3 = x job/minute. Given that x+2x+4x=1/56 > x=1/392 > (time) = (reciprocal of rate) = 392 minutes = 6 hours and 32 minutes. Answer: B. H Bunuel i am confused about wording: it says: Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. shouldnt it be vice versa :? The rate of pump 1 = x job/minute. The rate of pump 2 = 2x job/minute. The rate of pump 3 = 4x job/minute. also you summed up rates of three machines x+2x+4x=1/56 > x=1/392 And question asks about the time of only one pump ? thanks and regards, D. Hello niks18 , perhaps you can help ? still struggling with word problems, but improving a bit



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1142
Location: India
GPA: 3.82

Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
18 Jan 2018, 19:39
dave13 wrote: Bunuel wrote: Rock750 wrote: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?
A) 2hrs, 48mins B) 6hrs, 32mins C) 7hrs, 12mins D) 13hrs, 4mins E) 14hrs, 24mins The rate of pump 1 = 4x job/minute. The rate of pump 2 = 2x job/minute. The rate of pump 3 = x job/minute. Given that x+2x+4x=1/56 > x=1/392 > (time) = (reciprocal of rate) = 392 minutes = 6 hours and 32 minutes. Answer: B. H Bunuel i am confused about wording: it says: Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. shouldnt it be vice versa The rate of pump 1 = x job/minute. The rate of pump 2 = 2x job/minute. The rate of pump 3 = 4x job/minute. also you summed up rates of three machines x+2x+4x=1/56 > x=1/392 And question asks about the time of only one pump ? thanks and regards, D. Hello niks18 , perhaps you can help ? still struggling with word problems, but improving a bit Hi dave13Take a simple example. If we say rate of pump 2 is 2 l/hr, then as per the question and your understanding what should be the rate of pump 1? whether it will be 1 l/hr or 4 l/hr? Whose rate is higher Pump 1 or Pump 2? Posted from my mobile device



Director
Joined: 09 Mar 2016
Posts: 608

Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
19 Jan 2018, 09:44
Take a simple example. If we say rate of pump 2 is 2 l/hr, then as per the question and your understanding what should be the rate of pump 1? whether it will be 1 l/hr or 4 l/hr? Whose rate is higher Pump 1 or Pump 2? Posted from my mobile device[/quote] Hi niks18, thanks for nice question and reply hope you had a fantastic day if rate of pump TWO is 2 job/min than if pump 1's maximum rate is twice the maximum rate of pump TWO, HENCE the rate of pump ONE is 2*2 = 4 and since the rate of PUMP ONE is 4 job/min. Also if rate of pump ONE is four times the maximum rate of pump 3, then 2*3= 6 Am i correct ? my another question why did we sum up rates of all three pumps, when question asks about the time needed for only one pump to get the whole job done  which is pump number three many many thanks



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1142
Location: India
GPA: 3.82

Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
19 Jan 2018, 10:31
dave13 wrote: Take a simple example. If we say rate of pump 2 is 2 l/hr, then as per the question and your understanding what should be the rate of pump 1? whether it will be 1 l/hr or 4 l/hr? Whose rate is higher Pump 1 or Pump 2?
Posted from my mobile device Hi niks18, thanks for nice question and reply :) hope you had a fantastic day :) if rate of pump TWO is 2 job/min than if pump 1's maximum rate is twice the maximum rate of pump TWO, HENCE the rate of pump ONE is 2*2 = 4 and since the rate of PUMP ONE is 4 job/min. Also if rate of pump ONE is four times the maximum rate of pump 3, then 2*3= 6Am i correct ? :? :) my another question why did we sum up rates of all three pumps, when question asks about the time needed for only one pump to get the whole job done  which is pump number three :? many many thanks :)[/quote] Hi dave13, the highlighted portion is not correct. pump 1 is four time the rate of pump 3. as you calculated that rate of pump 1 is 4l/hr so shouldn't the rate of pump 3 be 1 l/hr? 1*4times=4. Didn't understand why you calculated 6. so in this problem we have rate of Pump1>Pump2>Pump3. Therefore as a general rule you should assume the lowest quantity as a variable. So here let Pump3=x, then Pump1=4x (this is 4 time the rate of pump2 & 2 times the rate of pump2) and Pump2=2x. Next we are adding all the rates because we are given total time when all the three pumps are working together. When three pumps work together the combined rate of flow will be =x+2x+4x=7x l/hr so time taken = total Capacity/combined rate Therefore total capacity = time*rate



Director
Joined: 09 Mar 2016
Posts: 608

Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]
Show Tags
21 Jan 2018, 02:58
niks18 many thanks for your kind explanation. yes, highlihed yellow part was a typo. One question: why as general rule we should assume the lowest quantity as a variable, and not the highest quantity ? have a great weelend thank you!




Marge has 3 pumps for filling her swimming pool. When all 3
[#permalink]
21 Jan 2018, 02:58



Go to page
1 2
Next
[ 21 posts ]



