It is currently 13 Dec 2017, 03:27

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
1 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 755

Kudos [?]: 2240 [1], given: 123

Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com [#permalink]

Show Tags

New post 22 Jan 2017, 00:00
1
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

61% (02:23) correct 39% (03:05) wrong based on 114 sessions

HideShow timer Statistics

Q.)
Operating at a constant rate, 2 pumps of Type 1 can completely fill a reservoir with water in 24 hours. A pump of Type 2 can also fill the same reservoir with water but it operates at a different constant rate. At 1 PM on 21 March, 3 pumps of Type 2 start filling the empty reservoir. At 3 PM, 6 pumps of Type 1 also start filling the reservoir with water. The reservoir is completely filled with water at 7 PM. If the 6 Type 1 pumps were not started, at what time would the reservoir have been completely filled with water? 

    A. 1 AM on 22 March

    B. 7 AM on 22 March

    C. 1 AM on 23 March

    D. 7 AM on 23 March

    E. 7 AM on 25 March


Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image
[Reveal] Spoiler: OA

_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2240 [1], given: 123

Expert Post
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 755

Kudos [?]: 2240 [0], given: 123

Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com [#permalink]

Show Tags

New post 22 Jan 2017, 00:02
The official solution has been posted. Looking forward to a healthy discussion..:)
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Last edited by EgmatQuantExpert on 27 Jan 2017, 21:51, edited 1 time in total.

Kudos [?]: 2240 [0], given: 123

Director
Director
User avatar
P
Joined: 05 Mar 2015
Posts: 966

Kudos [?]: 301 [0], given: 41

Re: Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com [#permalink]

Show Tags

New post 22 Jan 2017, 11:42
EgmatQuantExpert wrote:
Q.)
Operating at a constant rate, 2 pumps of Type 1 can completely fill a reservoir with water in 24 hours. A pump of Type 2 can also fill the same reservoir with water but it operates at a different constant rate. At 1 PM on 21 March, 3 pumps of Type 2 start filling the empty reservoir. At 3 PM, 6 pumps of Type 1 also start filling the reservoir with water. The reservoir is completely filled with water at 7 PM. If the 6 Type 1 pumps were not started, at what time would the reservoir have been completely filled with water? 

    A. 1 AM on 22 March

    B. 7 AM on 22 March

    C. 1 AM on 23 March

    D. 7 AM on 23 March

    E. 7 AM on 25 March


Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image


Let rate of Type 2 =B
& Type 1 =A
thus 2 type 1 can fill with rate= 1/24
thus A=1/48
similarly work done by 3 Pump Type 2 is 3/B
thus after starting type-2 1 PM it worked alone upto 3PM(2 hrs)
work done by type-2 for 2 hrs = (2*3)/B
for the next 4 hrs (7PM) both types of pump run.
contribution of 6 pump type 1 for 4 hrs = (6*4)/48 =1/2
contribution of 3 pump type 2 for 4 hrs = (3*12)/B

all three combined = work done by type-2 for initial 2 hrs + contribution of 6 pump type 1 for 4 hrs + contribution of 6 pump type 2 for 4 hrs
6/B + 12/B + 1/2 = 1
18/B = 1/2
or ( 3*6)/B = 1/2
3/B = 1/12
thus 3 type -2 pump can fill in 12 hrs
1 PM on 21st March +12 hrs
=1 AM on 22nd march

Ans A

Kudos [?]: 301 [0], given: 41

Intern
Intern
avatar
B
Joined: 11 Aug 2013
Posts: 46

Kudos [?]: 2 [0], given: 0

Re: Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com [#permalink]

Show Tags

New post 22 Jan 2017, 22:11
2 pumps fill empty reservoir in 24 hours
6 pumps fill in 6 hours

Type 1 worked from 3 to 7 PM --4 hours
hence type 1 completed the 4/6 work of the total work.

Work remaining done by type 2 pumps = 1-2/3 =1/3

now type 2 pumps worked for 6 hours ---3 pumps completed 1/3 work in 6 hours
therefore they would have taken 6*3 hours if type 1 did not start. which means 7 AM on march 22..Answer B

Kudos [?]: 2 [0], given: 0

Expert Post
1 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 755

Kudos [?]: 2240 [1], given: 123

Re: Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com [#permalink]

Show Tags

New post 23 Jan 2017, 21:58
1
This post received
KUDOS
Expert's post
ravisinghal wrote:
2 pumps fill empty reservoir in 24 hours
6 pumps fill in 6 hours

Type 1 worked from 3 to 7 PM --4 hours
hence type 1 completed the 4/6 work of the total work.

Work remaining done by type 2 pumps = 1-2/3 =1/3

now type 2 pumps worked for 6 hours ---3 pumps completed 1/3 work in 6 hours
therefore they would have taken 6*3 hours if type 1 did not start. which means 7 AM on march 22..Answer B


Hey ravisinghal,

There are few mistakes in your solution.

If 2 pumps fill in 24 hours
How can 6 pumps fill in 6 hours?
I think you have made a calculation mistake here. The correct way is -
    If 2 pumps fill in 24 hours
    1 pump will fill in 48 hours
    6 pumps will fill in 8 hours

This is one of the mistakes. Kindly go through your solution again and do try to solve once more. :)

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2240 [1], given: 123

1 KUDOS received
Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 859

Kudos [?]: 291 [1], given: 16

Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com [#permalink]

Show Tags

New post 24 Jan 2017, 08:42
1
This post received
KUDOS
1
This post was
BOOKMARKED
Operating at a constant rate, 2 pumps of Type 1 can completely fill a reservoir with water in 24 hours. A pump of Type 2 can also fill the same reservoir with water but it operates at a different constant rate. At 1 PM on 21 March, 3 pumps of Type 2 start filling the empty reservoir. At 3 PM, 6 pumps of Type 1 also start filling the reservoir with water. The reservoir is completely filled with water at 7 PM. If the 6 Type 1 pumps were not started, at what time would the reservoir have been completely filled with water? 

A. 1 AM on 22 March
B. 7 AM on 22 March
C. 1 AM on 23 March
D. 7 AM on 23 March
E. 7 AM on 25 March

rate of 1 T1 pump=1/(2*24)=1/48
in 4 hours 6 T1 pumps fill 24/48=1/2 of reservoir
in 6 hours 3 T2 pumps fill the other 1/2 of reservoir
thus, it would take 3 T2 pumps 12 hours to fill reservoir alone
1 AM on 22 March
A

Kudos [?]: 291 [1], given: 16

Expert Post
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 755

Kudos [?]: 2240 [0], given: 123

Re: Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com [#permalink]

Show Tags

New post 27 Jan 2017, 21:50
Hey,

PFB the official solution.

Given:

    • Let the total volume of the reservoir be V cubic units
    • Time taken by 2 "Type 1" pumps to fill V volume = 24 hours
      o So, Time taken by 1 "Type 1" pump to fill V volume = 24 x 2 = 48 hours
      o Filling Rate of Type 1 pump = \(\frac{V}{48}\) volume per hour
    • Let one "Type 2" pump take t hours to fill V volume
      o So, Filling Rate of "Type 2" pump = \(\frac{V}{t}\)volume per hour
    1 PM – 3 PM
      o 3 "Type 2" pumps start filling the empty reservoir
    3 PM – 7 PM
      o 3 "Type 2" pumps + 6 "Type 1" pumps fill the reservoir to fullness

To find:

    • At what time would 3 "Type 2" pumps alone have filled the reservoir?

Approach:

    1. (Time at which 3 "Type 2" pumps alone would have filled the reservoir) = 1 PM + (Volume to be filled/Filling rate of 3 "Type 2" pumps) hours
      o = 1 PM + \(\frac{V}{(3*\frac{V}{t})}\) hours
      o = 1 PM +\(\frac{t}{3}\) hours
      o So, to answer the question, we need to find the value of t
    2. We’re told that 3 "Type 2" pumps operating for 6 hours (from 1 PM to 7 PM) and 6 Type 1 pumps operating for 4 hours (from 3 PM to 7 PM) fill V cubic units of volume
      o We’ll use this information to find the value of t.

Working Out:

    Finding the value of t
      o (Volume filled by 3 "Type 2" pumps in 6 hours) + (Volume filled by 6 "Type 1" pumps in 4 hours) = (V, the total Volume of the Reservoir)
      o 3(Volume filled by 1 "Type 2" pump in 6 hours) + 6(Volume filled by 1 "Type 1" pump in 4 hours) = V
      o \(3*(\frac{V}{t}*6) + 6*(\frac{V}{48}*4) = V\)
      o \(\frac{18}{t} + \frac{1}{2} = 1\)
      o \(\frac{18}{t} = \frac{1}{2}\)
      o So, t = 36 hours

    Finding the required time
      o (Time at which 3 "Type 2" pumps alone would have filled the reservoir) = 1 PM + \(\frac{t}{3}\)hours
      o = 1 PM + \(\frac{36}{3}\) hours
      o = 1 PM + 12 hours
      o = 1 AM the next day

Looking at the answer choices, we see that the correct answer is Option A


Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2240 [0], given: 123

Expert Post
4 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 755

Kudos [?]: 2240 [4], given: 123

Re: Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com [#permalink]

Show Tags

New post 27 Jan 2017, 22:06
4
This post received
KUDOS
Expert's post
Alternative method – (without using variables)

We are given:

    • 2 “Type 1” pumps can fill the reservoir in 24 hours.
    • At 1 pm –
      o 3 pumps of “Type 2” start filling the reservoir and continue filling it till 7 pm.
      o That means it fills the reservoir for (7-1) = 6 hours
    • At 3 pm-
      o 6 pumps of “Type 1” also start filling the reservoir and it is also open till 7 pm.
      o That means it fills the reservoir for = (7-3) = 4 hours

Working out:

    • Now 2 pumps of “Type 1” fill the reservoir in 24 hours.
    • 1 pump of “Type 1” can fill the reservoir in 48 hours.
    • 6 pumps of “Type 1” can fill the reservoir in 8 hours.
      o But 6 reservoirs were open for 4 hours only.
      o So what can we conclude from this?
      o The reservoir was half filled by these 6 reservoirs.

    • The other half was filled by 3 pumps of “Type 2” which was open for 6 hours.
    • Therefore, to completely fill the reservoir, it will take double the time, which is 6 x 2 hours
. :)

So total time taken will be (1 pm + 12 hours) = 1 AM of 22nd March.


Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts :)

Image
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2240 [4], given: 123

Intern
Intern
avatar
B
Status: preparing
Joined: 30 Dec 2013
Posts: 39

Kudos [?]: 13 [0], given: 26

Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q45 V35
GMAT 2: 640 Q49 V28
GMAT 3: 640 Q49 V28
GMAT 4: 640 Q49 V28
GMAT 5: 640 Q49 V28
GPA: 2.84
WE: General Management (Consumer Products)
GMAT ToolKit User
Re: Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com [#permalink]

Show Tags

New post 30 Oct 2017, 01:29
Tricky!
I got A.

2 T1 can fill in 24 hours.
so 6 T1 can fill in 8 hours.

T2 rate is unknown.

3 T2 pumps start at 1pm and work till 7pm.
at 3pm joined by 6 T1 pumps, which work for 4 hours.

if 6 T1 can fill the full tank in 8 hours. In 4 hours, half of the tank was filled by these pumps.
which means, the other half of the tank was filled by 3 T2 pumps which worked for 6 hours in total.

so 3 T2 can fill half in 6 hours, therefore full tank in 12 hours.

1pm+ 12 hours= 1 am on 22nd

Kudos [?]: 13 [0], given: 26

Senior Manager
Senior Manager
User avatar
G
Joined: 22 Nov 2016
Posts: 251

Kudos [?]: 64 [0], given: 42

Location: United States
Concentration: Leadership, Strategy
GPA: 3.4
Reviews Badge CAT Tests
Re: Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com [#permalink]

Show Tags

New post 10 Nov 2017, 10:48
Once you find that the work done by both these types of pumps is the same, i.e 1/2, we can equate them.

Rate of type 1 * time the type 1 pumps worked = Rate of type 2 * time the type 2 pumps worked.

\(\frac{1}{8}*4=\frac{3}{x}*2\)

Thus, x =12.

Rate of type 2 pump is \(\frac{1}{12}\)
_________________

Kudosity killed the cat but your kudos can save it.

Kudos [?]: 64 [0], given: 42

Re: Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com   [#permalink] 10 Nov 2017, 10:48
Display posts from previous: Sort by

Word Problem - Operating at a constant rate, 2 pumps of Type 1 can com

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.