GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Oct 2019, 17:47

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

If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 28 Dec 2009
Posts: 6
If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post Updated on: 15 Mar 2019, 02:40
1
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

59% (00:37) correct 41% (00:58) wrong based on 180 sessions

HideShow timer Statistics

If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same task in 6 hours, how long will it take if both of them work together to complete the task?


A. 1 hour
B. 1.5 hours
C. 2 hours
D. 2.5 hours
E. 4.5 hours


This is a problem of Arithmetic, related to work and time. It is a very interesting problem but I am unable to solve it. I am still trying to solve it, I am thinking that it took (3 + 6) / 2 = 4.5, mean of the time taken by the two. But, my answer is wrong.

Please explain the logic.

Thanks

Originally posted by david01 on 08 Mar 2010, 03:00.
Last edited by Bunuel on 15 Mar 2019, 02:40, edited 2 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58445
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 09 Mar 2010, 02:43
5
1
nickk wrote:
I haven't seen anyone post the formula so I'll go ahead and do it

1/T = 1/A + 1/B + .... 1/N

so if you have N entities which can do the same job in different amounts of time (denoted by A, B, ..., N above), the total amount of time it takes them to do the same tas working together is T.

I think you can solve all similar problems using this formula.


The above is correct and it's good to memorize cases for two and three entities (workers, pumps, ...):

General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:

Given that \(a\) and \(b\) are the respective individual times needed for \(A\) and \(B\) workers (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{a*b}{a+b}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{a}+\frac{1}{b}=\frac{1}{t}\)).

General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:

\(T_{(A&B&C)}=\frac{a*b*c}{ab+ac+bc}\) hours.


Also for rate problems it's good to know that:

TIME to complete one job=Reciprocal of rate. eg 6 hours needed to complete one job (time) --> 1/6 of the job done in 1 hour (rate).

Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance.

Time*Rate=Distance
Time*Rate=Job


Hope it helps.
_________________
General Discussion
Senior Manager
Senior Manager
avatar
Status: Yeah well whatever.
Joined: 18 Sep 2009
Posts: 285
Location: United States
GMAT 1: 660 Q42 V39
GMAT 2: 730 Q48 V42
GPA: 3.49
WE: Analyst (Insurance)
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post Updated on: 08 Mar 2010, 08:20
I made tables. I hope this is right or I did a bunch of work for no reason. I picked the work to be traveling a distance of 12 miles

[list=]Separate
A B
R 4 mph 2 mph
T 3 hrs 6 hrs
D 12 mi 12 mi

Together
A B Together
R 4 mph 2 mph
T t t t
D 12-d d 12 mi


4t=12-d and 2t=d
t=3-d/4
so
2(3-d/4)=d
6-.5d=d
6=1.5d
d=4
so
Together with d set to 4
A B Together
R 4 mph 2 mph
T t t t
D 8 mi 4 mi 12 mi

4t=8
so
t=2 hrs
[/list]
_________________
He that is in me > he that is in the world. - source 1 John 4:4

Originally posted by vannbj on 08 Mar 2010, 08:08.
Last edited by vannbj on 08 Mar 2010, 08:20, edited 1 time in total.
Manager
Manager
avatar
Joined: 01 Feb 2010
Posts: 178
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 08 Mar 2010, 08:17
david01 wrote:
If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same task in 6 hours, how long will it take if both of them work together to complete the task?

This is a problem of Arithmetic, related to work and time. It is a very interesting problem but I am unable to solve it. I am still trying to solve it, I am thinking that it took (3 + 6) / 2 = 4.5, mean of the time taken by the two. But, my answer is wrong.

Please explain the logic.
Thanks

A do 1/3 task in 1 hour
B do 1/6 task in 1 hour

A & B together do 1/3 + 1/6 = 1/2 task in 1 hour.
So they complete task in 2 hours.
Manager
Manager
avatar
Joined: 29 Oct 2009
Posts: 156
Concentration: General Management, Sustainability
WE: Consulting (Computer Software)
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 08 Mar 2010, 08:19
If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same task in 6 hours, how long will it take if both of them work together to complete the task?

A can complete task in 3 hours. In 1 hour A can complete 1/3 of the work.
B can complete task in 6 hours. In 1 hour B can complete 1/6 of the work.

Both together can complete how much work in an hour = 1/3 + 1/6 = 3/6 = 1/2

So 1/2 work can be completed in 1 hour by A and B together.
How much time it takes to complete the work = 2/1 hours = 2 hours.

Hope it is clear.
Manager
Manager
avatar
Joined: 10 Aug 2009
Posts: 101
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 08 Mar 2010, 13:06
I haven't seen anyone post the formula so I'll go ahead and do it

1/T = 1/A + 1/B + .... 1/N

so if you have N entities which can do the same job in different amounts of time (denoted by A, B, ..., N above), the total amount of time it takes them to do the same tas working together is T.

I think you can solve all similar problems using this formula.
Manager
Manager
User avatar
Joined: 18 Feb 2010
Posts: 129
Schools: ISB
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 09 Mar 2010, 02:55
david01 wrote:
If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same task in 6 hours, how long will it take if both of them work together to complete the task?

This is a problem of Arithmetic, related to work and time. It is a very interesting problem but I am unable to solve it. I am still trying to solve it, I am thinking that it took (3 + 6) / 2 = 4.5, mean of the time taken by the two. But, my answer is wrong.

Please explain the logic.

Thanks


Let task be writing 18 pages (multiple of 3 and 6)\

A writes 18/3 = 6 pages an hour
B write 18/6 = 3 pages per hour

Both write 9 pages per hour
So total time required is 18/9=2 hours while working together...

Hope this helps you in solving such problems without working with x, y fractions.
_________________
CONSIDER AWARDING KUDOS IF MY POST HELPS !!!
Retired Moderator
User avatar
Status: The last round
Joined: 18 Jun 2009
Posts: 1171
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
GMAT ToolKit User
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 13 Mar 2010, 11:22
Bunuel wrote:
nickk wrote:
I haven't seen anyone post the formula so I'll go ahead and do it

1/T = 1/A + 1/B + .... 1/N

so if you have N entities which can do the same job in different amounts of time (denoted by A, B, ..., N above), the total amount of time it takes them to do the same tas working together is T.

I think you can solve all similar problems using this formula.


The above is correct and it's good to memorize cases for two and three entities (workers, pumps, ...):

General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:

Given that \(a\) and \(b\) are the respective individual times needed for \(A\) and \(B\) workers (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{a*b}{a+b}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{a}+\frac{1}{b}=\frac{1}{t}\)).

General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:

\(T_{(A&B&C)}=\frac{a*b*c}{ab+ac+bc}\) hours.


Also for rate problems it's good to know that:

TIME to complete one job=Reciprocal of rate. eg 6 hours needed to complete one job (time) --> 1/6 of the job done in 1 hour (rate).

Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance.

Time*Rate=Distance
Time*Rate=Job


Hope it helps.




Kudos Bunuel!!

Well, in some cases there are multiple persons doing the same job. e.g 5 men doing a job in 6 hours, while 9 women doing the same job in 6 hours & 10 boys doing the same job in 8 hours.

What's the formula for such cases?
_________________
Manager
Manager
avatar
Joined: 12 Oct 2011
Posts: 154
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 06 Jan 2012, 06:12
Hussain15 wrote:
Well, in some cases there are multiple persons doing the same job. e.g 5 men doing a job in 6 hours, while 9 women doing the same job in 6 hours & 10 boys doing the same job in 8 hours.
What's the formula for such cases?

Even I would be interested to know if there exists a formula for such problems. I am unusually weak in such work-rate problems and I struggle frequently. Any help would be appreciated.
_________________
Consider KUDOS if you feel the effort's worth it
Manager
Manager
User avatar
Joined: 29 Jul 2011
Posts: 75
Location: United States
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 06 Jan 2012, 21:05
This is a unit rate problem.

RULE:
1. When you are given something like, something takes x hours to complete, then the rate is 1/x
2.When working together, the rates add.

Here, A's rate is 1/3, B's rate is 1/6

So, working together, A + B = 1/3 + 1/6 = 3/6 = 1/2

Now inverse again to find the number of hours (since unit rate) = 2 hours
_________________
I am the master of my fate. I am the captain of my soul.
Please consider giving +1 Kudos if deserved!

DS - If negative answer only, still sufficient. No need to find exact solution.
PS - Always look at the answers first
CR - Read the question stem first, hunt for conclusion
SC - Meaning first, Grammar second
RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min
Manager
Manager
avatar
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 157
Location: Kuwait
Schools: Columbia university
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 07 Jan 2012, 12:26
here is the easiest approach.

A can complete 1/3 of the task in one hour, while B can complete 1/6 of the task is one hour. the formula to use is as following to get how much can they both achieve in one hour:

1/3+1/6=1/x

common denominator====>6

2/6+1/6=3/6 after simplification becomes 1/2

so both of them can finish the one half of the task in one hour, and in order to get the number of hours for the whole task just reverse the fraction, which will be 2

hope this helps
_________________
Sky is the limit
Intern
Intern
avatar
Joined: 01 Apr 2012
Posts: 8
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 10 Sep 2012, 07:56
Though this was posted long ago, the questions raised by Hussain and Siddrat are quite good.I also need Bunuel here. But, my take on Hussain's question is:
if m, w and b represent the times a man, a woman and a boy take in that order. I think we could get the rate for a single person of each category: 1/( No. of worker * Time for all workers)
Thus, the rates for a single person: man=1/(5*6) , woman =1/(9*6), boy=1/(10*8)
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 401
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 13 Nov 2012, 23:00
\(\frac{1}{6}+\frac{1}{3}=\frac{1}{x}\)

\(\frac{1}{x}=\frac{1}{2}\)

Answer: time = reciprocal of rate = 2 hours
_________________
Impossible is nothing to God.
Intern
Intern
avatar
Joined: 14 Jun 2019
Posts: 1
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta  [#permalink]

Show Tags

New post 15 Jun 2019, 01:05
A=1/3
B=1/2
A+B=(1/3)+(1/2)
=3/4
A and B can do in 4 hours=(3/4)×(4/1)=3

Posted from my mobile device
GMAT Club Bot
Re: If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta   [#permalink] 15 Jun 2019, 01:05
Display posts from previous: Sort by

If ‘A’ can complete a task in 3 hours and ‘B’ can complete the same ta

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





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