Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: DDay is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 263
Location: Kuwait
Schools: Columbia university

Two consultants can type up a report in 12.5 hours and edit [#permalink]
Show Tags
16 Jan 2012, 10:01
17
This post was BOOKMARKED
Question Stats:
65% (03:20) correct
35% (03:01) wrong based on 309 sessions
HideShow timer Statistics
Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done? A. 41.4 B. 34.1 C. 13.4 D. 12.4 E. 10.8
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Sky is the limit
Last edited by Bunuel on 19 Jul 2013, 11:55, edited 1 time in total.
Edited the OA.



Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4130

Re: Two consultants can type up a report [#permalink]
Show Tags
16 Jan 2012, 13:14
6
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Hi there. I'm happy to help with this. The BIG idea to keep in mind: when two people are working together, what you add are the rates. You never add or subtract the times it takes to work. You add rates. The question: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?I'm going to use the notation: Rmt = the rate at which Mary types Rme = the rate at which Mary edits Rjt = the rate at which Jim types Rje = the rate at which Jim edits Rct = the combined typing rate Rtt = the combined editing rate The first two numbers tell us about combined rates. If they type a report together in 12.5 = 25/2 hr, then their combined typing rate is Rtt = (1 report)/(25/2 hr) = 2/25. If they edit a report together in 7.5 = 15/2 hr, then their combined editing rate is Rte = (1 report)/(15/2 hr) = 2/15. Mary types one report in 30 hours, so Rmt = 1/30. ADD RATES > Rtt = Rmt + Rjt > Rjt = Rtt  Rmt = (2/25)  (1/30) = (2/25)(6/6)  (1/30)(5/5) = 12/150  5/150 = 7/150 Jim's typing rate is 7/150, so he types one report in a time of 150/7 hr, approx 21 & change hours. Jim edits one report in 12 hours, so Rje = 1/12 ADD RATES > Rte = Rme + Rje > Rme = Rte  Rje = 2/15  1/12 = (2/15)(4/4)  (1/12)(5/5) = 8/60  5/60 = 3/60 = 1/20 Mary's editing rate is 1/20, so she edits one report in a time of 20 hr. So, the total time = (21 & change) hours for Jim to type + 20 hrs for Mary to edit = 41 and change hours That's closest to answer choice A. I'm sorry, but I disagree with what you posted as the OA. Is it possible that you miscopied? Does my work here make sense? Please let me know if you have any questions on what I've said here. Mike
_________________
Mike McGarry Magoosh Test Prep



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: Two consultants can type up a report [#permalink]
Show Tags
16 Jan 2012, 13:54
9
This post received KUDOS
Expert's post
10
This post was BOOKMARKED
manalq8 wrote: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?
41.4 34.1 13.4 12.4 10.8
I think this one is pretty hard, can someone please help me with it Break down the problem into two pieces: typing and editing. "Mary needs 30 hours to type the report" > Mary's typing rate = 1/30 (rate reciprocal of time) (point 1 in theory below); "Mary and Jim can type up a report in 12.5" and > 1/30+1/x=1/12.5=2/25 (where x is the time needed for Jim to type the report alone) (point 2&3 in theory below)> x=150/7; "Jim needs 12 hours to edit the report" > Jim's editing rate = 1/12; "Mary and Jim can edit a report in 7.5" and > 1/y+1/12=1/7.5=2/15 (where y is the time needed for Mary to edit the report alone) > y=20; "How many hours will it take if Jim types the report and Mary edits it immediately after he is done" > x+y=150/7+20=~41.4 Answer: A. THEORYThere are several important things you should know to solve work problems: 1. Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.\(time*speed=distance\) <> \(time*rate=job \ done\). For example when we are told that a man can do a certain job in 3 hours we can write: \(3*rate=1\) > \(rate=\frac{1}{3}\) job/hour. Or when we are told that 2 printers need 5 hours to complete a certain job then \(5*(2*rate)=1\) > so rate of 1 printer is \(rate=\frac{1}{10}\) job/hour. Another example: if we are told that 2 printers need 3 hours to print 12 pages then \(3*(2*rate)=12\) > so rate of 1 printer is \(rate=2\) pages per hour; So, time to complete one job = reciprocal of rate. For example if 6 hours (time) are needed to complete one job > 1/6 of the job will be done in 1 hour (rate). 2. We can sum the rates.If we are told that A can complete one job in 2 hours and B can complete the same job in 3 hours, then A's rate is \(rate_a=\frac{job}{time}=\frac{1}{2}\) job/hour and B's rate is \(rate_b=\frac{job}{time}=\frac{1}{3}\) job/hour. Combined rate of A and B working simultaneously would be \(rate_{a+b}=rate_a+rate_b=\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\) job/hour, which means that they will complete \(\frac{5}{6}\) job in one hour working together. 3. For multiple entities: \(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}\), where \(T\) is time needed for these entities to complete a given job working simultaneously.For example if: Time needed for A to complete the job is A hours; Time needed for B to complete the job is B hours; Time needed for C to complete the job is C hours; ... Time needed for N to complete the job is N hours; Then: \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}\), where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously. 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 \(t_1\) and \(t_2\) 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 \(T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}\)). General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:\(T_{(A&B&C)}=\frac{t_1*t_2*t_3}{t_1*t_2+t_1*t_3+t_2*t_3}\) hours. Some work problems with solutions: timenworkproblem82718.html?hilit=reciprocal%20ratefacingproblemwiththisquestion91187.html?highlight=rate+reciprocalwhatamidoingwrongtobunuel91124.html?highlight=rate+reciprocalgmatprepps93365.html?hilit=reciprocal%20ratequestionsfromgmatpreppracticeexampleasehelp93632.html?hilit=reciprocal%20rateagoodone98479.html?hilit=ratesolutionrequired100221.html?hilit=work%20rate%20doneworkproblem98599.html?hilit=work%20rate%20donehourstotypepages102407.html?hilit=answer%20choices%20or%20solve%20quadratic%20equation.%20RHope it helps.
_________________
New to the Math Forum? Please read this: 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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7443
Location: Pune, India

Re: Two consultants can type up a report [#permalink]
Show Tags
17 Jan 2012, 03:31
7
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
manalq8 wrote: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?
41.4 34.1 13.4 12.4 10.8
I think this one is pretty hard, can someone please help me with it Yes it is a tricky one but you can use some logic to arrive at the answer quickly. The explanation I will write down will be long but when you do it in your head, it will take less than a minute, I promise. Total time taken to type the report = 12.5 hrs Time taken by Mary alone = 30 hrs Time taken by Jim alone? Let's see. If Jim were to take 30 hrs alone too, together they would have taken 15 hrs. But together they took only 12.5 hrs. My guess is that Jim takes close to 20 hrs alone. Let's see: 1/30 + 1/20 = 5/60 Time taken together = 60/5 = 12 hrs. Close! It means Jim takes a little more than 20 hrs and I would take it as 21 and move on. Total time taken to edit the report = 7.5 hrs Time taken by Jim alone = 12 hrs Time taken by Mary alone? Now, if Mary were to take 12 hrs too, they could have edited it together in 6 hrs. But they took 7.5 hrs together. So Mary must take more than 12 hrs to edit it alone. I would guess 20 again. Let's see: 1/12 + 1/20 = 8/60 Time taken together = 60/8 = 7.5 hrs  Exactly! So Jim alone takes 21 hrs (apprx) to type it and Mary alone takes 20 hrs to edit it. Together they take 21+20 = 41 hrs (apprx) Answer (A)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7443
Location: Pune, India

Re: Two consultants can type up a report [#permalink]
Show Tags
17 Jan 2012, 03:37
By the way, I have assumed that you will understand some things (e.g. if two people working alone take 30 hrs each, together they will take 15 hrs) since you got a Q42 in your last GMAT. If you need an explanation of these, let me know.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Senior Manager
Status: DDay is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 263
Location: Kuwait
Schools: Columbia university

Two consultants can type up a report in [#permalink]
Show Tags
23 Jan 2012, 14:29
Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done? 41.4 34.1 13.4 12.4 10.8 does anyone please care to explain. i am having a problem solving this problem
_________________
Sky is the limit



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: Two consultants can type up a report in [#permalink]
Show Tags
23 Jan 2012, 16:44



Intern
Joined: 29 Jan 2012
Posts: 6

Re: Two consultants can type up a report [#permalink]
Show Tags
10 Mar 2012, 13:30
The OA of this problem is wrong. It says C, but it should be A... A is the correct Answer...



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15989

Re: Two consultants can type up a report in 12.5 hours and edit [#permalink]
Show Tags
26 Nov 2013, 02:49
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Two consultants can type up a report in 12.5 hours and edit [#permalink]
Show Tags
03 Apr 2014, 22:49
2
This post received KUDOS
MaryRate of type \(= \frac{1}{30}\) Rate of edit \(= \frac{1}{b} (Consider)\) JimRate of type \(= \frac{1}{c} (Consider)\) Rate of edit \(= \frac{1}{12}\) Typing rate combined\(= \frac{1}{30} + \frac{1}{c} = \frac{1}{12.5}\)......... (1) Editing rate combined \(= \frac{1}{b} + \frac{1}{12} = \frac{1}{7.5}\) ........... (2) Solving above equations for values of b & c Time taken for Jim typing \(= c = \frac{150}{7}\) Time taken for Mary editing = b = 20 Total time taken for Jim typing & Mary editing = b+c = \(\frac{150}{7} + 20\) \(= \frac{290}{7}\) = 41.4 = Answer = A
_________________
Kindly press "+1 Kudos" to appreciate



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15989

Re: Two consultants can type up a report in 12.5 hours and edit [#permalink]
Show Tags
27 Apr 2015, 06:30
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Verbal Forum Moderator
Joined: 29 Apr 2015
Posts: 897
Location: Switzerland
Concentration: Economics, Finance
WE: Asset Management (Investment Banking)

Re: Two consultants can type up a report in 12.5 hours and edit [#permalink]
Show Tags
14 May 2015, 02:57
mikemcgarry wrote: Hi there. I'm happy to help with this. The BIG idea to keep in mind: when two people are working together, what you add are the rates. You never add or subtract the times it takes to work. You add rates. The question: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?I'm going to use the notation: Rmt = the rate at which Mary types Rme = the rate at which Mary edits Rjt = the rate at which Jim types Rje = the rate at which Jim edits Rct = the combined typing rate Rtt = the combined editing rate The first two numbers tell us about combined rates. If they type a report together in 12.5 = 25/2 hr, then their combined typing rate is Rtt = (1 report)/(25/2 hr) = 2/25. If they edit a report together in 7.5 = 15/2 hr, then their combined editing rate is Rte = (1 report)/(15/2 hr) = 2/15. Mary types one report in 30 hours, so Rmt = 1/30. ADD RATES > Rtt = Rmt + Rjt > Rjt = Rtt  Rmt = (2/25)  (1/30) = (2/25)(6/6)  (1/30)(5/5) = 12/150  5/150 = 7/150 Jim's typing rate is 7/150, so he types one report in a time of 150/7 hr, approx 21 & change hours. Jim edits one report in 12 hours, so Rje = 1/12 ADD RATES > Rte = Rme + Rje > Rme = Rte  Rje = 2/15  1/12 = (2/15)(4/4)  (1/12)(5/5) = 8/60  5/60 = 3/60 = 1/20 Mary's editing rate is 1/20, so she edits one report in a time of 20 hr. So, the total time = (21 & change) hours for Jim to type + 20 hrs for Mary to edit = 41 and change hours That's closest to answer choice A. I'm sorry, but I disagree with what you posted as the OA. Is it possible that you miscopied? Does my work here make sense? Please let me know if you have any questions on what I've said here. Mike Seriously, how to solve such a question in 2 minutes. It already takes 1 minute to put everything together or even more than one minute ...
_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!
PS Please send me PM if I do not respond to your question within 24 hours.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15989

Re: Two consultants can type up a report in 12.5 hours and edit [#permalink]
Show Tags
02 Jun 2016, 12:10
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15989

Re: Two consultants can type up a report in 12.5 hours and edit [#permalink]
Show Tags
06 Jun 2017, 05:44
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1082

Re: Two consultants can type up a report in 12.5 hours and edit [#permalink]
Show Tags
08 Jun 2017, 16:42
manalq8 wrote: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many hours will it take if Jim types the report and Mary edits it immediately after he is done?
A. 41.4 B. 34.1 C. 13.4 D. 12.4 E. 10.8 We can let Jim’s typing time = j, and thus his rate = 1/j. Since Mary needs 30 hours to type the report alone, Mary’s typing rate is 1/30. Since together they can type the report in 12.5 hours, their combined rate is 1/12.5 and we can create the following equation to determine j: 1/j + 1/30 = 1/12.5 1/j + 1/30 = 2/25 Multiplying the equation by 150j, we have: 150 + 5j = 12j 150 = 7j 150/7 = j j = 21.4 We can let Mary’s editing time = m, and thus her editing rate = 1/m. Since Jim needs 12 hours to edit the report, his editing rate is 1/12. Since together they can edit the report in 7.5 hours, their combined editing rate is 1/7.5 and we can create the following equation to determine m: 1/m + 1/12 = 1/7.5 1/m + 1/12 = 2/15 Multiplying the equation by 120m, we have: 120 + 10m = 16m 120 = 6m 20 = m Thus, if Jim types the report and Mary edits the report, it will take 21.4 + 20 = 41.4 hours. Answer: A
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: Two consultants can type up a report in 12.5 hours and edit
[#permalink]
08 Jun 2017, 16:42







