Find all School-related info fast with the new School-Specific MBA Forum

It is currently 30 Aug 2014, 10:24

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Two consultants can type up a report in 12.5 hours and edit

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior 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: 275
Location: Kuwait
Schools: Columbia university
Followers: 4

Kudos [?]: 37 [0], given: 52

GMAT Tests User
Two consultants can type up a report in 12.5 hours and edit [#permalink] New post 16 Jan 2012, 09:01
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (03:21) correct 35% (02:25) wrong based on 149 sessions
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
[Reveal] Spoiler: OA

_________________

Sky is the limit


Last edited by Bunuel on 19 Jul 2013, 10:55, edited 1 time in total.
Edited the OA.
Expert Post
3 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2048
Followers: 495

Kudos [?]: 2028 [3] , given: 30

Re: Two consultants can type up a report [#permalink] New post 16 Jan 2012, 12:14
3
This post received
KUDOS
Expert's post
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

Image

Image

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25207
Followers: 3419

Kudos [?]: 25089 [2] , given: 2702

Re: Two consultants can type up a report [#permalink] New post 16 Jan 2012, 12:54
2
This post received
KUDOS
Expert's post
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.

THEORY
There 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:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
questions-from-gmat-prep-practice-exam-please-help-93632.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate
solution-required-100221.html?hilit=work%20rate%20done
work-problem-98599.html?hilit=work%20rate%20done
hours-to-type-pages-102407.html?hilit=answer%20choices%20or%20solve%20quadratic%20equation.%20R

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
4 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4688
Location: Pune, India
Followers: 1084

Kudos [?]: 4872 [4] , given: 163

Re: Two consultants can type up a report [#permalink] New post 17 Jan 2012, 02:31
4
This post received
KUDOS
Expert's post
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

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4688
Location: Pune, India
Followers: 1084

Kudos [?]: 4872 [0], given: 163

Re: Two consultants can type up a report [#permalink] New post 17 Jan 2012, 02:37
Expert's post
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

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Senior 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: 275
Location: Kuwait
Schools: Columbia university
Followers: 4

Kudos [?]: 37 [0], given: 52

GMAT Tests User
Two consultants can type up a report in [#permalink] New post 23 Jan 2012, 13:29
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

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25207
Followers: 3419

Kudos [?]: 25089 [0], given: 2702

Re: Two consultants can type up a report in [#permalink] New post 23 Jan 2012, 15:44
Expert's post
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


does anyone please care to explain. i am having a problem solving this problem


Merging similar questions. manalq8 you are posting the same question the second time, please ask if anything in above explanations was unclear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 29 Jan 2012
Posts: 5
GMAT 1: 650 Q49 V28
Followers: 0

Kudos [?]: 1 [0], given: 1

GMAT ToolKit User GMAT Tests User
Re: Two consultants can type up a report [#permalink] New post 10 Mar 2012, 12:30
The OA of this problem is wrong. It says C, but it should be A... A is the correct Answer...
SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2223
Followers: 185

Kudos [?]: 36 [0], given: 0

Premium Member
Re: Two consultants can type up a report in 12.5 hours and edit [#permalink] New post 26 Nov 2013, 01:49
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

Director
Director
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 830
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 203 [0], given: 165

Re: Two consultants can type up a report in 12.5 hours and edit [#permalink] New post 03 Apr 2014, 21:49
Mary

Rate of type = \frac{1}{30}

Rate of edit = \frac{1}{b} (Consider)

Jim

Rate 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 :)

Re: Two consultants can type up a report in 12.5 hours and edit   [#permalink] 03 Apr 2014, 21:49
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Up to how long can I edit my posts? Mentalist 5 17 Jan 2013, 17:12
7 Experts publish their posts in the topic If two typists can type two pages in two minutes, how many t arkle 10 10 Sep 2012, 16:06
3 125 hours left to prepare for GMAT? naychi 14 18 Sep 2010, 02:31
A type A machine can complete a job in 5 hours and a type B GMATT73 14 01 Dec 2005, 05:40
Display posts from previous: Sort by

Two consultants can type up a report in 12.5 hours and edit

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.