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

It is currently 28 Aug 2015, 00:03
GMAT Club Tests

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

Working together, Jose and Jane can complete an assigned task in 20

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
avatar
Joined: 12 Jun 2006
Posts: 532
Followers: 1

Kudos [?]: 41 [0], given: 1

Working together, Jose and Jane can complete an assigned task in 20 [#permalink] New post 09 Apr 2007, 19:23
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

46% (03:37) correct 54% (03:17) wrong based on 41 sessions
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose

A. 25 days
B. 30 days
C. 60 days
D. 65 days
E. 36 days
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Jul 2015, 03:41, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Manager
Manager
avatar
Joined: 28 Feb 2007
Posts: 197
Location: California
Followers: 2

Kudos [?]: 6 [0], given: 0

Re: Working together, Jose and Jane can complete an assigned task in 20 [#permalink] New post 09 Apr 2007, 19:46
ggarr wrote:
Working together, Jose and Jane can complete an assigned task in 20 days. However, if Jose worked alone and completes half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will Jose take to complete the task if if he worked alone? Assume that Jane is more efficient than Jose?

Please show ALL work


No answer choices?

Let Jose finish work in x days and Jane in y days. So to finish half task jose will take x/2 days and Jane will take y/2 days.

By given info we have x/2 + y/2 = 45 or (x + y) = 90 ---(1)---

Also when both work together we have 1/x + 1/y = 1/20
or (x+y)/xy = 1/20
0r xy = 20 * (x + y) = 1800

Since jane is efficient this means x > y

we know (x - y)^2 = (x + y)^2 - 4xy
or (x - y)^2 = 8100 - 7200 = 900
or x - y = 30
Since x + y = 45 on solving we get x = 75/2 = 37.5 and y is 7.5
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5067
Location: Singapore
Followers: 24

Kudos [?]: 212 [0], given: 0

Re: Working together, Jose and Jane can complete an assigned task in 20 [#permalink] New post 09 Apr 2007, 20:50
Assume:

Jose does 1 job in x days, so Jose does 1/x job in a day
Jane does 1 job in y days, so Jane does 1/y job in a day

Together, they does (x+y)/xy job in a day. This is equals to 1/20. So

(x+y)/xy = 1/20
20(x+y) = xy

Next, we're told 1 job takes 45 days to complete if Jose and Jane each does half the work. So since Jose does 1 job in x days, he wil need x/2 days to do half the job. Jane similarly will need y/2 days to do the other half.

x/2 + y/2 = 45
x+y = 90

So
xy = 1800

The answer choices are:
25 days
30 days
60 days
65 days
36 days

From the answer choices, 25,30 and 36 days are out since they result in Jane being less efficient. 65 days gives a fractional days (technically allowed, but I think we're thinking of whole numbers). So I'll go for 60 days for Jose and 30 days for Jane.
Intern
Intern
avatar
Joined: 11 Feb 2007
Posts: 30
Followers: 0

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

Re: Working together, Jose and Jane can complete an assigned task in 20 [#permalink] New post 11 Apr 2007, 12:37
jose = x days
jane = y days

Jose rate = Rx = 1/x
Jane rate = Ry = 1/y

Rx+y = 1/20

Let Tx be the time for Jose to finish the work by himself. When half the work is done,
Rx = (1/2)/Tx
Ry = (1/2)/(45-Tx)

Rx+y = Rx + Ry
1/20 = 1/2*Tx + 1/2*(45-Tx)

Solve for Tx,
Tx = 30 or 15 days

If Tx = 15 days, then Ty = 30 days. Not possible since Jane is more efficient than Jose.

Tx = 30 days.

That is for half the work. For the entire amount, Tx = 60days.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5067
Location: Singapore
Followers: 24

Kudos [?]: 212 [0], given: 0

 [#permalink] New post 19 Aug 2007, 21:32
Jose -> 1 job in x days -> 1/x job in 1 day
Jane -> 1 job in y days -> 1/y job in 1 day

Together, 1/x + 1/y = 1/20
x+y/xy = 1/20
20x+20y = xy

Jose takes x/2 days to finish 1/2 a job. Jane takes y/2 days to finish 1/2 a job. Together, x/2 + y/2 = 45 --> x+y = 90

So

20(x+y) = xy
20(90) = x(90-x)
1800 = 90x - x^2
x^2 - 90x + 1800 = 0
x = 60 days or 30 days. But we are told Jane is more efficient, so x = 60 days.
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 432

Kudos [?]: 2341 [0], given: 359

GMAT ToolKit User Premium Member
 [#permalink] New post 17 Nov 2007, 13:10
Expert's post
1
This post was
BOOKMARKED
C

1. 1/2Jose+1/2Jane=45 => Jose+Jane=90 => Jose>45 (C or D)

for C:

Jose=60 => Jane=30 => 20*(1/60+1/30)=1 therefore C correct.
VP
VP
User avatar
Joined: 09 Jul 2007
Posts: 1105
Location: London
Followers: 6

Kudos [?]: 78 [0], given: 0

 [#permalink] New post 17 Nov 2007, 13:29
walker wrote:
C

1. 1/2Jose+1/2Jane=45 => Jose+Jane=90 => Jose>45 (C or D)

for C:

Jose=60 => Jane=30 => 20*(1/60+1/30)=1 therefore C correct.


this is based on assumptions,

any other inputs
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 432

Kudos [?]: 2341 [0], given: 359

GMAT ToolKit User Premium Member
 [#permalink] New post 17 Nov 2007, 13:49
Expert's post
OK

Jone- x (days), Jane -y (days)

1. xy/(x+y)=20
2. 1/2*(x+y)=45 => x+y=90

for first: xy=20(x+y)= 1800

xy=1800 and x+y=90 => x,y e {30,60} => x=60, y=30 (x>y)

C.

first version seems is faster :)
VP
VP
User avatar
Joined: 09 Jul 2007
Posts: 1105
Location: London
Followers: 6

Kudos [?]: 78 [0], given: 0

 [#permalink] New post 17 Nov 2007, 15:02
walker wrote:
OK

Jone- x (days), Jane -y (days)

1. xy/(x+y)=20
2. 1/2*(x+y)=45 => x+y=90

for first: xy=20(x+y)= 1800

xy=1800 and x+y=90 => x,y e {30,60} => x=60, y=30 (x>y)

C.

first version seems is faster :)


i guess this is the only sound way to come to the conclusion on this problem. as it says one of the guys is more efficient than the other. so 30 and 60 is logical conclusion.

thanks Walker!
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 432

Kudos [?]: 2341 [0], given: 359

GMAT ToolKit User Premium Member
 [#permalink] New post 17 Nov 2007, 15:07
Expert's post
pmenon wrote:
isnt it 1/x + 1/y = 1/20 ?

sp x+y/xy = 1/20 ?


1/x+1/y=1/20 <==> xy/(x+y)=20. they are equivalent.
VP
VP
User avatar
Joined: 09 Jul 2007
Posts: 1105
Location: London
Followers: 6

Kudos [?]: 78 [0], given: 0

 [#permalink] New post 17 Nov 2007, 15:10
yeh, it might nt be from gmatleague but it is included as gmatquant practice PS
2 KUDOS received
Manager
Manager
avatar
Joined: 11 Sep 2009
Posts: 129
Followers: 5

Kudos [?]: 241 [2] , given: 6

Re: Work/Rate [#permalink] New post 16 Nov 2011, 01:36
2
This post received
KUDOS
1
This post was
BOOKMARKED
Let A represent the number of days it would take Jose to complete the task if he worked alone (i.e. 1/A is Jose's work rate).
Let B represent the number of days it would take Jane to complete the task if he worked alone (i.e. 1/B is Jane's work rate).

Working together, Jose and Jane can complete an assigned task in 20 days.
20 (1/A + 1/B) = 1 (1)

However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 45 days.

A/2 + B/2 = 45
A + B = 90
B = 90 - A (2)

Sub in (2) into (1):

\(20 (\frac{1}{A} + \frac{1}{{90-A}}) = 1\)

\(\frac{{(90-A)+A}}{{A(90-A)}} = \frac{1}{20}\)

\(\frac{{90}}{{90A-A^2}} = \frac{1}{20}\)

\(90A - A^2 = 1800\)

\(A^2 - 90A + 1800 = 0\)

\((A - 60)(A - 30) = 0\)

So Jose's completion time on his own can be either 30 or 60 days. However, since the problem states that he is more inefficient than Jane, we can eliminate 30. Therefore, the answer is C: 60.
2 KUDOS received
Current Student
User avatar
Status: Enjoying the MBA journey :)
Joined: 09 Sep 2011
Posts: 137
Location: United States (DC)
Concentration: General Management, Entrepreneurship
GMAT 1: 710 Q49 V38
WE: Corporate Finance (Other)
Followers: 17

Kudos [?]: 96 [2] , given: 16

Re: Work/Rate [#permalink] New post 16 Nov 2011, 01:41
2
This post received
KUDOS
Hi

As you've got numbers in the answer choices, I'd prefer using the answer choices and working backwards to arrive at the required answer. It's always good to start with the middle/third option.
Also, if you can see numbers that might be related in some way (multiples, divisors, etc), try to use them.

In the question stem, we've got the numbers 20 and 45 - both are multiples of 5. So, I'd personally use a multiple of 5 present in the answer choices to begin with. Here, 4 of the 5 choices are multiples of 5, making it a bit difficult to choose a number - so I'd go with option 3.

Let the days taken by Jose be 'A' days and that taken by Jane be 'B' days. We're told that Jane is more efficient than Jose which means that Jane will take fewer number of days to complete the work as compared to Jose. Therefore, A > B

Now, using option C i.e. 60 days to be the time taken by Jose to complete the work,

Working together, A and B take 20 days to complete the work.
Therefore, 1/A + 1/B = 1/20
Substituting A = 60 and solving for B, we get B = 30 days

We know that Jose works and completes half of the work. Since Jose takes 60 days to complete the work, he would take 30 days to complete half the work.
Similarly, since Jane takes 30 days to complete the work, she would take 15 days to complete half the work.
So, in total, Jose and Jane take 45 days to complete the work - which is what is given in the question stem.

Hence Option C is the correct answer.

Hope this helps :)

Cheers!
_________________

MBA Candidate 2015 | Georgetown University
McDonough School of Business

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6079
Followers: 340

Kudos [?]: 68 [0], given: 0

Premium Member
Re: Work/Rate [#permalink] New post 07 Jul 2015, 03:22
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

Re: Work/Rate   [#permalink] 07 Jul 2015, 03:22
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic Angela, Bernie, and Colleen can complete a job, all working together, Bunuel 7 13 Jul 2015, 23:56
6 machines working at a constant rate can complete one task saadiagha 2 05 Aug 2014, 09:10
16 Experts publish their posts in the topic Working together, John and Jack can type 20 pages in one hou Barkatis 13 09 Oct 2010, 00:26
13 John can complete a given task in 20 days. Jane will take arjtryarjtry 9 20 Jul 2008, 04:23
9 Experts publish their posts in the topic Matt and Peter can do together a piece of work in 20 days prasannar 14 11 Mar 2008, 02:56
Display posts from previous: Sort by

Working together, Jose and Jane can complete an assigned task in 20

  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®.