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

It is currently 03 May 2016, 17:38
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

Two musicians, Maria and Perry, work at independent constant

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

Hide Tags

5 KUDOS received
Senior Manager
Senior Manager
User avatar
Status: Final Lap
Joined: 25 Oct 2012
Posts: 287
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)
Followers: 3

Kudos [?]: 220 [5] , given: 85

Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 08 Jun 2013, 08:13
5
This post received
KUDOS
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

68% (02:00) correct 32% (01:58) wrong based on 310 sessions

HideShow timer Statictics

Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at twice Maria’s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?

A. 1 hr 20 min
B. 1 hr 45 min
C. 2 hr
D. 2 hr 20 min
E. 3 hr
[Reveal] Spoiler: OA

_________________

KUDOS is the good manner to help the entire community.

"If you don't change your life, your life will change you"

7 KUDOS received
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1123
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 168

Kudos [?]: 1685 [7] , given: 219

GMAT ToolKit User
Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 08 Jun 2013, 08:22
7
This post received
KUDOS
5
This post was
BOOKMARKED
\(rate*time=work\)

Working together :
\((P+M)*\frac{3}{4}=1\)
If P=2M:
\((2M+M)*\frac{1}{3}=1\) from this we get \(M=1\).

We plug M=1 in the above equation:

\(\frac{3}{4}P+\frac{3}{4}=1\) or \(\frac{3}{4}P=\frac{1}{4}\) \(P=\frac{1}{3}\).

So it would take 3 hours to complete the job, \(\frac{1}{3}*3h=1job\)
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32602
Followers: 5647

Kudos [?]: 68556 [2] , given: 9815

Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 08 Jun 2013, 08:30
2
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
Rock750 wrote:
Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at twice Maria’s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?

A. 1 hr 20 min
B. 1 hr 45 min
C. 2 hr
D. 2 hr 20 min
E. 3 hr


Let the whole work be 180 units.

In this case combined rate of Maria and Perry is 180/45=4 units per minute --> M+P=4, where M and P are individual rates of Maria and Perry.

If Perry were to work at twice Maria’s rate, they would take only 20 minutes --> in this case combined rate of Maria and Perry is 180/20=9 units per minute --> M+2M=9 --> M=3 units per minute.

M+P=4 --> 3+P=4 --> P=1 unit per minute.

Time to do 180 units = (job)/(rate) = 180/1 =180 minutes = 3 hours.

Answer: E.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

2 KUDOS received
Manager
Manager
User avatar
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 138
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23
GMAT 2: 560 Q42 V26
GPA: 3.5
WE: Consulting (Computer Hardware)
Followers: 1

Kudos [?]: 34 [2] , given: 39

Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 08 Sep 2013, 12:09
2
This post received
KUDOS
Rock750 wrote:
Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at twice Maria’s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?

A. 1 hr 20 min
B. 1 hr 45 min
C. 2 hr
D. 2 hr 20 min
E. 3 hr



Sol:

Lets Perry Rate be P and Rate of Maria be M
(rate)*(time)= Work or rate = work/time

first equation=> P+M = 1/45
converting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3

second equation => M+2M =>1/20
converting it to hrs 3M=1/(20/60) =>1/(1/3) =>3

therefore M= 1 and P=1/3

Rate of Perry = 1/3
time= work/rate (work = 1 job)
Time= 3 hrs
Intern
Intern
avatar
Joined: 07 Sep 2013
Posts: 25
Concentration: Entrepreneurship
GMAT 1: Q V
GPA: 3.52
Followers: 0

Kudos [?]: 9 [0], given: 0

Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 08 Sep 2013, 16:55
Hi all

Can't this question be solved with the Work Formula?

t1000
Intern
Intern
avatar
Joined: 14 Oct 2013
Posts: 16
Location: India
Concentration: General Management
Followers: 1

Kudos [?]: 7 [0], given: 31

Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 21 Jan 2014, 00:48
Hi Bunuel,

I cant seem to understand what I am doing wrong by solving it like this.. please guide me ..

given: let call maria =m perry = p
working together we have \(\frac{1}{m} + \frac{1}{p} = \frac{1}{45}\) ----------eq 1.

now if perry works twice at maria's rate we get .... \(\frac{1}{m} + \frac{1}{2m} = \frac{1}{20}\)
solving this we get... M = 30

now substituting it in the first eq 1.
\(\frac{1}{30} + \frac{1}{p} = \frac{1}{45}\)

obviously since I am solving inccorectly i get a negative value .. I understand the simple methods give in the above discussions .. i get it .. but what em i doing wrong.. i need to rectify my thought process otherwise I will keep approaching such problems in a similar fashion even in the future..

so comment will be greatly appreciated Bunuel .. Thanks a ton! :idea:
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32602
Followers: 5647

Kudos [?]: 68556 [2] , given: 9815

Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 21 Jan 2014, 03:02
2
This post received
KUDOS
Expert's post
rawjetraw wrote:
Hi Bunuel,

I cant seem to understand what I am doing wrong by solving it like this.. please guide me ..

given: let call maria =m perry = p
working together we have \(\frac{1}{m} + \frac{1}{p} = \frac{1}{45}\) ----------eq 1.

now if perry works twice at maria's rate we get .... \(\frac{1}{m} + \frac{1}{2m} = \frac{1}{20}\)
solving this we get... M = 30

now substituting it in the first eq 1.
\(\frac{1}{30} + \frac{1}{p} = \frac{1}{45}\)

obviously since I am solving inccorectly i get a negative value .. I understand the simple methods give in the above discussions .. i get it .. but what em i doing wrong.. i need to rectify my thought process otherwise I will keep approaching such problems in a similar fashion even in the future..

so comment will be greatly appreciated Bunuel .. Thanks a ton! :idea:


In your solution m and p are individual times, while 1/m and 1/p are respective rates. If Perry were to work at twice Maria’s rate, then his rate would be 2*(1/m), not 1/(2m). Therefore the correct equations are 1/m+1/p=1/45 and 1/m+2/m=1/20
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 14 Oct 2013
Posts: 16
Location: India
Concentration: General Management
Followers: 1

Kudos [?]: 7 [0], given: 31

Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 21 Jan 2014, 06:23
how dumb of me... :evil: :x ... Thank you so much Bunuel! .. I get it now... :D
Intern
Intern
avatar
Joined: 13 Aug 2013
Posts: 3
Followers: 0

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

Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 04 Feb 2014, 04:49
Bunuel wrote:
rawjetraw wrote:
Hi Bunuel,

I cant seem to understand what I am doing wrong by solving it like this.. please guide me ..

given: let call maria =m perry = p
working together we have \(\frac{1}{m} + \frac{1}{p} = \frac{1}{45}\) ----------eq 1.

now if perry works twice at maria's rate we get .... \(\frac{1}{m} + \frac{1}{2m} = \frac{1}{20}\)
solving this we get... M = 30

now substituting it in the first eq 1.
\(\frac{1}{30} + \frac{1}{p} = \frac{1}{45}\)

obviously since I am solving inccorectly i get a negative value .. I understand the simple methods give in the above discussions .. i get it .. but what em i doing wrong.. i need to rectify my thought process otherwise I will keep approaching such problems in a similar fashion even in the future..

so comment will be greatly appreciated Bunuel .. Thanks a ton! :idea:


In your solution m and p are individual times, while 1/m and 1/p are respective rates. If Perry were to work at twice Maria’s rate, then his rate would be 2*(1/m), not 1/(2m). Therefore the correct equations are 1/m+1/p=1/45 and 1/m+2/m=1/20


buneul

by the equations 1/m+2/m =1/ 20 => m = 60.

when i substituted in 1/m+1/p = 1/45. i got p = 18.

How to proceed after that??
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32602
Followers: 5647

Kudos [?]: 68556 [0], given: 9815

Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 04 Feb 2014, 07:15
Expert's post
nishanthadithya wrote:
Bunuel wrote:
rawjetraw wrote:
Hi Bunuel,

I cant seem to understand what I am doing wrong by solving it like this.. please guide me ..

given: let call maria =m perry = p
working together we have \(\frac{1}{m} + \frac{1}{p} = \frac{1}{45}\) ----------eq 1.

now if perry works twice at maria's rate we get .... \(\frac{1}{m} + \frac{1}{2m} = \frac{1}{20}\)
solving this we get... M = 30

now substituting it in the first eq 1.
\(\frac{1}{30} + \frac{1}{p} = \frac{1}{45}\)

obviously since I am solving inccorectly i get a negative value .. I understand the simple methods give in the above discussions .. i get it .. but what em i doing wrong.. i need to rectify my thought process otherwise I will keep approaching such problems in a similar fashion even in the future..

so comment will be greatly appreciated Bunuel .. Thanks a ton! :idea:


In your solution m and p are individual times, while 1/m and 1/p are respective rates. If Perry were to work at twice Maria’s rate, then his rate would be 2*(1/m), not 1/(2m). Therefore the correct equations are 1/m+1/p=1/45 and 1/m+2/m=1/20


buneul

by the equations 1/m+2/m =1/ 20 => m = 60.

when i substituted in 1/m+1/p = 1/45. i got p = 18.

How to proceed after that??


From 1/60 + 1/p = 1/45 it follows that p = 180 minutes, not 18. p there denotes is time Perry needs to compete the job alone, and this is what we need to find, hence p = 180 minutes = 3 hours is the answer.

Hope it's clear.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 43

Kudos [?]: 456 [0], given: 355

GMAT ToolKit User
Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 14 Apr 2014, 15:05
1
This post was
BOOKMARKED
So we have the following

1/M + 1/P = 1/45

We also know that 1/M + 2/M = 1/20

Therefore we know that M=60 and by substituting in the first equation we have that 1/P = 1/180

Therefore P = 180 = 3 hours

Hope this clarifies
Cheers!
J :)
Intern
Intern
avatar
Joined: 05 Apr 2014
Posts: 15
GMAT 1: 610 Q49 V25
Followers: 0

Kudos [?]: 2 [0], given: 46

GMAT ToolKit User Reviews Badge
Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 04 Aug 2014, 10:27
Hello Bunuel,
If rates are 1/m & 1/p then pm/(p+m)=45. Now if 1/p=2/m, I substituted m=2p in pm/(p+m)=20, which resulted in p=30... where I am going wrong... Please help.
_________________

If anything above makes any sense to you, please let me and others know by hitting the "+1 KUDOS" button

Manager
Manager
avatar
Joined: 11 Jun 2014
Posts: 57
Concentration: Technology, Marketing
GMAT 1: 770 Q50 V45
WE: Information Technology (Consulting)
Followers: 4

Kudos [?]: 28 [0], given: 3

Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 04 Aug 2014, 21:08
1/P + 1/M = 1/45

2/M + 1/M = 1/20

3/M = 1/20 => M=60

1/P + 1/60 = 1/45

P=180 mins, =3 hours
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9273
Followers: 455

Kudos [?]: 115 [0], given: 0

Premium Member
Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 22 Aug 2015, 09:38
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

Manager
Manager
avatar
Joined: 20 Sep 2008
Posts: 85
Followers: 2

Kudos [?]: 53 [0], given: 165

Reviews Badge
Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 14 Nov 2015, 15:10
shuvabrata88 wrote:
Hello Bunuel,
If rates are 1/m & 1/p then pm/(p+m)=45. Now if 1/p=2/m, I substituted m=2p in pm/(p+m)=20, which resulted in p=30... where I am going wrong... Please help.


Made same mistake.

if rate p = 2m then time p = m/2. So:

[m/2 * m] / [ m/2 + m] = 20. Calculate and you will get m = 60.
Manager
Manager
avatar
Joined: 07 Dec 2014
Posts: 214
Followers: 0

Kudos [?]: 22 [0], given: 0

Re: Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 14 Nov 2015, 21:36
maria's rate=m
if 3m=1/20, then m=1/60
1/45-1/60=1/180=perry's rate
perry needs 180 minutes=3 hours to complete job alone
SVP
SVP
avatar
Joined: 17 Jul 2014
Posts: 1562
Location: United States
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
GPA: 3.56
WE: General Management (Transportation)
Followers: 9

Kudos [?]: 148 [0], given: 100

GMAT ToolKit User Premium Member Reviews Badge
Two musicians, Maria and Perry, work at independent constant [#permalink]

Show Tags

New post 28 Feb 2016, 11:12
Rock750 wrote:
Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at twice Maria’s rate, they would take only 20 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?

A. 1 hr 20 min
B. 1 hr 45 min
C. 2 hr
D. 2 hr 20 min
E. 3 hr


first of all. the question is ambiguous from the start. is 45 min the rate they work both together? or each independently?

I suppose together...
so
\(\frac{1}{M}+\frac{1}{P}=\frac{1}{45}\)
then
we are told:
\(\frac{2}{M}+\frac{1}{M}=\frac{1}{20}\)

we can find the rate for M:
\(\frac{1}{60}\) -> so M needs 60 min to finish the job.

now, we are given \(\frac{1}{M}\), we can find \(\frac{1}{P}\)

\(\frac{1}{60}+\frac{1}{P}=\frac{1}{45}\)
\(\frac{1}{P}=\frac{1}{180}\)
So M needs 180 mins, or 3hours to complete the job alone.
Two musicians, Maria and Perry, work at independent constant   [#permalink] 28 Feb 2016, 11:12
    Similar topics Author Replies Last post
Similar
Topics:
13 Experts publish their posts in the topic Working simultaneously and independently at an identical constant rate Bunuel 11 18 Oct 2015, 13:12
9 Experts publish their posts in the topic At 8am on Thursday, two workers, A and B, each start working independe Bunuel 5 04 May 2015, 05:42
72 Experts publish their posts in the topic Six machines, each working at the same constant rate srkaleem 15 05 Feb 2012, 23:28
13 Experts publish their posts in the topic Working simultaneously and independently at an identical ajit257 9 10 Dec 2010, 06:21
15 Experts publish their posts in the topic Six machines, each working at the same constant rate zz0vlb 18 26 Apr 2010, 21:53
Display posts from previous: Sort by

Two musicians, Maria and Perry, work at independent constant

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


cron

GMAT Club MBA Forum Home| About| 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®.