Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 12 Aug 2015
Posts: 277
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)

A professional janitor can clean a certain high school in 8 hours, wor
[#permalink]
Show Tags
30 Jan 2016, 10:25
Question Stats:
71% (02:33) correct 29% (02:58) wrong based on 258 sessions
HideShow timer Statistics
A professional janitor can clean a certain high school in 8 hours, working at a constant rate. A student sentenced to detention can clean that same high school in 20 hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together? A. $56 B. $6 C. $0 D. $6 E. $8
Official Answer and Stats are available only to registered users. Register/ Login.




GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4876
Location: Canada

A professional janitor can clean a certain high school in 8 hours, wor
[#permalink]
Show Tags
Updated on: 01 Apr 2020, 04:37
shasadou wrote: A professional janitor can clean a certain high school in 8 hours, working at a constant rate. A student sentenced to detention can clean that same high school in 20 hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?
A. $56 B. $6 C. $0 D. $6 E. $8 For work questions, there are two useful rules: Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the jobExample: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire jobExample: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job. Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job. Let’s use these rules to solve the question. . . . A professional janitor can clean a certain high school in 8 hoursSo (applying rule #1), the janitor can clean 1/8 of the school in ONE HOUR A student sentenced to detention can clean that same high school in 20 hoursSo (applying rule #1), the student can clean 1/20 of the school in ONE HOUR So, COMBINED, the student and janitor can clean (1/8 + 1/20) of the school in ONE HOUR 1/8 + 1/20 = 5/40 + 2/40 = 7/40 So, in ONE HOUR they can clean 7/40 of the school. Applying rule #2, it will take them 40/7 hours to clean the ENTIRE school. The janitor earns $21/hour and the student earns $7/hour, so their combined rate is $28/hour. Their combined wages = (pay rate)(time) = ( $28/hour)( 40/7 hours) = $160Working ALONE, the janitor takes 8 hours and earns $21/hour So, working alone, the janitor's earnings = (pay rate)(time) = ($21/hour)(8 hours) = $168 $168  $160 = $8, so the answer is E Here's a free video on solving work problems: http://www.gmatprepnow.com/module/gmat ... /video/917Afterwards, here's a practice question to reinforce your learning: http://www.gmatprepnow.com/module/gmat ... /video/918Cheers, Brent
_________________
Test confidently with gmatprepnow.com




Intern
Joined: 19 Sep 2016
Posts: 1

Re: A professional janitor can clean a certain high school in 8 hours, wor
[#permalink]
Show Tags
19 Sep 2016, 19:07
GMATPrepNowHi Brent. Why shouldn't I consider the whole hour for the wage of the janitor plus the student, since they are paid hourly? Total cost to pay the student and the janitor to do the job together would be 42/7 (in order to be an integer) *($28/hour)=$168 Thanks



GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4876
Location: Canada

Re: A professional janitor can clean a certain high school in 8 hours, wor
[#permalink]
Show Tags
20 Sep 2016, 05:10
mmss wrote: GMATPrepNowHi Brent. Why shouldn't I consider the whole hour for the wage of the janitor plus the student, since they are paid hourly? Total cost to pay the student and the janitor to do the job together would be 42/7 (in order to be an integer) *($28/hour)=$168 Thanks There's nothing in the question to suggest that the workers must be paid in 1hour increments. So, for example, if you work for 0.5 hours, then you receive half of your hourly rate. Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Director
Joined: 25 Dec 2018
Posts: 620
Location: India
Concentration: General Management, Finance
GMAT Date: 02182019
GPA: 3.4
WE: Engineering (Consulting)

Re: A professional janitor can clean a certain high school in 8 hours, wor
[#permalink]
Show Tags
05 Jan 2020, 03:20
shasadou wrote: A professional janitor can clean a certain high school in 8 hours, working at a constant rate. A student sentenced to detention can clean that same high school in 20 hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?
A. $56 B. $6 C. $0 D. $6 E. $8 Correct Answer: (E) Start by determining how long it will take each group to do the task. We’re told the janitor will take a flat 8 hours, so that part’s easy: the cost to pay him alone is 8 * $21 = $168. The student can do the job in 20 hours, so they perform 1/20 of the job per hour.. The janitor can perform 1/8 of the job per hour, and the student and the janitor combined can do 1/8 of the job + 1/20 of the job in one hour, or 7/40 of the job. Take the reciprocal to find the number of hours it takes the student and janitor combine to complete the entire job: 40/7 hours. Together, they are paid $28/hour. Multiply 40/7 by 28 to find a total of $160. The janitor gets paid $8 more to do the job alone.



Intern
Joined: 25 Nov 2015
Posts: 7
Location: Brazil
Concentration: General Management, Operations
WE: General Management (Consumer Products)

Re: A professional janitor can clean a certain high school in 8 hours, wor
[#permalink]
Show Tags
12 Jan 2020, 15:52
shasadou wrote: A professional janitor can clean a certain high school in 8 hours, working at a constant rate. A student sentenced to detention can clean that same high school in 20 hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?
A. $56 B. $6 C. $0 D. $6 E. $8 Given: J = \(\frac{1}{8}\) S =\(\frac{1}{20}\) J + S = \(\frac{7}{40}\) To find: [J PMT]  [J+S PMT] = ? Approach:  J PMT = \(8 * 21\)  J+S PMT = \(\frac{40}{7}*(21+7)\) [J PMT]  [J+S PMT] = \(8*21  \frac{40}{7}*(21+7) = 8 * 21  \frac{40}{7}*28 = 8 * 21  \frac{8*5}{1}*4\) \(8 * 21  8 * 20 = 8 * 1\)



Senior Manager
Joined: 27 Feb 2014
Posts: 276
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE: Engineering (Education)

Re: A professional janitor can clean a certain high school in 8 hours, wor
[#permalink]
Show Tags
12 Jan 2020, 20:43
Using equation RT=W Rate of Janitor = 1/8 Rate of Student = 1/20 Combined rate = 7/40 Time taken by both working together = 40/7 Combined cost = (40/7)*28 = 160 Cost when only Janitor does the work = 8*21 = 168 Extra amount = 8$ E is correct
_________________
Inspired by great content in some best books on GMAT, I have created my own YouTube channelQUANT MADE EASY! I would love some support and feedback. Please hit subscribe and check it out! https://www.youtube.com/channel/UCvdY0kJNbnJzPEOsT5PMFRQ



VP
Joined: 18 Dec 2017
Posts: 1364
Location: United States (KS)
GMAT 1: 600 Q46 V27

Re: A professional janitor can clean a certain high school in 8 hours, wor
[#permalink]
Show Tags
30 Mar 2020, 15:41
shasadou wrote: A professional janitor can clean a certain high school in 8 hours, working at a constant rate. A student sentenced to detention can clean that same high school in 20 hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?
A. $56 B. $6 C. $0 D. $6 E. $8 Official ExplanationStart by determining how long it will take each group to do the task. We’re told the janitor will take a flat 8 hours, so that part’s easy: the cost to pay him alone is 8 * $21 = $168. The student can do the job in 20 hours, so they perform 1/20 of the job per hour.. The janitor can perform 1/8 of the job per hour, and the student and the janitor combined can do 1/8 of the job + 1/20 of the job in one hour, or 7/40 of the job. Take the reciprocal to find the number of hours it takes the student and janitor combine to complete the entire job: 40/7 hours. Together, they are paid $28/hour. Multiply 40/7 by 28 to find a total of $160. The janitor gets paid $8 more to do the job alone.
_________________
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long Why You Don’t Deserve A 700 On Your GMAT
Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topicYou are missing on great learning if you don't know what this is: Project SC Butler



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10569
Location: United States (CA)

Re: A professional janitor can clean a certain high school in 8 hours, wor
[#permalink]
Show Tags
04 Apr 2020, 13:27
shasadou wrote: A professional janitor can clean a certain high school in 8 hours, working at a constant rate. A student sentenced to detention can clean that same high school in 20 hours, also working at a constant rate. If the student is paid $7 total per hour and the janitor is paid $21 per hour, how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together?
A. $56 B. $6 C. $0 D. $6 E. $8 If the janitor cleans the school by himself, it will cost the school 21 x 8 = $168. The janitor’s rate is 1/8, and the student’s rate is 1/20. If we let t = the number of hours it takes if the janitor works together with the student to clean the school, we can create the equation: (1/8 + 1/20) x t = 1 t/8 + t/20 = 1 5t + 2t = 40 7t = 40 t = 40/7 Therefore, if they work together, it will cost the school 21 x 40/7 + 7 x 40/7 = 120 + 40 = $160. We see that it will cost the school 168  160 = $8 more if the janitor works alone. Answer: E
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.




Re: A professional janitor can clean a certain high school in 8 hours, wor
[#permalink]
04 Apr 2020, 13:27




