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# A professional janitor can clean a certain high school in 8 hours, wor

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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]

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30 Jan 2016, 10:25
2
14
00:00

Difficulty:

55% (hard)

Question Stats:

71% (02:33) correct 29% (02:58) wrong based on 258 sessions

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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 ##### Most Helpful Expert Reply GMAT Club Legend Joined: 11 Sep 2015 Posts: 4876 Location: Canada GMAT 1: 770 Q49 V46 A professional janitor can clean a certain high school in 8 hours, wor [#permalink] ### Show Tags Updated on: 01 Apr 2020, 04:37 4 3 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 job
Example: 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 job
Example: 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 hours
So (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 hours
So (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) = $160 Working 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/917 Afterwards, here's a practice question to reinforce your learning: http://www.gmatprepnow.com/module/gmat- ... /video/918 Cheers, Brent _________________ Test confidently with gmatprepnow.com Originally posted by BrentGMATPrepNow on 30 Jan 2016, 11:28. Last edited by BrentGMATPrepNow on 01 Apr 2020, 04:37, edited 1 time in total. ##### General Discussion 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 GMATPrepNow Hi 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 GMAT 1: 770 Q49 V46 Re: A professional janitor can clean a certain high school in 8 hours, wor [#permalink] ### Show Tags 20 Sep 2016, 05:10 Top Contributor mmss wrote: GMATPrepNow Hi 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 1-hour 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: 02-18-2019 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

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 Schools: IESE '21 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
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]

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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 channel-QUANT 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 Explanation

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. _________________ 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 topic You 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 1 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.

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