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# A part-time employee whose hourly wage was increased by 25

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Director
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A part-time employee whose hourly wage was increased by 25 [#permalink]  22 Oct 2006, 07:25
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Difficulty:

5% (low)

Question Stats:

81% (02:37) correct 19% (00:57) wrong based on 92 sessions
A part-time employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?

(A) 12.5%
(B) 20%
(C) 25%
(D) 50%
(E) 75%
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Feb 2014, 08:34, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
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Re: Number of hours worked [#permalink]  04 Aug 2011, 23:23
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Although most of the others have provided their explanations using formulae, if you are not comfortable, you can use the below to solve the problem.

Its the same as the formulaes depicted below but i guess easier to undestand.

let the employee work for $100 an hour and a total of 100 hours per month. His current salary will therefore be 100*100 his salary increases by 25 % --> new salary = 125 since total salary is same therefore 100*100 = 125 * x where x is the new hours he needs to work to maintain his monthly inclome calculating u find x = 80 --> the hours has decreased from 100 to 80 or a 20 % decrease SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1859 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 26 Kudos [?]: 1067 [2] , given: 193 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 30 Sep 2014, 20:57 2 This post received KUDOS Wage ........... No. of Hrs .................. Total 10 ...................... 10 ............................ 100 (Initially) 12.5 .................... 10 .............................. 125 (After increment of 10% wage) 12.5 ...................... x .......................... 100 (Lets say no. of hrs worked = x for 100) $$x = \frac{100}{12.5} = 8$$ Reduction percentage $$= \frac{10-8}{10} * 100 = 20%$$ Answer = B _________________ Kindly press "+1 Kudos" to appreciate Manager Joined: 28 May 2011 Posts: 196 Location: United States Concentration: General Management, International Business GMAT 1: 720 Q49 V38 GPA: 3.6 WE: Project Management (Computer Software) Followers: 2 Kudos [?]: 50 [1] , given: 7 Re: Number of hours worked [#permalink] 23 Jul 2011, 21:37 1 This post received KUDOS enigma123 wrote: A part time employee whose hourly wage was increased by 25% decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced? Ans: 20% Can anyone please tell me the approach to solve this question? Number of Hours he works today = N Hourly Wage today = P Number of Hours he works today = M Hourly wage after increase = P + 25% = P(1+25/100) = P * (5/4) To keep the total wage constant : N*P = M * P * (5/4) M / N = 4/5 (N-M) / N = 1/5 (fraction by which Number of hours can be decreased while keeping total wage same) To get the percentage , multiply both side by 100 percent of the number of hours worked be reduced ((N-M) *100/ N) = 100/5 = 20% _________________ ------------------------------------------------------------------------------------------------------------------------------- http://gmatclub.com/forum/a-guide-to-the-official-guide-13-for-gmat-review-134210.html ------------------------------------------------------------------------------------------------------------------------------- Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5863 Location: Pune, India Followers: 1481 Kudos [?]: 7967 [1] , given: 190 Re: Number of hours worked [#permalink] 04 Aug 2011, 21:38 1 This post received KUDOS Expert's post enigma123 wrote: A part time employee whose hourly wage was increased by 25% decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced? Ans: 20% Can anyone please tell me the approach to solve this question? Consider this: Total Income = Hourly Wage * No of hours If we want to keep the total income same, Hourly Wage * No of hours = New Hourly Wage * New No of hours Hourly Wage * No of hours = 5/4 * Hourly Wage * New No of hours So New No of hours/No of hours = 4/5 A decrease of 1/5 i.e. 20% Or think of it this way: Since total income has to remain the same, Hourly wage *No of hours has to remain the same. If Hourly wage gets multiplied by 5/4 (an increase of 25%), no of hours should be multiplied by 4/5 to keep their product same i.e. no of hours should be reduced by 1/5 i.e. 20%. For more on fraction-percentage conversions, check: http://www.veritasprep.com/blog/2011/02 ... rcentages/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Director
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Re: Number of hours worked [#permalink]  05 Aug 2011, 07:33
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Hourly Wage

Initial New

$P$125P/100

X hours <X (lets say Y)

given

PX = (125P/100)Y

=> X = (125/100)Y

% decrease = ((x - y)/x )*100

= 20%
Intern
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Re: Number of hours worked [#permalink]  05 Aug 2011, 11:45
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w1 * h1 = w2 * h2

w1 * h1 = 1.25 w1 * h2 => h2 = 4 h1/ 5 = 0.8 h1 => 20% decrease
Manager
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Re: Number of hours worked [#permalink]  05 Aug 2011, 19:47
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hahaha...If you read this question and are a consultant who is paid hourly wages....you will think :

Hey, my current hourly rate is 100 $. Now it has increased by 25%.I can reduce the time I work, because I am now earning more and want to spend time on some of my hobbies/free time :D So how much % time can I work less !!! 100$ per hr(1 hr) = 125$per hr(new time in hrs) ==> new time = 100/125 hrs = 100/25.5 = 20/25 = 80/100 Old time = 1 hr Time decrease = 1-80/100 = 20/100 or 20% I am not putting any approach, just a practical way I would have seen this problem... _________________ Labor cost for typing this post >= Labor cost for pushing the Kudos Button kudos-what-are-they-and-why-we-have-them-94812.html Manager Joined: 05 Oct 2011 Posts: 167 GMAT 1: 720 Q V Followers: 9 Kudos [?]: 43 [1] , given: 60 Re: Number of hours worked [#permalink] 07 Nov 2011, 11:27 1 This post received KUDOS By far the quickest way to solve this problem is by using number plugging as the question is asking a percent in the end. assume: Employee initial salary =$100
Old hours: 20
New salary = $125 New hours: x 20 * 100 = x * 125 x = 16 Percent of reduction = 4/20 * 100 = 20% Answer: B Senior Manager Joined: 01 Oct 2006 Posts: 498 Followers: 1 Kudos [?]: 21 [0], given: 0 [#permalink] 22 Oct 2006, 08:09 Let original hourly wage be x and let the no of hours worked be y Total wage will be =x*y After the increment the wage will be=1.25 x Now we need to find number of hours worked so that x*y=1.25x*z i.e z=4/5 y %decrease = (y-4/5y)/y *100=100/5=20%. Thus my answer is B. Correct me if I am wrong. Intern Joined: 04 May 2011 Posts: 9 Followers: 0 Kudos [?]: 1 [0], given: 7 Re: Number of hours worked [#permalink] 23 Jul 2011, 21:58 A = hours of work BEFORE wage increase B= hours of work AFTER wage increase when answering about increase or decrease, we need to make the denomenator being the old one. Here we know that to get the same total wage, A must be 1.25 times of B; (x is a multiple of #hours, it will get cancel out) Decrease of hrs = (Bx-Ax)/Ax = (1-1.25)/1.25 = 0.2 = 20% Manager Joined: 25 Sep 2010 Posts: 85 Schools: HBS, LBS, Wharton, Kelloggs, Booth Followers: 0 Kudos [?]: 3 [0], given: 15 Re: Number of hours worked [#permalink] 04 Aug 2011, 04:28 Let initial salary be X. Then new salary is 1.25X. Let the initial no. of hours = h1 and final no. of hours = h2; given: X(h1) = 1.25X(h2) => h1 = 1.25(h2) (cancelling X on both sides) We need to find the percent change in no. of hours: Formula: Percent change = (New - Original)/Original * 100 => (h2 - h1)/h1 * 100 Now, We know that h1 = 1.25(h2) => h2/h1 = 1/1.25; Using dividendo; we get (h2 - h1)/h1 = (1-1.25)/1.25 ------(1) We get our answer by multiplying (1) with 100 Manager Joined: 21 Aug 2013 Posts: 114 Schools: ISB '15 Followers: 2 Kudos [?]: 16 [0], given: 58 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 11 Feb 2014, 08:24 Hi, Please add OA. Thanks _________________ Veritas Prep - 650 MGMAT 1 590 MGMAT 2 640 (V48/Q31) Please help the community by giving Kudos. Math Expert Joined: 02 Sep 2009 Posts: 29170 Followers: 4734 Kudos [?]: 49950 [0], given: 7517 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 11 Feb 2014, 08:36 Expert's post seabhi wrote: Hi, Please add OA. Thanks ______________ Done. Added the OA. _________________ Senior Manager Joined: 23 Jan 2013 Posts: 375 Schools: Cambridge'16 Followers: 2 Kudos [?]: 33 [0], given: 33 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 23 Sep 2014, 23:40 Picking works better 100- old wage 50 - old hours 100+25=125 - new wage 50*100=125x x=40, so 50-40*100/50=20% B Intern Joined: 11 Oct 2013 Posts: 35 Concentration: Marketing, General Management GMAT Date: 10-29-2014 Followers: 0 Kudos [?]: 10 [0], given: 59 Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 26 Aug 2015, 20:32 Hours * Wage per hour = Wage New Wage - Hours * 1.25 * Wage per hour = 1.25 * Wage So, New Wage = 1.25 * Old Wage Now, forget Hours or Wage per hour. We need to decrease New Wage to make it equal to Old Wage. So % decrease is (New Wage - Old Wage)/New Wage = (1.25 - 1)/1.25 = 0.25/1.25 = 1/5 = 20% _________________ Its not over.. Re: A part-time employee whose hourly wage was increased by 25 [#permalink] 26 Aug 2015, 20:32 Similar topics Replies Last post Similar Topics: 5 A part-time employee whose hourly wage was decreased by 20 percent dec 6 10 Feb 2015, 07:36 1 Ian is paid an hourly wage, totaling$400 for h hours of work in a wee 7 21 Jan 2015, 01:23
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