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#### Lengthy word translation in data sufficiency

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 Post subject: Lengthy word translation in data sufficiency  Posted: Thu May 24, 2012 8:14 pm
 Students

Posts: 4
 Here is the problem from Question pack oneLast month Grace worked and was paid for, a total of x hours. Some of the hours were on day shift & some on night shift.Her hourly pay is 20% higher fro the night shift then the day shift. How many hours did Grace work on the day shift last month1) X =552) Grace's pay for the hours she worked on dayshift last month was exactly 50% of her total gross pay for last monthUsing three variables i.e one for day shift hours the other i.e X for total hours & the hourly wage rate I am able to solve this problem but it takes over 4 minutes. Is there any shorter way of solving this

 Post subject: Re: Lengthy word translation in data sufficiency  Posted: Mon May 28, 2012 12:39 am
 ManhattanGMAT Staff

Posts: 4404
Location: Southwest Airlines, seat 21C
 of course - don't solve it! :) once you realize you have enough information to solve for what you need you can stop solving at that point. that's the beauty of data sufficiency.. _________________Tim SandersManhattan GMAT Instructor

 Post subject: Re: Lengthy word translation in data sufficiency  Posted: Sun Sep 30, 2012 1:08 pm
 Course Students

Posts: 90
 hi Tim - can you please explain how you would know you have enough info to solve this problem? there's a lot going on in it and i dont feel comfotrable to just be able to look at this one and deduce i do/don't have enough info?

 Post subject: Re: Lengthy word translation in data sufficiency  Posted: Mon Oct 01, 2012 5:00 am
 ManhattanGMAT Staff

Posts: 8087
 v_prbk wrote:Here is the problem from Question pack oneLast month Grace worked and was paid for, a total of x hours. Some of the hours were on day shift & some on night shift.Her hourly pay is 20% higher fro the night shift then the day shift. How many hours did Grace work on the day shift last month1) X =552) Grace's pay for the hours she worked on dayshift last month was exactly 50% of her total gross pay for last monthUsing three variables i.e one for day shift hours the other i.e X for total hours & the hourly wage rate I am able to solve this problem but it takes over 4 minutes. Is there any shorter way of solving thiswell, you should be able to tell pretty quickly that the two individual statements are insufficient.1/ these 55 hours could be divided up in any way at all.2/ this is just a ratio, with no indication of any absolute number of hours. so it's going to determine, at most, some ratio of day- to night-shift hours, but it won't let you figure an actual number (as required in the problem).so, let's combine the statements.no need for three variables. we have a total of 55 hours, so you can split that into x hours on the day shift and (55 - x) hours on the night shift.for the wage, let's say W dollars/hour for the day shift. then the night shift wage is 20% more than this, or 1.2W per hour. (you can actually pick a number for the wage here, but picking constant values is a risky proposition in DS problems.)so you have x hours at W dollars/hour, and (55 - x) hours at 1.2W dollars/hour.that's a total of xW + (55 - x)(1.2W) = xW + 66W - 1.2xW= 66W - 0.2xW dollars.the pay for day shift is xW dollars.therefore:xW = 50% of (66W - 0.2xW)xW = 33W - 0.1xWx = 33 - 0.1xthis is an equation you can solve, so, you're done. (c). _________________Being well-dressed gives a feeling of inward tranquillity [that] religion is powerless to bestow.C.F. Forbes

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