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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Carmen currently works 30 hours per week at her part-time jo ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Carmen currently works 30 hours per week at her part-time jo ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by$1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?

(1) Her gross weekly pay is currently $225.00. (2) An increase of$1.50 would represent an increase of 20 percent of her current gross hourly wage.

OA D

Source: Official Guide

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BTGmoderatorDC wrote:
Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase? (1) Her gross weekly pay is currently$225.00.
(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage. Rate and time have a RECIPROCAL relationship. If the hourly rate DOUBLES, then the same income will be yielded in 1/2 the total time. Statement 1: Actual hourly rate = 225/30 =$7.50, implying that an additional $1.50 per hour will increase the hourly rate to$9.
(increased hourly rate)/(actual hourly rate) = 9/7.5 = 18/15 = 6/5.
Implication:
The same income will be yielded in 5/6 of the actual time -- a decrease of 1/6:
(1/6)(30) = 5 fewer hours.
SUFFICIENT.

Statement 2:
Since $1.50 increases the hourly rate by 20%, we get: (increased hourly rate)/(actual hourly rate) = 120/100 = 6/5. Implication: The same income will be yielded in 5/6 of the actual time -- a decrease of 1/6: (1/6)(30) = 5 fewer hours. SUFFICIENT. The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Top Reply BTGmoderatorDC wrote: Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by$1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?

(1) Her gross weekly pay is currently $225.00. (2) An increase of$1.50 would represent an increase of 20 percent of her current gross hourly wage.
Given: Carmen currently works 30 hours per week

Target question: If Carmen's gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase? This is a good candidate for rephrasing the target question Let H = Carmen's CURRENT hourly pay rate So, 30H = Carmen's CURRENT weekly salary (since she works 30 hours each week) H + 1.5 = Carmen's HYPOTHETICAL hourly pay rate Let x = the number of FEWER hours Carmen can work. Aside: our goal is to determine the value of x So, (30 - x) = the number of hours Carmen would HYPOTHETICALLY works So, (30 - x)(H + 1.5) = Carmen's HYPOTHETICAL weekly salary We want the two salaries (current and hypothetical) to be equal So, we can write: 30H = (30 - x)(H + 1.5) Expand right side: 30H = 30H + 45 - xH - 1.5x Subtract 30H from both sides: 0 = 45 - xH - 1.5x Add xH and 1.5x to both sides to get: xH + 1.5x = 45 Factor left side: x(H + 1.5) = 45 Divide both sides by (H + 1.5) to get x = 45/(H + 1.5) IMPORTANT: Our goal is to find the value of x (the number of FEWER hours Carmen can work). Now that we know that x = 45/(H + 1.5), we can see that, in order to find the value of x, we need only find the value of H. So, we can REPHRASE our target question to get.... REPHRASED target question: What is the value of H (Carmen's CURRENT hourly wage)? Aside: Hereâ€™s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100 Statement 1: Her gross weekly pay is currently$225.00.
So, Carmen presently earns $225 per week (after working for 30 hours) We can write: 30H =$225
Solve: H = 225/30 = 7.5
The answer to the REPHRASED target question is H = 7.5
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values

Statement 2: An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage. We can write:$1.50 = 20% of Carmen's CURRENT hourly wage
In other words: $1.50 = 20% of H Or:$1.50 = 0.20H
Solve: H = 1.5/0.2 = 15/2 = 7.5
The answer to the REPHRASED target question is H = 7.5
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

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BTGmoderatorDC wrote:
Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase? (1) Her gross weekly pay is currently$225.00.
(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage. OA D Source: Official Guide Say Carmen currently earns$x per hour; thus, she earns $30x per week. Now her per hour wage increased to$(x + 1.50). Thus, to earn the same gross weekly wages, she must work 30x / (x + 1.50) hours.

We have to get the value of x.

Let's take each statement one by one.

(1) Her gross weekly pay is currently $225.00. => 30x = 225 => x =$7.5. Sufficient

(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage. => 30x + 20% of 30x = 30(x + 1.50) 1.2x = x + 1.50 => x =$7.5. Sufficient

Hope this helps!

-Jay
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Manhattan Review GMAT Prep

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