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Carmen currently works \(30\) hours per week at her part-time job. If her gross hourly wage were to increase by $1.50

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Carmen currently works \(30\) hours per week at her part-time job. If her gross hourly wage were to increase by $1.50

by M7MBA » Tue Nov 10, 2020 6:36 am

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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.

Answer: D

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Re: Carmen currently works \(30\) hours per week at her part-time job. If her gross hourly wage were to increase by $1.5

by deloitte247 » Sun Nov 15, 2020 12:02 pm

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00:00

Your Answer

A

B

C

D

E

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Working hours = 30 hours/week if her gross hourly wage increases by $1.5.
Target question: How many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?
Let her gross hourly wage = w;
no. of fewer hours to work = h
Previous gross weekly pay = working hours per week * gross hourly wage
Previous gross weekly pay = 30w
Since previous gross weekly pay is expected to equal to new gross weekly pay
Therefore, 30w = (30 - h)(w + 1.50)

Statement 1: Her gross weekly pay is currently $225.00
30w = 225
So, w = 225/30 == $7.5
From the question stem, 30w = (30 - h)(w + 1.50)
30(7.5) = (30 - h)7.5 + 1.5)
225 = 9(30 - h)
225 = 270 - 9h
9h = 270 - 225
h = 45/9 = 5 hours
Therefore, statement 1 is SUFFICIENT.

Statement 2:An increase of $1.50 would represent an increase of 20% percent of her current gross hourly wage.
$1.5 = 20% of w
1.5 = 0.2w
w = 1.5/0.2 = $7.50
From the question stem, 30w = (30 - h)(w + 1.50)
This is similar to the information derived in statement 1, hence, h will result into hours. Therefore, statement 2 is SUFFICIENT.

Since each statement is sufficient alone, then, option D is the correct answer.
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