Carmen's weekly pay

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Carmen's weekly pay

by EricKryk » Fri Feb 21, 2014 8:31 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

2) An increase of $1.50 would represent an increase of 20 percent of her gross hourly wage

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Carmen's weekly pay

by Patrick_GMATFix » Fri Feb 21, 2014 8:47 am

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weekly pay = wage * hours. If we knew Carmen's initial wage, we would know the new wage, and we would know how to adjust hours to keep wage * hours constant. Rephrase to: "What is Carmen's wage"?. Each statement gives us a way to find this wage.

The full solution below is taken from the GMATFix App.

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by [email protected] » Fri Feb 21, 2014 2:29 pm

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Hi EricKryk,

This DS question includes some great "system" short-cuts that are work knowing:

We're told that Carmen works 30 hours per week at a certain pay rate. We're told that her hourly pay will increase by $1.50. The question asks how many FEWER hours would she need to work to get the same total weekly pay.

From the prompt, we can create the following equations:

30(X) = pay/week X = pay/hour
(30-H)(X + 1.50) = same pay/week H = number of fewer hours

Fact 1: Weekly pay = 225

With this info, we now know....

30X = 225, so we CAN solve for X. With THAT value, we can plug into the second equation:

(30-H)(Value + 1.50) = 225

With 1 variable and 1 equation, we can solve for H and answer the question.
Fact 1 is SUFFICIENT

Fact 2: The $1.50 increase would be an increase of 20% over the normal hourly wage

This info can be rewritten as...

1.50 = .2(X)

Just as in Fact 1, we CAN solve for X, then we CAN solve for H.
Fact 2 is SUFFICIENT

Final Answer: D

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by Jeff@TargetTestPrep » Mon Jul 30, 2018 5:11 pm

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EricKryk 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

2) An increase of $1.50 would represent an increase of 20 percent of her gross hourly wage
We are given that Carmen works 30 hours per week and that her wage is to increase by $1.50 per hour. We must determine how many fewer hours she could work and still earn the same gross weekly pay as she earned before the increase. We can set up an equation to determine how many fewer hours she could work. We can let:

h = the reduction in hours, and then (30 - h) = the reduced number of hours she could work

w = Carmen's current hourly wage and then (w + 1.5) = Carmen's hourly wage after her raise

Thus, we have:

(30 - h)(w + 1.5) = 30w

We need to determine a value for h. Thus, if we can determine the value of w, we can answer the question.

Statement One Alone:

Her gross weekly pay is currently $225.

With the information from statement one, we know that:

30w = 225

w = 7.5

Since we have a value for w, we can substitute in to the equation, (30 - h)(w + 1.5) = 30w, and determine h.

(30 - h)(7.5 + 1.5) = 30(7.5)

(30 - h)(9) = 225

30 - h = 25

h = 5

Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

An increase of $1.50 would represent an increase of 20 percent of her gross hourly wage.

We can translate statement two into an equation:

1.5 + w = 1.2(w)

1.5 = 0.2w

1.5/0.2 = w

15/2 = w

7.5 = w

Since we know w = 7.5, we know that we can determine the value of h. Statement two is also sufficient to answer the question.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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