Carmen currently works 30 hours per week at her part-time

Question

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.

Bunuel · Accepted Answer

SOLUTION:

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?

Let  w  be Carmen's gross hourly wage and  t  be the number of hours fewer Carmen will need to work. We need to find such  t  that  30w=(30-t)(w+1.5) .

(1) Her gross weekly pay is currently $225.00 -->  30w=225  --> we can find  w , so in  30w=(30-t)(w+1.5)  we'll be left with only one unknown:  t , which means that we can solve for it. Sufficient.

(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage -->  1.5=0.2w . The same here: we can find  w , so we can find  t . Sufficient.

Answer: D.

JeffTargetTestPrep · Answer

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

Using the general equation that (hours) x (hourly wage) = total gross pay, we have:

(30 – h)(w + 1.5) = 30w

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

The answer is D.

shlbatra · Answer

Hi,

I have a query with this question.

From option 1, after solving, we get that the new number of hours is 25 i.e, 5 hours less.

Option 2 states, that there was a 20% inc in the per hour wage. Can we use the concept of ratios here.
To keep total wage constant, if we increase per hour wage by 20%, we need to decrease the number of hours worked by 20% too.
=> New No. of Hours worked = 30-20%(30)= 24
This option does not provide the same answer as 1. Can you please explain the reason why ?
The relation used : Total Wage/month = No. of Hours worked * Wage/Hour

Thanks,
Sahil

aeglorre · Answer

We are initally given the equation x*30 = Total Salary, and then the question is if we can solve (x + 1.5) * 30 = Total Salary, so we have two unknown values we need to solve for

1) Solves total salary, so now we have one equation and one unknown, which means 1 is sufficient.
2) Gives us the ability to solve for x, so now we have one equation and one variable (Total salary), this is also sufficient.

So, D.

BrentGMATPrepNow · Answer

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)? The video below has tips on rephrasing the target question 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: https://www.gmatprepnow.com/articles/dat ... lug-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 Answer: D Cheers, Brent RELATED VIDEO https://www.youtube.com/watch?v=MyG1K3ee69w

GMATGuruNY · Answer

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  = \frac{225}{30} =  $7.50, implying that an additional $1.50 per hour will increase the hourly rate to $9.
 \frac{increased-hourly-rate}{actual-hourly-rate} = \frac{9}{7.5} = \frac{18}{15} = \frac{6}{5} 
Implication:
The same income will be yielded in  \frac{5}{6}  of the actual time -- a decrease of  \frac{1}{6} :
 \frac{1}{6} * 30 = 5  fewer hours.
SUFFICIENT.

Statement 2: 
Since $1.50 increases the hourly rate by 20%, we get:
 \frac{increased-hourly-rate}{actual-hourly-rate} = \frac{120}{100} = \frac{6}{5} 
Implication:
The same income will be yielded in  \frac{5}{6}  of the actual time -- a decrease of  \frac{1}{6} :
 \frac{1}{6} * 30 = 5  fewer hours.
SUFFICIENT.

D

AdarshSambare · Answer

You're absolutely right.

We start with 
x⋅30 = Total Salary
x⋅30=Total Salary.

The question asks whether we can evaluate 
(x+1.5)⋅30

(1) gives Total Salary directly. 
Then we can back-solve x
x, and hence compute

(x+1.5)⋅30

Sufficient.

(2) gives

x directly. Plugging into x⋅30=Total Salary

(x+1.5)⋅30

(x+1.5)⋅30. Sufficient.

So both statements are sufficient independently.

Answer: D

totaltestprepNick · Answer

D https://www.youtube.com/watch?v=2fORq0f1M5Q Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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