Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
For 7 days from July 30 to Aug 4, type Coupon Code "SUCCESS2 " at check out to get 20% off from the original price. This is your chance to score an excellent Q49-51 just like 70% of our students.
TJ hit 770 on his first try. He had studied for about a year on and off beforehand, and studied very seriously (2+ hours per day) in the 6 months leading up to the exam.
Last week, seven of our students scored a 700+ score (including two 760’s). To celebrate our students and help future aspirants, we are offering our GMAT Prep package at a massive 57% OFF. Valid only for a limited period of time. Hurry!
In each webinar, we teach game-changing techniques and strategies for solving some of the most high-value GMAT quant questions. In addition, we will provide you with the opportunity to ask questions regarding how to best prepare for the GMAT.
Most students struggle to cross GMAT 700 because they lack a strategic plan of action. Attend this Free Strategy Webinar, where we will discuss 3 vital skills that can help you score a 760 on GMAT ‘effectively’.
82%
(01:36)
correct
18%
(01:47)
wrong
based on 1455
sessions
HideShow
timer Statistics
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.
Practice Questions Question: 28 Page: 277 Difficulty: 650
Re: Carmen currently works 30 hours per week at her part-time
[#permalink]
31 Aug 2012, 01:50
10
Kudos
9
Bookmarks
Expert Reply
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.
Re: Carmen currently works 30 hours per week at her part-time
[#permalink]
22 Aug 2013, 01:48
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
Re: Carmen currently works 30 hours per week at her part-time
[#permalink]
10 Jan 2014, 07:07
1
Kudos
Bunuel 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.
Practice Questions Question: 28 Page: 277 Difficulty: 650
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.
Re: Carmen currently works 30 hours per week at her part-time
[#permalink]
10 May 2016, 06:41
4
Kudos
1
Bookmarks
Expert Reply
Bunuel 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.
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.
Carmen currently works 30 hours per week at her part-time
[#permalink]
Updated on: 17 May 2021, 08:42
1
Kudos
Expert Reply
Top Contributor
Bunuel 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)?
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
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
Re: Carmen currently works 30 hours per week at her part-time
[#permalink]
11 Mar 2019, 11:56
1
Kudos
Expert Reply
Bunuel 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 \(= \frac{225}{30} =\) $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.
Re: Carmen currently works 30 hours per week at her part-time
[#permalink]
20 Mar 2020, 09:47
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
One of the fastest-growing graduate business schools in Southern California, shaping the future by developing leading thinkers who will stand at the forefront of business growth. MBA Landing | School of Business (ucr.edu)