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EMPOWERgmatRichC
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Marcie started working a part-time job at the beginning of the summer Updated on: 20 Oct 2024, 10:11
Originally posted by EMPOWERgmatRichC on 18 Oct 2019, 18:12.
Last edited by Bunuel on 20 Oct 2024, 10:11, edited 2 times in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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35% (medium)

Question Stats:

79% (02:07) correct 21% (02:45) wrong based on 421 sessions

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Marcie started working a part-time job at the beginning of the summer. After four weeks, she increased the number of hours she worked each week by 1/5. After another four weeks, she decreased the number of hours she worked each week by 1/3. From then on, she worked 20 hours weekly. How many hours was she working each week when she began working at the beginning of the summer?

(A) 5
(B) 10
(C) 16
(D) 25
(E) 30


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Pack 3, Question 5


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Marcie started working a part-time job at the beginning of the summer 19 Oct 2019, 01:16
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EMPOWERgmatRichC


Marcie started working a part-time job at the beginning of the summer. After four weeks, she increased the number of hours she worked each week by 1/5. After another four weeks, she decreased the number of hours she worked each week by 1/3. From then on, she worked 20 hours weekly. How many hours was she working each week when she began working at the beginning of the summer?

(A) 5
(B) 10
(C) 16
(D) 25
(E) 30
Show more

Let us solve back wards..
Quote:
she decreased the number of hours she worked each week by 1/3. From then on, she worked 20 hours weekly
Show more
Let initial time be t...So, \(20=t-\frac{t}{3}=\frac{2t}{3}....t=20*\frac{3}{2}=30\)

Quote:
she increased the number of hours she worked each week by 1/5.
Show more
Let the start time be s...So, \(30=s+\frac{s}{5}=\frac{6s}{5}....s=30*\frac{5}{6}=25\)

D
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Marcie started working a part-time job at the beginning of the summer 19 Oct 2019, 17:14
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let initial working each week is x hrs
initial increase in hrs ;x/5 ; new time ; 6x/5
the tricky word line she decreased the number of hours she worked each week by 1/3
i.e x-x/3 ; 2x/3
2x/3 = 20
x=30 hrs
6/5*x=30
x= 25 hrs
IMO D



EMPOWERgmatRichC
EMPOWERgmat PS Series:
Pack 3, Question 5

Marcie started working a part-time job at the beginning of the summer. After four weeks, she increased the number of hours she worked each week by 1/5. After another four weeks, she decreased the number of hours she worked each week by 1/3. From then on, she worked 20 hours weekly. How many hours was she working each week when she began working at the beginning of the summer?

(A) 5
(B) 10
(C) 16
(D) 25
(E) 30



48 Hour Window To Win An $85 EMPOWERgmat Tuition Credit (1 Month Free!)
Share your explanation! The GMAT Club member with the most verified Kudos in total on the 10 question PS & DS Block 3 question packs will win an $85 EMPOWERgmat tuition credit, which will entitle the winner to a full month of complete access to the EMPOWERgmat system. Even if you're not sure about your answer or your rationale, share your explanation to help boost your learning and earn a chance to win. We have increased the contest window to 2 weeks from the posted date of the question - so that you can maximize your chances and answer all of the questions in each set!

To be eligible, your explanation must be submitted within the 2 week window after this post was created and should explain your reasoning why the answer you chose is correct

The OA will be held until a 1 week window has lapsed.

Links to the entire list of Quant and Verbal questions can be found here: EMPOWERgmat Forum Contest!...
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Marcie started working a part-time job at the beginning of the summer 20 Oct 2024, 07:05
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I found the language of the question tricky so I am explaining it here in case someone struggles with it too!

Quote:
Marcie started working a part-time job at the beginning of the summer. After four weeks, she increased the number of hours she worked each week by 1/5.
Show more

Let's say x is the number of hours Marcie worked initially per week.
After 4 weeks, she increased her hours by 1/5:
New hours = x + (1/5)x = (6/5)x

Quote:
After another four weeks, she decreased the number of hours she worked each week by 1/3. From then on, she worked 20 hours weekly.
Show more
After another 4 weeks, she decreased these new hours by 1/3:
Final hours = (6/5)x - (1/3)((6/5)x) = (6/5)x - (2/5)x = (4/5)x
We're told that this final amount is 20 hours:
(4/5)x = 20

Quote:
How many hours was she working each week when she began working at the beginning of the summer?
Show more


Now we can solve for x: x = 20 ÷ (4/5) = 20 × (5/4) = 25

Therefore, Marcie was working 25 hours per week when she began at the start of summer.

The correct answer is (D) 25.
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Marcie started working a part-time job at the beginning of the summer 03 Nov 2024, 13:40
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I solved it like this:

Probably a calculative guess
Increase of 20% and decrease of 33%

Tried option 25 hr directly as increasing 20% would give 30 hr and hereby reducing 33% would give 20hr

Or making such calculative guess can be troublesome?
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Marcie started working a part-time job at the beginning of the summer 15 Aug 2026, 13:44
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1. My issue is if it is saying it increased each week by 1/5 and not 1/5th why shouldnt we consider it exactly as 1/5
2. It says it increased 1.5 each week and then it mentions decreased after four weeks so the 1/5 increase should happen four times, no?
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Marcie started working a part-time job at the beginning of the summer 15 Aug 2026, 17:01
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1. My issue is if it is saying it increased each week by 1/5 and not 1/5th why shouldnt we consider it exactly as 1/5

You have a point there. It would have been more apt to use 1/5th. However, the scenario you mention requires 1/5 to be written as 1/5 hr.


2. It says it increased 1.5 each week and then it mentions decreased after four weeks so the 1/5 increase should happen four times, no?
No, it is not given 'by 1/5 each week', in which case it would mean exactly what you infer. It would be compounded then.
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