Running at their respective constant rates, Machine X takes 2 days longer to produce w widgets than Machine Y. At these rates, if the two machines together produce (5/4)w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
4
6
8
10
12
Machine x and y, w widgets
This topic has expert replies
- Patrick_GMATFix
- GMAT Instructor
- Posts: 1052
- Joined: Fri May 21, 2010 1:30 am
- Thanked: 335 times
- Followed by:98 members
This can be solved algebraically, but it gets a bit nasty.
I would use reverse engineering: work backwards to find out which of the answer choices fit all restrictions in the question.
I'd start by plugging in an easy number for w (here easy means a common factor of our other numbers). In the attached work, I made w=60 widgets and worked from there.
The right answer(E) is the answer that agrees with "Machine X takes 2 days longer to produce w widgets than Machine Y". The answer is E
I would use reverse engineering: work backwards to find out which of the answer choices fit all restrictions in the question.
I'd start by plugging in an easy number for w (here easy means a common factor of our other numbers). In the attached work, I made w=60 widgets and worked from there.
The right answer(E) is the answer that agrees with "Machine X takes 2 days longer to produce w widgets than Machine Y". The answer is E
- Check out my site: GMATFix.com
- To prep my students I use this tool >> (screenshots, video)
- Ask me about tutoring.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let w=12.Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets.
A. 4
B. 6
C. 8
D. 10
E. 12
In 3 days, the number of widgets that must be produced = (5/4)w = (5/4)*12 = 15 widgets.
To produce 15 widgets in 3 days, the required rate = 15/3 = 5 widgets per day.
We can plug in the answers, which represent the time for X to produce 2w=24 widgets.
Answer choice C: 8 days for X to produce 24 widgets
Here, the time for X to produce 12 widgets = 4 days.
Since X takes 2 days longer than Y, the time for Y to produce 12 widgets = 2 days.
Rate for X = w/t = 12/4 = 3 widgets per day.
Rate for Y = w/t = 12/2 = 6 widgets per day.
Combined rate for X+Y = 3+6 = 9 widgets per day.
Since the required rate = 5 widgets per day, X and Y are working at almost TWICE the required rate.
Since X and Y need to work MUCH MORE SLOWLY, X needs to take MUCH LONGER to produce 2w widgets.
Answer choice E: 12 days for X to produce 24 widgets
Here, the time for X to produce 12 widgets = 6 days.
Since X takes 2 days longer than Y, the time for Y to produce 12 widgets = 4 days.
Rate for X = w/t = 12/6 = 2 widgets per day.
Rate for Y = w/t = 12/4 = 3 widgets per day.
Combined rate for X+Y = 2+3 = 5 widgets per day.
Success!
The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3