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
OA is E
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
Running at their respective constant rates, machine X takes
This topic has expert replies
-
rakeshd347
- Master | Next Rank: 500 Posts
- Posts: 391
- Joined: Sat Mar 02, 2013 5:13 am
- Thanked: 50 times
- Followed by:4 members
-
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.rakeshd347 wrote: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.
Last edited by GMATGuruNY on Fri Oct 04, 2013 4:51 am, edited 1 time in total.
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
-
theCodeToGMAT
- Legendary Member
- Posts: 1556
- Joined: Tue Aug 14, 2012 11:18 pm
- Thanked: 448 times
- Followed by:34 members
- GMAT Score:650
5w/4 = 3 days
w = 12/5 days
X = A + 2
Y = A
Total time for 1w = XY/(X+Y)
12/5 = (A)(A+2)/(2A+2)
24/5 = (A)(A+2)/(A+1)
4*6/5 = (A)(A+2)/(A+1)
So, A = 4
X = 6
6 days for 1w
12 days for 2w
Answer [spoiler]{E}[/spoiler]
w = 12/5 days
X = A + 2
Y = A
Total time for 1w = XY/(X+Y)
12/5 = (A)(A+2)/(2A+2)
24/5 = (A)(A+2)/(A+1)
4*6/5 = (A)(A+2)/(A+1)
So, A = 4
X = 6
6 days for 1w
12 days for 2w
Answer [spoiler]{E}[/spoiler]
R A H U L
GMATGuruNY wrote:Let w=12.rakeshd347 wrote: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.
dear @GMATGuruNY
I've learned work with answer choice from you and since that time I always check the solution with "beatthegmat" to see your way...
it's always amazing
Thank you for your help and your time
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7269
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can let x = the number of days it takes Machine X to produce w widgets, and thus x - 2 = the number of days it takes Machine Y to produce w widgets. Furthermore, the rate of Machine X is w/x, and the rate of Machine Y is w/(x - 2). We are given that they can produce 5w/4 widgets in 3 days. Thus, we have:rakeshd347 wrote: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
OA is E
3(w/x) + 3[w/(x - 2)] = 5w/4
Dividing both sides by w, we have:
3/x + 3/(x - 2) = 5/4
Multiplying both sides by 4x(x - 2), we have:
12(x - 2) + 12x = 5x(x - 2)
12(x - 2) + 12x = 5x(x - 2)
12x - 24 + 12x = 5x^2 - 10x
5x^2 - 34x + 24 = 0
(5x - 4)(x - 6) = 0
x = 4/5 or x = 6
However, x can't be 4/5; if it were, y would be negative. Thus, x must be 6. Since it takes Machine X 6 days to produce w widgets, it will take 12 days to produce 2w widgets.
Alternate Solution:
If the two machines working together produce 5w/4 widgets in 3 days, then they would produce w widgets in 3/(5/4) = 12/5 days.
Let y be the number of days for machine Y to produce w widgets. Then, machine X produces w widgets in y + 2 days. In one day, machine Y will produce 1/y of w widgets and machine X will produce 1/(y + 2) of w widgets. We also know that working together it takes them 12/5 days to produce w widgets; therefore in one day, working together, they produce 1/(12/5) = 5/12 of w widgets. Thus, we can form the following equation:
1/y + 1/(y + 2) = 5/12
(2y + 2)/[y(y+2)] = 5/12
24y + 24 = 5y^2 + 10y
5y^2 - 14y - 24 = 0
(5y + 6)(y - 4) = 0
y = -6/5 or y = 4
Since y cannot be negative, y is 4. Thus, it takes machine X 4 + 2 = 6 days to produce w widgets, and therefore, it will take machine X 6 * 2 = 12 days to produce 2w widgets.
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
One approach is to assign a nice value to the job (w)rakeshd347 wrote: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
OA is E
Let's say that w = 12.
GIVEN: Running at their respective constant rates, machine X takes 2 days longer to produce 12 widgets than machine Y
Let t = time for machine Y to produce 12 widgets
So, t+2 = time for machine X to produce 12 widgets
RATE = output/time
So, machine X's RATE = 12 widgets/(t + 2 days) = 12/(t+2) widgets per day
And machine Y's RATE = 12 widgets/(t days) = 12/t widgets per day
The two machines together produce 5w/4 widgets in 3 days
In other words, The two machines together produce 5(12)/4 widgets in 3 days
Or the two machines together produce 15 widgets in 3 days
This means the COMBINED RATE = 5 widgets per day
So, we can write: 12/(t+2) + 12/t = 5
Multiply both sides by (t+2)(t) to get: 12t + 12t + 24 = 5(t+2)(t)
Simplify: 24t + 24 = 5t² + 10t
Rearrange: 5t² - 14t - 24 = 0
Factor to get: (5t + 6)(t - 4) = 0
So, EITHER t = -6/5 OR t = 4
Since the time cannot be negative, it must be the case that t = 4
If t = 4, then it takes Machine Y 4 days to produce 12 widgets
And it takes Machine X 6 days to produce 12 widgets
How many days would it take machine X alone to produce 2w widgets?
In other words, how many days would it take machine X alone to produce 24 widgets? (since w = 12)
If it takes Machine X 6 days to produce 12 widgets, then it will take Machine X 12 days to produce 24 widgets
Answer: E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
