Running at their respective constant rates, machine X takes

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rakeshd347: Master | Next Rank: 500 Posts; Posts: 391; Joined: Sat Mar 02, 2013 5:13 amFollowed by: 4 members; Thanked: 50 times

by rakeshd347 » Thu Oct 03, 2013 7:33 pm

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

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Oct 03, 2013 8:02 pm

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

Let w=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.

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varun289: Master | Next Rank: 500 Posts; Posts: 298; Joined: Sun Jun 03, 2012 6:42 amFollowed by: 7 members; Location: New delhi; Thanked: 10 times; GMAT Score:590

by varun289 » Thu Oct 03, 2013 8:16 pm

plz read file

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machines x y.xlsx: (8.48 KiB) Downloaded 192 times

https://freegmat.in

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Thu Oct 03, 2013 10:56 pm

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]

R A H U L

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soudeh: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Thu Apr 20, 2017 7:39 pm

by soudeh » Sat Oct 21, 2017 8:10 am

GMATGuruNY wrote:
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
Let w=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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8147; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Nov 20, 2019 6:04 pm

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

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:

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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Nov 21, 2019 7:06 am

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

One approach is to assign a nice value to the job (w)

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 = 5tÂ² + 10t
Rearrange: 5tÂ² - 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

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