Welcome! Check out our free B-School Guides to learn how you compare with other applicants.

## how many days would it take machine X alone to produce 2w

This topic has 1 expert reply and 7 member replies
netigen GMAT Destroyer!
Joined
19 Feb 2008
Posted:
631 messages
Followed by:
2 members
Thanked:
29 times
how many days would it take machine X alone to produce 2w Fri May 30, 2008 11:44 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
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?
A. 4
B. 6
C. 8
D. 10
E. 12

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
aatech Really wants to Beat The GMAT!
Joined
29 Apr 2008
Posted:
192 messages
Thanked:
14 times
Fri May 30, 2008 12:07 pm
ANS 12..

Suppose machine Y produces w widgets in d days

so, X produces same in d+2 days

In 1 day Y produces w/d and X produces w/(d+2) widgets

Working together they will produce w/d + w/(d+2) = [2w(d+1)]/[d(d+2)] widgets in 1 day

in 3 days they produce 3*[2w(d+1)]/[d(d+2)] = 5w/4

Solve to get d =4

x produces w widgets in 4+2 = 6 days

so, 2w widgets will be produces in 12 days

OA???

netigen GMAT Destroyer!
Joined
19 Feb 2008
Posted:
631 messages
Followed by:
2 members
Thanked:
29 times
Fri May 30, 2008 12:21 pm
OA is E

niraj_a GMAT Destroyer!
Joined
01 Jun 2008
Posted:
708 messages
Thanked:
12 times
Mon Dec 15, 2008 7:42 pm
i realize this is an old post but could someone show me the actual calculation that goes from this step -

in 3 days they produce 3*[2w(d+1)]/[d(d+2)] = 5w/4

to this step -

Solve to get d =4

i seem to be making a simple error somewhere...

parallel_chase GMAT Titan
Joined
20 Jun 2007
Posted:
1153 messages
Followed by:
1 members
Thanked:
139 times
Target GMAT Score:
V50
Tue Dec 16, 2008 4:42 am
Let the no. of days that Y takes is d

then no. of days that X takes will be d+2

X's rate = w/(d+2)
Y's rate = w/d

[w/d + w/(d+2)] * 3 = 5w/4

(w(d+2) + wd) /d(d+2) = 5w/12

wd + 2w + wd = 5wd(d+2)/12

24w(d+1) = 5wd(d+2)

24(d+1) = 5d(d+2)

24d + 24 = 5d^2 + 10d

5d^2 -14d - 24 = 0

5d^2 - 20d + 6d -24 = 0

(5d+6) ( d-4) = 0

d=-6/5 or 4

time cannot be negative, hence d=4

X produces w in d+2 = 4+2

2w will be produced in 6+6 = 12 days

Hope this helps.

_________________
No rest for the Wicked....

gmatusa2010 Really wants to Beat The GMAT!
Joined
25 Jul 2010
Posted:
134 messages
Followed by:
1 members
Wed Dec 22, 2010 3:37 am
anybody know the source of this problem? or think its realistic gmat problem?

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
6114 messages
Followed by:
1043 members
Thanked:
5294 times
GMAT Score:
790
Wed Dec 22, 2010 6:27 am
netigen wrote:
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?
A. 4
B. 6
C. 8
D. 10
E. 12
This question is from GMATPrep. An efficient way to solve this problem is to plug in the answer choices.

Let w=12.
In 3 days, X and Y need to produce 5/4*w = 5/4*12 = 15 widgets.
The answer choices represent the time for X to produce 2w=24 widgets.

Answer choice C: 8 days for X to produce 24 widgets
Thus, X produces 12 widgets in 4 days.
Since X takes 2 days longer, Y produces 12 widgets in 4-2=2 days.
Rate for X = w/t = 12/4 = 3/day.
Rate for Y = w/t = 12/2 = 6/day.
Combined rate for X+Y = 3+6 = 9/day .
Work completed in 3 days = r*t = 9*3 = 27 widgets.
Incorrect: almost DOUBLE the required number of widgets (15) is being produced.
Thus, X and Y need to work MUCH MORE SLOWLY, implying that the time for X to produce 24 widgets must be MUCH LONGER.

Answer choice E: 12 days for X to produce 24 widgets
Thus, X produces 12 widgets in 6 days.
Since X takes 2 days longer, Y produces 12 widgets in 6-2=4 days.
Rate for X = w/t = 12/6 = 2/day.
Rate for Y = w/t = 12/4 = 3/day.
Combined rate for X+Y = 2+3 = 5/day.
Work completed in 3 days = r*t = 5*3 = 15 widgets. Success!

_________________
Mitch Hunt
GMAT Private Tutor and Instructor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Contact me about long distance tutoring!

Last edited by GMATGuruNY on Mon Nov 07, 2011 11:02 am; edited 1 time in total

Thanked by: DonPaw, ariz, atishay, EOV
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
kaulnikhil GMAT Destroyer!
Joined
17 Apr 2009
Posted:
338 messages
Followed by:
3 members
Thanked:
9 times
Target GMAT Score:
7**
Sun May 08, 2011 10:28 pm
GMATGuruNY wrote:
netigen wrote:
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?
A. 4
B. 6
C. 8
D. 10
E. 12
This question is from GMATPrep. An efficient way to solve this problem is to plug in the answer choices.

Let w=12.
In 3 days, X and Y need to produce 5/4*w = 5/4*12 = 15 widgets.
The answer choices represent the time for X to produce 2w=24 widgets.

Answer choice C: 8 days for X to produce 24 widgets
Thus, X produces 12 widgets in 4 days.
Since X takes 2 days longer, Y produces 12 widgets in 4-2=2 days.
Rate for X = w/t = 12/4 = 3/day.
Rate for Y = w/t = 12/2 = 6/day.
Combined rate for X+Y = 3+6 = 9/day .
Work completed in 3 days = r*t = 9*3 = 27 widgets.
Incorrect. We need much less work to get done, so the time for X must be much longer.

Answer choice E: 12 days for X to produce 24 widgets
Thus, X produces 12 widgets in 6 days.
Since X takes 2 days longer, Y produces 12 widgets in 6-2=4 days.
Rate for X = w/t = 12/6 = 2/day.
Rate for Y = w/t = 12/4 = 3/day.
Combined rate for X+Y = 2+3 = 5/day.
Work completed in 3 days = r*t = 5*3 = 15 widgets. Success!

NICE

jean.spellman Just gettin' started!
Joined
15 Apr 2013
Posted:
1 messages
Mon May 13, 2013 5:33 pm
Hello,

Can anyone please explain how to get from:
w/d + w/(d+2)

To

[2w(d+1)]/[d(d+2)]?

Ty!

### Best Conversation Starters

1 varun289 31 topics
2 sana.noor 23 topics
3 killerdrummer 21 topics
4 Rudy414 19 topics
5 sanaa.rizwan 14 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

199 posts
2 GMATGuruNY

The Princeton Review Teacher

134 posts
3 Jim@StratusPrep

Stratus Prep

106 posts
4 Anju@Gurome

Gurome

47 posts