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

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

This topic has 1 expert reply and 7 member replies
Bookmark
Previous Topic Next Topic
netigen GMAT Destroyer! Default Avatar
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 Post 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! Default Avatar
    Joined
    29 Apr 2008
    Posted:
    192 messages
    Thanked:
    14 times
    Post 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! Default Avatar
    Joined
    19 Feb 2008
    Posted:
    631 messages
    Followed by:
    2 members
    Thanked:
    29 times
    Post Fri May 30, 2008 12:21 pm
    OA is E

    niraj_a GMAT Destroyer! Default Avatar
    Joined
    01 Jun 2008
    Posted:
    708 messages
    Thanked:
    12 times
    Post 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 Default Avatar
    Joined
    20 Jun 2007
    Posted:
    1153 messages
    Followed by:
    1 members
    Thanked:
    139 times
    Target GMAT Score:
    V50
    Post 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! Default Avatar
    Joined
    25 Jul 2010
    Posted:
    134 messages
    Followed by:
    1 members
    Post 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
    Most Active Expert Most Responsive Expert Most Thanked Expert
    Post 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!

    The correct answer is E.

    _________________
    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! Default Avatar
    Joined
    17 Apr 2009
    Posted:
    338 messages
    Followed by:
    3 members
    Thanked:
    9 times
    Target GMAT Score:
    7**
    Post 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!

    The correct answer is E.
    NICE

    jean.spellman Just gettin' started! Default Avatar
    Joined
    15 Apr 2013
    Posted:
    1 messages
    Post 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 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    		 199 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    		 134 posts
    3 image description Jim@StratusPrep

    Stratus Prep

    		 106 posts
    4 image description Anju@Gurome

    Gurome

    		 47 posts
    5 image description Jon@Admissionado

    Admissionado

    		 39 posts
    See More Top Beat The GMAT Experts