• Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

Four staff members

This topic has 1 expert reply and 3 member replies
alex.gellatly Master | Next Rank: 500 Posts Default Avatar
Joined
16 Nov 2011
Posted:
435 messages
Followed by:
16 members
Thanked:
48 times

Four staff members

Post Wed Aug 08, 2012 8:32 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    For staff members at a certain company worked on a project. The amounts of time that the four members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?

    80
    96
    160
    192
    240

    Is there a faster approach?
    Thanks

    _________________
    A useful website I found that has every quant OG video explanation:

    http://www.beatthegmat.com/useful-website-with-og-video-explanations-t112985.html#475231

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    truplayer256 Master | Next Rank: 500 Posts Default Avatar
    Joined
    15 Jan 2009
    Posted:
    392 messages
    Thanked:
    76 times
    Post Wed Aug 08, 2012 8:40 pm
    Let the total number of hours that the four staff members worked on the project be T. It can then be written that:

    2x + 3x + 5x + 6x = T
    Note that if one of the four staff members worked on the project for 30 hours, x can take on the values x = 15 for the worker who worked for 2x hours, x = 10 for the worker who worked 3x hours, x = 6 for the worker who worked 5x hours and finally x = 5 for the worker who worked 6x hours.

    When x = 15, T = 30 + 45 + 75 + 90 = 240
    When x = 10, T = 20 + 30 + 50 + 60 = 160
    We can stop here since we know that for x = 6 and x = 5, we'll get lower values of T than 160 and 240. Therefore, the only option that works is:

    Choice D

    Thanked by: alex.gellatly
    vk_vinayak Legendary Member
    Joined
    03 Jun 2008
    Posted:
    502 messages
    Followed by:
    21 members
    Thanked:
    98 times
    Post Wed Aug 08, 2012 8:50 pm
    alex.gellatly wrote:
    For staff members at a certain company worked on a project. The amounts of time that the four members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?

    80
    96
    160
    192
    240

    Is there a faster approach?
    Thanks
    Total hours worked is: 2x + 3x + 5x + 6x = 16x. So, if any of the answer choices is not a multiple of 16, choose that, but all are multiples of 16. So, we need to check each option:

    If 6x worked for 30 hrs, then x is 5. And 16*5 = 80. Eliminate A
    If 5x worked for 30 hrs, then x is 6. And 16*6 = 96. Eliminate B.

    On the similar lines. 16*10 = 160 and 16*15=240. So, eliminate C and E.
    D remains.

    _________________
    - VK

    I will (Learn. Recognize. Apply)

    Thanked by: anuprajan5, alex.gellatly
    Post Thu Aug 09, 2012 2:49 am
    alex.gellatly wrote:
    For staff members at a certain company worked on a project. The amounts of time that the four members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?

    80
    96
    160
    192
    240
    Let the 4 workers be W, X, Y and Z.
    W:X:Y:Z = 2:3:5:6.
    Since the sum of the parts of the ratio = 2+3+5+6 = 16, the total amount of time must be a multiple of 16.
    When a problem seems to require that all 5 answers be checked, the correct answer is likely to be D or E, with the result that the average test-taker will waste time checking A, B and C.
    Since D and E are the greatest answer choices, try to MAXIMIZE the total amount of time.
    W and X work for the least amounts of time.
    Thus, the total amount of time will be MAXIMIZED if either W or X works for 30 hours.

    If W works for 30 hours, the multiplier for the ratio is 15 -- since 15*2 = 30 -- with the result that the total amount of time = 15*16 = 240.
    Eliminate E.

    If X works for 30 hours, the multiplier for the ratio is 10 -- since 10*3 = 30 -- with the result that the total amount of time = 10*16 = 160.
    Eliminate C.

    If Y or Z works for 30 hours, the total amount of time will be LESS than 160.

    The correct answer is D.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

    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.
    Post Wed Apr 22, 2015 6:39 am
    alex.gellatly wrote:
    For staff members at a certain company worked on a project. The amounts of time that the four members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?

    80
    96
    160
    192
    240

    Is there a faster approach?
    Thanks
    Solution:

    We are given that the amounts of time that the four members worked on the project were in the ratio 2 to 3 to 5 to 6. A straightforward approach is to create a ratio with x multipliers. The ratio becomes: 2x : 3x : 5x : 6x, where 2x was person 1’s time, 3x was person 2’s time, 5x was person 3’s time, and 6x was person 4’s time.

    From this information, we can determine that the total time worked by all the members is the sum of our ratios: 2x + 3x + 5x + 6x = 16x.

    We are also given that one of the members worked for 30 hours. Thus, we can create 4 different equations to get 4 different possible x values.

    Option 1) If Person 1 was the individual who worked 30 hours, then 2x = 30 and x = 15

    Option 2) If Person 2 was the individual who worked 30 hours, then 3x = 30 and x = 10

    Option 3) If Person 3 was the individual who worked 30 hours, then 5x = 30 and x = 6

    Option 4) If Person 4 was the individual who worked 30 hours, then 6x = 30 and x = 5

    The above results show the 4 different options for the total number of hours an individual staff member worked.

    Now, remember that the entire group worked for 16x hours. We substitute each of the 4 possible values for x into this expression:

    Option 1: 16x = (16)(15) = 240 hours

    Option 2: 16x = (16)(10) = 160 hours

    Option 3: 16x = (16)(6) = 96 hours

    Option 4: 16x = (16)(5) = 80 hours

    The only value that we did not get was 192 hours, so D is the correct answer.

    _________________
    Jeffrey Miller Head of GMAT Instruction

    Best Conversation Starters

    1 Vincen 180 topics
    2 lheiannie07 65 topics
    3 Roland2rule 49 topics
    4 ardz24 44 topics
    5 LUANDATO 23 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    147 posts
    2 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    103 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    102 posts
    4 image description EconomistGMATTutor

    The Economist GMAT Tutor

    94 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    76 posts
    See More Top Beat The GMAT Experts