• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

John takes 15 hours to complete a certain job, while Bill ta

This topic has 2 expert replies and 1 member reply

John takes 15 hours to complete a certain job, while Bill ta

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

OA B

Source: Veritas Prep

  • +1 Upvote Post
  • Quote
  • Flag
Top Reply
Post
BTGmoderatorDC wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes

OA B

Source: Veritas Prep
John’s rate is 1/15, and Bill’s rate is 1/6.

If Steve is as fast as John, his rate is 1/15, and the combined rate would be 1/15 + 1/6 + 1/15 = 2/30 + 5/30 + 2/30 = 9/30 = 3/10. Therefore, it would take the three men 1/(3/10) = 10/3 = 3 " = 3 hours and 20 minutes to complete the job.

On the other hand, if Steve is as fast as Bill, his rate is 1/6, and the combined rate would be 1/15 + 1/6 + 1/6 = 2/30 + 5/30 + 5/30 = 12/30 = 2/5. Therefore, it would take the three men 1/(2/5) = 5/2 = 2 1/2 = 2 hours and 30 minutes to complete the job.

Since Steve is faster than John but slower than Bill, it will take them between 2 hours and 30 minutes and 3 hours and 20 minutes to complete the job. We see that of all the answer choices, only choice B, 2 hours and 45 minutes, satisfies the criteria.

Answer: B

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag
Top Reply
Post
We can find two extreme ends, which are just out of the range

1) Lower end j=15h, b=6h, and j=15h
all three will take1(1/15+1/15+1/6)= 2h 30 min.

2) Higher end j=15h, b=6h, and j=6h
all three will take1(1/15+1/6+1/6)= 3h 20 min.

Only __B__ is within this range

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
BTGmoderatorDC wrote:
John takes 15 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?

A. 2 hours, 30 minutes
B. 2 hours, 45 minutes
C. 3 hours, 20 minutes
D. 3 hours, 45 minutes
E. 4 hours, 10 minutes
Let's first see what happens if Steven works as fast as possible.
Since Bill can complete the job in 6 hours, Steven must complete the job in a little more than 6 hours.
For example, we COULD see what happens if Steven takes 6.000000000000001 hours to complete the job.
Unfortunately, 6.000000000000001 is an awful number to work with.
So, for convenience sake, let's just see what happens if it takes Steven 6 hours to complete the job

----ASIDE-------
For work questions, there are two useful rules:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.
---------------------
Let’s use these rules to solve the question. . . .

From Rule #1, we can conclude that:
- In ONE hour, John completes 1/15 of the job
- In ONE hour, Bill completes 1/6 of the job
- In ONE hour, Steven completes 1/6 of the job
So, COMBINED, the amount of the job completed after ONE hour = 1/15 + 1/6 + 1/6
= 2/30 + 5/30 + 5/30
= 12/30
= 2/5

Rule #2 tells us that, the total time to complete the job = 5/2 hours
In other words, when Steven works as FAST as possible, it takes the 3 men 5/2 hours to complete the job.
Of course, this calculation is based on Steven working at the SAME SPEED as Bill.
Since Steven is supposed to work SLOWER than Bill, the time it takes the 3 men to complete the job must be GREATER than 5/2 hours (aka 2 hours and 30 minutes)

IMPORTANT: We know that the correct answer must be GREATER than 2 hours and 30 minutes. So, we can eliminate answer choice A because it is too small.
We also know that, IF we were to also use Steven's SLOWEST work speed to calculate the upper limit for the time it takes all 3 men to complete the job, we'd be able to eliminate 3 more answer choices because they're too big.
Based on this, we should see that we can automatically eliminate the 3 biggest remaining answer choices (C, D, E), which leaves us with B

Answer: B

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • 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
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

Top First Responders*

1 Ian Stewart 49 first replies
2 Brent@GMATPrepNow 39 first replies
3 Jay@ManhattanReview 35 first replies
4 GMATGuruNY 29 first replies
5 ceilidh.erickson 14 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

206 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

82 posts
4 image description Ian Stewart

GMATiX Teacher

56 posts
5 image description GMATGuruNY

The Princeton Review Teacher

50 posts
See More Top Beat The GMAT Experts