work

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

vaibhav101: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon May 01, 2017 11:56 pm; Thanked: 4 times

work

by vaibhav101 » Sun Jun 03, 2018 9:47 am

Timer

00:00

Your Answer

Global Stats

2 workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3rd as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:

A 21/4 days
B 25/4 days
C 15/2 days
D 75/8 days
E none of these

Quote

Source: Beat The GMAT — Problem Solving | Sun Jun 03, 2018 9:47 am

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

by GMATGuruNY » Sun Jun 03, 2018 11:42 am

vaibhav101 wrote:2 workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3rd as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:

A 21/4 days
B 25/4 days
C 15/2 days
D 75/8 days
E none of these

Let the job = 15 units.

Since A and B take 5 days to produce the 15-unit job, A+B = w/t = 15/5 = 3 units per day.
Thus:
A+B = 3.

Since 2A and (1/3)B take 3 days to produce the 15-unit job, 2A + (1/3)B = w/t = 15/3 = 5 units per day.
Thus:
2A + (1/3)B = 5
6A + B = 15.

Subtracting the red equation from the blue equation, we get:
(6A + B) - (A+B) = 15 - 3
5A = 12
A = 12/5 units per day.

Since A's rate = 12/5 units per day, the time for A alone to produce the 15-unit job = 15/(12/5) = 75/12 = 25/4 days.

The correct answer is B.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Jun 05, 2018 9:38 am

vaibhav101 wrote:2 workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3rd as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:

A 21/4 days
B 25/4 days
C 15/2 days
D 75/8 days
E none of these

The rate of A is 1/A and the rate of B is 1/B.

If A works twice as efficiently, the new rate is 1/A x 2 = 2/A

The new rate of B is 1/3 x 1/B = 1/(3B)

So we have two equations:

1/A + 1/B = 1/5

Multiplying by 2, we have:

2/A + 2/B = 2/5

and

2/A + 1/(3B) = 1/3

Subtracting the 2nd equation from the first, we have:

2/B - 1/(3B) = 2/5 - 1/3

Multiplying by 15B, we have:

30 - 5 = 6B - 5B

25 = B

Let's now determine A:

1/A + 1/25 = 1/5

Multiplying by 25A, we have:

25 + A = 5A

25 = 4A

25/4= A

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]