Together, 15 type A machines and 7 type B machines can

Expert replies

Previous Topic Next Topic

M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Mon Apr 15, 2019 1:47 am

Timer

00:00

Answers

Stats

Difficulty—

Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours.

Together 8 type B machines and 15 type C machines can complete the same job in 11 hours.

How many hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?

(A) 22 hours
(B) 30 hours
(C) 44 hours
(D) 60 hours
(E) It cannot be determined from the information above.

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

Like this post

Source: Beat The GMAT — Problem Solving | Mon Apr 15, 2019 1:47 am

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

by GMATGuruNY » Mon Apr 15, 2019 2:46 am

M7MBA wrote:Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours.

Together 8 type B machines and 15 type C machines can complete the same job in 11 hours.

How many hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?

(A) 22 hours
(B) 30 hours
(C) 44 hours
(D) 60 hours
(E) It cannot be determined from the information above.

Let the job = 44 units.

Since 15A+7B take 4 hours to complete the 44-unit job, the rate for 15A+7B = w/t = 44/4 = 11 units per hour.
Since 8B+15C take 11 hours to complete the 44-unit job, the rate for 8B+15C = w/t = 44/11 = 4 units per hour.

Adding together 15A+7B=11 and 8B+15C=4, we get:
15A + 15B + 15C = 15 units per hour
A+B+C = 1 unit per hour
Since the rate for A+B+C = 1 unit per hour, the time for A+B+C to complete the 44-unit job = w/r = 44/1 = 44 hours.

The correct answer is C.

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

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8151; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Apr 16, 2019 4:57 pm

M7MBA wrote:Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours.

Together 8 type B machines and 15 type C machines can complete the same job in 11 hours.

How many hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?

(A) 22 hours
(B) 30 hours
(C) 44 hours
(D) 60 hours
(E) It cannot be determined from the information above.

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

Let a, b, and c be the times, in hours, it takes for 1 type A, B, and C machine to finish the job by itself, respectively. So we can create the equations (notice that, for example, 1/a will be the work done by 1 type A machine per hour and n/a will be the work done by n type A machines per hour):

4(15/a) + 4(7/b) = 1

and

11(8/b) + 11(15/c) = 1

If we divide the first equation by 4 and the second by 11, we have:

15/a + 7/b = 1/4

And

8/b + 15/c = 1/11

Now, adding the two new equations, we have:

15/a + 15/b + 15/c = 1/4 + 1/11

15(1/a + 1/b + 1/c) = 15/44

1/a + 1/b + 1/c = 1/44

Thus, the combined rate of 1 type A, B and C machine is 1/44. That is, together they finish 1/44 of the job in one hour. Therefore, it will take them 1/(1/44) = 44 hours to finish the job.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review