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

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

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

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

by M7MBA » Mon Apr 15, 2019 1:47 am

Timer

00:00

Your Answer

Global Stats

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

Quote

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 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; 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

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 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]