Toy Factory Machine

Expert replies

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Sep 10, 2017 1:54 am

Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?

A. 20

B. 25

C. 30

D. 40

E. 50

How to come up with the right answer?
What is the perfect solution to this problem? Can some experts help me?

OA A

Like this post

Source: Beat The GMAT — Problem Solving | Sun Sep 10, 2017 1:54 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 » Sun Sep 10, 2017 3:29 am

lheiannie07 wrote:Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?

A. 20

B. 25

C. 30

D. 40

E. 50

Since the GCF of the two times is 6, calculate the number of toys produced every 6 minutes.
Let the number of machines = 10.

10 old machines:
Since each old machine produces 1 toy in 3 minutes, 10 old machines produce 10 toys in 3 minutes.
Thus, the number of toys produced in 6 minutes -- double the amount of time -- is 20.

When 40% of the old machines are replaced by new machines, the number of new machines = (40/100)(10) = 4.

4 new machines:
Since each new machine produces 1 toy in 2 minutes, 4 toys are produced in 2 minutes.
Thus, the number of toys produced in 6 minutes -- triple the amount of time -- is 12.
6 old machines:
Since 6 old machines produce 6 toys in 3 minutes, the number of toys produced in 6 minutes -- double the amount of time -- is 12.
Total toys produced in 6 minutes by 4 new machines and 6 old machines = 12+12 = 24.

Percent increase from 20 to 24 = (difference)/(original) * 100 = (24-20)/20 * 100 = 20%.

The correct answer is A.

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

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Sep 10, 2017 9:43 am

Hi lheiannie07 ,

This question can be solved by TESTing VALUES.

We're told that each machine can currently create one toy every 3 minutes. We're then told that 40 percent of the machines will be replaced by new machines that can assemble one toy every 2 minutes. We're asked for the percent increase in the number of toys assembled in one hour by all the machines at the factory.

Since we're replacing 40% of the machines, let's TEST 5 total machines.
One toy every 3 minutes = 20 toys/hour
One toy every 2 minutes = 30 toys/hour

Original Machines
(5 machines)(20 toys/hour) = 100 toys/hour produced

New 'mix' of Machines
(3 machines)(20 toys/hour) = 60 toys/hour produced
(2 machines)(30 toys/hour) = 60 toys/hour produced
Total = 120 toys/hour produced

Percent Change = (New - Old)/(Old) = (120 - 100)/100 = 20/100 = 20%

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Oct 12, 2017 1:50 pm

GMATGuruNY wrote:
lheiannie07 wrote:Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?

A. 20

B. 25

C. 30

D. 40

E. 50
Since the GCF of the two times is 6, calculate the number of toys produced every 6 minutes.
Let the number of machines = 10.

10 old machines:
Since each old machine produces 1 toy in 3 minutes, 10 old machines produce 10 toys in 3 minutes.
Thus, the number of toys produced in 6 minutes -- double the amount of time -- is 20.

When 40% of the old machines are replaced by new machines, the number of new machines = (40/100)(10) = 4.

4 new machines:
Since each new machine produces 1 toy in 2 minutes, 4 toys are produced in 2 minutes.
Thus, the number of toys produced in 6 minutes -- triple the amount of time -- is 12.
6 old machines:
Since 6 old machines produce 6 toys in 3 minutes, the number of toys produced in 6 minutes -- double the amount of time -- is 12.
Total toys produced in 6 minutes by 4 new machines and 6 old machines = 12+12 = 24.

Percent increase from 20 to 24 = (difference)/(original) * 100 = (24-20)/20 * 100 = 20%.

The correct answer is A.

Thanks a lot!

Like this post

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Oct 12, 2017 1:51 pm

[email protected] wrote:Hi lheiannie07 ,

This question can be solved by TESTing VALUES.

We're told that each machine can currently create one toy every 3 minutes. We're then told that 40 percent of the machines will be replaced by new machines that can assemble one toy every 2 minutes. We're asked for the percent increase in the number of toys assembled in one hour by all the machines at the factory.

Since we're replacing 40% of the machines, let's TEST 5 total machines.
One toy every 3 minutes = 20 toys/hour
One toy every 2 minutes = 30 toys/hour

Original Machines
(5 machines)(20 toys/hour) = 100 toys/hour produced

New 'mix' of Machines
(3 machines)(20 toys/hour) = 60 toys/hour produced
(2 machines)(30 toys/hour) = 60 toys/hour produced
Total = 120 toys/hour produced

Percent Change = (New - Old)/(Old) = (120 - 100)/100 = 20/100 = 20%

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Thank you so much!

Like this post

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Oct 12, 2017 8:55 pm

And in case anybody wants the algebra, it'd look like this:

We start with t machines that each produce (1/3) of a toy per minute. That nets us (t/3) toys per minute.

After the replacement, we've got 0.6t machines that each produce (1/3) of a toy per minute and 0.4t machines that each produce (1/2) of toy per minute. That nets us 0.6t/3 + 0.4t/2 toys per minute, or 0.4t toys per minute, or (2/5)t toys per minute.

We've gone from (1/3)t to (2/5)t per minute, a percent increase of (2/5 - 1/3)/(1/3), or 1/5, or 20%.

Save $100 on any VP online course!

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8177; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Nov 24, 2019 5:26 pm

BTGmoderatorDC wrote:Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?

A. 20

B. 25

C. 30

D. 40

E. 50

How to come up with the right answer?
What is the perfect solution to this problem? Can some experts help me?

OA A

The rate of one old machine is 20 toys per hour. The rate of one new machine is 30 toys per hour.

Let's assume that there are 10 old machines. So, before any of them are replaced, the number of toys produced in an hour is 10 x 20 = 200.

Since 40 percent of the old machines are replaced with new machines, we have now 6 old machines and 4 new machines, and the number of toys produced in an hour is 6 x 20 + 4 x 30 = 240.

Therefore, the percent increase in the productivity per hour is:

(New - Old)/Old x 100 = (240 - 200)/200 x 100 = 40/200 x 100 = 20 percent

Answer: A

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