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Toy Factory Machine

This topic has 3 expert replies and 2 member replies

Toy Factory Machine

Post 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

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GMAT/MBA Expert

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Post 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.

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Post 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

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Contact Rich at Rich.C@empowergmat.com

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Post 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!

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Post Thu Oct 12, 2017 1:51 pm
Rich.C@EMPOWERgmat.com 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!

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Post 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%.

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