Each machine at a toy factory assembles a certain kind of toy at a co

Question

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

A. 20 %

B. 25 %

C. 30 %

D. 40 %

E. 50 %

Bunuel · Accepted Answer

Only the highlighted part is needed to answer the question. We can plug all other values ourselves.

Say the rate is 100 toys by 100 old machines in 1 unit of time (1 toy per 1 machine in 1 unit of time).
 
40 of the machines are replaced with new ones which are 1.5 times as efficient as the old ones, so they will produce 60 toys in 1 unit of time. Total = 60 + 60 = 120.

Percent increase = 20%.

Answer: A.

generis · Answer

We have two rates and hence two different total number of toys produced: 100% of original machines at original rate, then 40% of machines at a new rate and 60% of machines at original rate

Assume 100 machines. 
Change rates in minutes to rates in hours. 
And assume time = 1 hour 
Finally, 40% of 100 are new = 40 new machines and 60 old machines

Number of machines * R * T = Work

Rates in minutes --> rates in hours

Original rate:
  \frac{1 toy}{3 mins} = \frac{20 toys}{60 mins}= \frac{20 toys}{1 hr}   , =  \frac{20}{1}  
and

New rate FOR 40 MACHINES:   \frac{1 toy}{2 mins} =\frac{30 toys}{60 mins} = \frac{30 toys}{1 hr}   =  \frac{30}{1}

(1) . Original number of toys produced

100 machines at the original rate of  \frac{20}{1}  produce (100 *  \frac{20}{1} * 1) =  2,000 toys originally produced

(2) . Some old plus some new machines at different rates = new number of toys produced

So total toys produced now are made by 60 machines at original rate + 40 machines at new rate

Total toys that 60 machines produce: (60 *  \frac{20}{1}  * 1) = 1,200 toys

Total toys that 40 machines produce: (40 *  \frac{30}{1}  * 1) = 1,200 toys

1,200 + 1,200 =  2,400 total toys now produced

(3) . Percent change:   \frac{change}{original}    x 100 : 
 \frac{400}{2000} * 100 = 20%

Answer A

adstudy · Answer

We know,

Rate * Time = Work
 
For Old Machines -

Work = 1 Toy; Time = 3 minutes

Hence,  Rate =  \frac{1}{3}

For New Machines -

Work = 1 Toy; Time = 2 minutes

Hence,  Rate =  \frac{1}{2}

To find percent increase -

(\frac{(New Combined Rate - Old Combined Rate)}{Old Combined rate}) * 100  ------------ (1)

New Combined Rate = 40% of New Machines + 60% of Old Machines

=  (0.4 * \frac{1}{2} + 0.6 * \frac{1}{3})  
= 0.2 + 0.2 
= 0.4
=  \frac{2}{5}  --------- (2)

Old Combined Rate = 100% of Old machines

=  (1 * \frac{1}{3}) 
=  \frac{1}{3}  --------------- (3)

Using above three equations -

(\frac{2}{5} - \frac{1}{3})/\frac{1}{3}* 100

On solving  Percent Increase = 20%

Hence A

sananoor · Answer

okay lets suppose that initially 10 machines were working and their rate was one toy per 3 mins. so it means 20 toys per hour. So total 10*20 = 200 toys with old machines
now 40% of machines are replaced with new one, it means 4 new machines and each machine rate is one toy per 2 mins. so it means 60/2 = 30 toys in an hour
4*30 + 6*20 (old rate) = 120 +120 = 240 (40 extra toys)
240-200/200 = 1/5 or 20..its A

CyberStein · Answer

Old Machine
New Machine

Old Rate
New Rate

If one old machine works at old rate rate, then it will produce 20 toys every hour
If one new machine works at new rate, then it will produce 30 toys every hour

Suppose for simplicity sake that there was 10 old machines ; therefore 200 toys are produced every hour
60 percent of 200 equals 120
10 new machine = 300 toys
40 percent of 300 = 120
therefore, 6 old machines plus 4 new machines = 240 toys
original toys is 200

percent increase = change / original = 40/ 200 = 20% increase

Answer A

they do give you a lot of info in this, not all of it needed. So it is best just to not blindly plug in numbers

EMPOWERgmatRichC · Answer

Hi All,

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

MonkeyWork21 · Answer

Jot down the main points...

- Current machines 1 toy per 3 mins
- New machines 1 toy per 2 mins
- Replace 40% of some unknown # of machines with the faster/better machines!

In your head...

- Hmmm... well a good place to start is how much more efficient are these new machines?
- However, our rates aren't equivalent so we need to make them comparable first...
- 3 mins vs. 2 mins...let's look at how these machines perform over 6 minutes!

On paper/scratch pad...

- current machines produce 2 toys in 6 minutes
- new machines produce 3 toys in 6 minutes
- 1/2 = 50% increase (BUT remember this is if we swap 100% i.e. one current machine for a new machine)
- Only swapping out 40% of the machine fleet so only get 40% of the efficiency increase i.e. 40% of 50% = 20%

Answer = A

JeffYin · Answer

Here are my two GMAT Timing Tips for this question, both of which have been demonstrated in this thread already:

1)  Work with integers instead of fractions or decimals : By converting the rate from 1/3 or 1/2 toy per minute to 20 or 30 toys per hour, you can make the calculations easier and faster.

2)  Choose 100 as the original value for a percent change : You can set the original value for toys per hour to 100 by assuming that you have 5 machines, and converting 40% of these 5 machines is also an easy calculation (2 machines). When you calculate that the new value for toys per hour is 120, it’s easy to see that this is a 20% increase over the original value of 100.

The links above will have growing lists of questions that you can use to practice each timing tip.

Please let me know if you have any questions about how I would do this question most efficiently, and I'd be happy to post a video solution!

Salsanousi · Answer

Assume we have 10 machines.

1 machine can produce  \frac{1}{3} * 60 = 20  toys in 1 hour

10 * 20 = 200

now if we replace 4 out of 10

we have 6 working at 20 toys per hour so 120

The four remaining work at  \frac{1}{2} * 60 = 30  toys per hour

30 * 4 = 120

New productivity = 120 + 120 = 240

Percentage =  \frac{240 - 200}{200} * 100 = \frac{40}{200} = \frac{4}{20} = \frac{1}{5} * 100 = 20 percent

answer choice A

ScottTargetTestPrep · Answer

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 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

fireagablast · Answer

Rate 1: 1 toy every 3min = 60/3 * 1 = 20 toys per hour
Rate 2: 1 toy every 2min = 60/2 * 1 = 30 toys per hour

Old rate = 20 toys per hour
new rate = 3/5(20) + 2/5(30) = 12 + 12 = 24 --> 3/5 = 60% rate 1, 2/5 = 40% rate 2
% difference = 24-20/24 = 4/20 = 1/5 = 20%

ag153 · Answer

Hi, can you pls tell me the approach to this question to solve it more efficiently?

EMPOWERgmatRichC · Answer

Hi avyagarg,

Most GMAT questions can be solved in more than one - and there's often a strategic approach that is faster than a traditional 'math' approach. 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%

A

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

sete1703 · Answer

Bunuel  I've seen this question on the OG Guide 2021 Quant Review. How is it possible? Thank you

EMPOWERgmatRichC · Answer

Hi sete1703,

Are you asking why this question appears in more than one version of that book? To start, many questions in the Official Guides are carry-overs from the prior version (with the main Official Guide, only about 10% - 15% of the questions are removed and replaced with 'new' prompts each year - and the GMAT2021 book has almost all the exact same questions as the GMAT2020 book). Since most GMATers buy just one version of the book, keeping some of the same material won't make a difference to those people. In addition, the cost of organizing, editing and printing a large book of GMAT questions is an expensive, time-consuming task - so using some of the same 'pieces' from the prior version cuts down on those expenses.
 
GMAT assassins aren't born, they're made,
Rich

SrAD · Answer

Hi Bunuel could you explain your solution a little bit more? How did you get 1.5 times as efficient and how did you arrive at 60?

Bunuel · Answer

Old machine assembles 1 toy in 3 minutes
New machine assembles 1 toy in 2 minutes. So,  1.5  toys in 3 minutes.

sharmashagun770 · Answer

I used a different logic:
Let us say there are 100 machines. Now, the 60 machines will produce the same number of toys before and after the change. So, we need the value of the increase in the rate of output produced by these 40-odd machines.

Now, 
old rate per machine = 1/3 toy per minute
new rate per machine = 1/2 toy per minute

Now the increase in toys produced by these 40 machines =
((Increase in rate per machine/Old rate)*Number of machines)= (1/2-1/3)/(1/3) * 40= *40 = 1/2*40=20

Note: We have not multiplied by 100 to calculate the percentage because we are already taking the rate and % age is essentially a rate per 100. However, we only need output for these 40, not all 100.

Bunuel , can you correct if I am wrong?

Bunuel · Answer

20 you get there is the number of additional toys produced by 40 new machines in 3 minutes. 40 old machines produce 40 toys in 3 minutes and 40 new machines, working at 1.5 times the rate of old machines, will produce 60. So, your solution is not complete.

Each machine at a toy factory assembles a certain kind of toy at a co

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