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

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Each machine at a toy factory assembles a certain kind of toy at a co  [#permalink]

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23 Jul 2017, 11:00
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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 %

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Each machine at a toy factory assembles a certain kind of toy at a co  [#permalink]

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23 Jul 2017, 11:47
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carcass 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

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%

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Re: Each machine at a toy factory assembles a certain kind of toy at a co  [#permalink]

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23 Jul 2017, 23:54
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carcass 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

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%.

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Re: Each machine at a toy factory assembles a certain kind of toy at a co  [#permalink]

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24 Jul 2017, 00:20
1
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
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Re: Each machine at a toy factory assembles a certain kind of toy at a co  [#permalink]

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10 Sep 2017, 01:25
1
carcass 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

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

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
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Re: Each machine at a toy factory assembles a certain kind of toy at a co  [#permalink]

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07 Dec 2017, 14:58
1
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%

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Re: Each machine at a toy factory assembles a certain kind of toy at a co  [#permalink]

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09 Aug 2018, 23:48
1
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!

- 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!

- 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%

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Re: Each machine at a toy factory assembles a certain kind of toy at a co  [#permalink]

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10 Aug 2018, 00:37
1
carcass 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 %

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
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Re: Each machine at a toy factory assembles a certain kind of toy at a co  [#permalink]

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10 Aug 2018, 09:34
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!
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Re: Each machine at a toy factory assembles a certain kind of toy at a co  [#permalink]

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22 Oct 2018, 11:07
carcass 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 %

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

Re: Each machine at a toy factory assembles a certain kind of toy at a co &nbs [#permalink] 22 Oct 2018, 11:07
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