VeritasKarishma Bunuel egmat,

I find this approach pretty easy and to the point , plz advice whether this is okay ?

Yes, perfectly fine.
_________________

Using longer sentences.

What we know
>1 machine produces 1 toy every 3 mins
> hence 1 machine makes 1/3 or a toy in 1 min
> hence 1 machine will make X Toys @ 1/3 *60
> hence 1 machine will make 20 toys in 60 mins or 1hr

> 40% of the machines are to be replaced
>>hence 60% of the machine will work at the same rate

Let's solve
1. Let's say 10 machines are there
> 10 machines * 20 toys per machine = 200 toys in 60 mins of 1/3. THE ORIGINAL PRODUCTION QUANTITY

2. Since 40% are replaced
PART 1. NEW MACHINE output
>((40/100)*10*) = number of new machines
> 4 new machines
> 4 NM make 1 toy every 2 mins individually
> hence 1 NM work @ 1/2 toy every min
> hence 1 NM 1/2 toy * 60 mins
> hence 1 NM 30 toys in 1 hour
> hence 4 NM make 30 *4 in 1 hour
> Total NM output = 120 in 1 hour

PART 2. Original Machine output
> 6 machines * 20 toys per 1 hour
> hence OM make 6*20 per 1 hour
> hence OM makes 120 per 1 hour

PART 3.
NM + OM = 240

PART 4.
> Change/Original * 100%
> ((240-200)/200)* 100%
> hence (40/200)*100
> hence 20%

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

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%



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

The new rate:
0.6/3+0.4/2=1/x
2.4/6=1/x
x=2.5

New number of toys per hour:
60/2.5=24

% change:
(24-20)*100/20 = 100/5=20

I really wished my brain worked like this.

Let the total number of machines are 10.

1 machine = 1 toy = 3 minutes.
1 machine = 1 hour [60 minutes = 3 * 20] = 20 toys.
10 machines = 1 hour [60 minutes] = 200 toys.

40% replaced by new: [New machine: 4 and Old machine: 6]

6 old machines = 1 hour = 6 * 20 = 120 toys
1 new machines = 1 hour [60 minutes = 2 * 30] = 30 toys.
4 new machines = 1 hour [60 minutes] = 4 * 3 = 120 toys.

Total toys = 120 + 120 = 240.

Percent increase: (240 - 200)/200 * 100 = 50%

Answer A
_________________

Let total old machines are= 100
Rate of one machine 1/3*60 = 20 per minute
Total machines produce in one hour 100*20 = 2000 Toys

40 percent or 40 machines new
Their rates in one hour = 1/2*60 =30
Their total production =30*40 = 1200 toys

Old 60 produce 20*60 = 1200 Toys

New Assemble (old + new = 60+40) produce 2400

so the percentage increase = 400/2000*100 = 20%

Answer A.
_________________

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

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
_________________

This problem can be solved without any equations.

Lets say we have 5 machines. If each machine created a toy every 3 minutes, each machine will create 20 toys in one hour. Since we have 5 machines, that's 100 toys per hour.

Now, we replace 2 of those machines (40%) with new machines that create 30 toys per hour. Now we have our 3 toys creating 60 toys per hour AND our new machines creating 30 * 2 (60 toys), giving us a total of 120 toys per hour.

100 to 120 is a 20% increase, giving us answer choice A.
_________________

Old Rate= \(\frac{1}{3}\)

New Rate = \(\frac{1}{2}\)

To make whole number: \(\frac{1}{3}\)*\(6\), \(\frac{1}{2}\)*\(6\)
\(Old Rate : New Rate=2:3\)

TOTAL RATE 2+5

\(INCREASE:\) \(\frac{3-2}{5}\)*\(100\)=20%

THE ANSWER IS A.

Bunuel I will appreciate you check my process.
_________________

I want to plug in a number which is easily divisible with all percentage or fraction; Let the number is 60

Rate is (Before replacing) 1/3 per minute

60 machine produces in one hour =1/3*0*60=1200

Production after new policy:
\(60*60\)% \(=36\) (as 40 machine is being replaced) \frac{= [fraction]1}{3}*36*60=720[/fraction]

\(60*40\)%=24, whose rate is \(\frac{1}{2}\) per minute; \(\frac{1}{2}*24*60=720\)

Total production at new policy \(= 720+720=1440\)

Total production before new policy \(=1200\)

Increase \(= 1440-1200=240\)

Percentage increase \(= \frac{240}{1200}*100\)=20%

The answer is A
_________________

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?

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

Lets assume there is 10 machine.

the current production is 60/3 *10 = 200 for all 10 machines

if we assume all the machines be replaced we will have 300 toys i.e. 100 more toys , but only 40% of machines is replaced.
Hence will take only 40% of production increase. i.e. 40 more toys
therefore 240 is total toys, 40/200*100 = 20% increase
_________________