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A certain form letter is to be sent to prospective customer

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A certain form letter is to be sent to prospective customer [#permalink] New post 11 Jan 2020, 07:00
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Question Stats:

75% (00:36) correct 25% (01:02) wrong based on 20 sessions
A certain form letter is to be sent to prospective customers. If 4 model-X computers working independently can do a combined total of 4 of the letters in 4 minutes, then 100 model-X computers working independently can do a combined total of 100 of the letters in exactly how many minutes?

(A) 4 min

(B) 10 min

(C) 25 min

(D) 40 min

(E) 100 min


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[Reveal] Spoiler: OA

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Re: A certain form letter is to be sent to prospective customer [#permalink] New post 11 Jan 2020, 09:15
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This question is based on Rate and Work. There are three theories involved
1. Rate * Time = Work Done
2. If two people are working together then their rates get added up.
3. If n number of machines with same rate(let sat R) are working together then their rates get added up and combined rate is nR.

Coming to the question:
Let rate of each computer be R. So rate of 4 computer will be 4R.
Using Rate * Time = Work Done
4R * 4mins = 4 letters
=> R = 1/4 Letters/min
Rate of 100 computers will be 100R = 100* 1/4 letters/min = 25 letters/min

Using Rate * Time = Work done
25 letters/min * Time = 100 letters
=> Time = 100/25 min = 4 mins.
So, Answer will be A

Hope it helps!
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Re: A certain form letter is to be sent to prospective customer [#permalink] New post 14 Jan 2020, 03:47
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Carcass wrote:
A certain form letter is to be sent to prospective customers. If 4 model-X computers working independently can do a combined total of 4 of the letters in 4 minutes, then 100 model-X computers working independently can do a combined total of 100 of the letters in exactly how many minutes?

(A) 4 min

(B) 10 min

(C) 25 min

(D) 40 min

(E) 100 min


Kudos for the right answer and explanation


Using the relation between Work(W) Men (M) and Time(T)



To put this into a formula



[W1][/W2]= [M1 * T1][/M2 * T2]

[4][/100] = [4 * 4][/100 * T2]

T2 = 4 Mins
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Re: A certain form letter is to be sent to prospective customer [#permalink] New post 14 Jan 2020, 23:25
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Similar formula:
(Man1*Day1)/(Work1)=(Man2*Day2)/(Work2)
Man1=4
Day1=4 min
Work1=4
Man2=100
Day=??? min
Work2=100.
So, Day2=4 mins
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Re: A certain form letter is to be sent to prospective customer [#permalink] New post 25 Apr 2020, 08:27
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The beauty of these sort of exercises is that they don't have to be done with formulas.
My approach:

machines.........letter..........minutes
4.....................4................4

now with the given, we have to establish that there is always an inverse with machines and minutes, wish we not touch the letters for the time being.

Meaning if there are more minutes, there will consequently be less machines, which will reflect itself in such a way that it would take LONGER to make 4 letters.

For instance we want to see how many machines we will have if it takes 8 minutes to make 4 letters. We multiply minutes and we divide machines.

Yielding back:

machines.........letter..........minutes
2.....................4................8


Now in our case we are interested to see how how long it would take 100 machines to make 100 letters.

We set up our equation

machines.........letter..........minutes
4.....................4................4

Following this we start off with how long it would take 100 machines to make 4 letter.-->25*4 (machines) and 4min/25 (min)

machines.........letter..........minute
100.....................4................0,16

Now we come back to the letters.

Letters and minutes have a direct relationship, yet such that only when we increase (or decrease) the letters do the minutes change. I prefer to look at it from a non-reciprocal point of view due to simplicity, meaning if we change minutes, we play around with machines instead of letters.

Now we multiply 4*25=100 letter and 0,16min*25= 4min

AND we get:

machines.........letter..........minute
100.....................100................4


Now this system works for me marvellously, I usually manage to solve these exercises in about 30-45 sec.

On top of everything, for me it always works best when I can draw a picture, just easier than using formulas.

CHeers!
Re: A certain form letter is to be sent to prospective customer   [#permalink] 25 Apr 2020, 08:27
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