A company has two models of computers, model M and model N

Question

A company has two models of computers, model M and model N. Operating at a constant rate, a model M computer can complete a certain task in 18 minutes and a model N computer can complete the same task in 9 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model M computers were used?

(A) 2

(B) 3

(C) 6

(D) 9

(E) 12

Source: Gmat Hacks 1800

(A) 2

(B) 3

(C) 6

(D) 9

(E) 12

Source: Gmat Hacks 1800

KarishmaB · Accepted Answer

Time taken by model M computer to complete 1 work = 18 mins so Rate of work of model M = 1/18 work/min
Time taken by model N computer to complete 1 work = 9 mins so Rate of work of model N = 1/9 work/min

1 work was completed in 1 min so combined rate of work of x computers of M type and x computers of N type = 1 work/min
(because Work = Rate*Time)

x/18 + x/9 = 1 (Rates are additive)
x = 6

Answer (C)

There are only two things to remember in work rate questions:
1. Rates are Additive.
2. Work = Rate*Time 
(which implies Rate = 1/Time)

MacFauz · Answer

Let's say 1 work is processing 18 gb of data.

Model M : 1 gb per min

Model N : 2 gb per min

Working together, 1 M and 1 N = 3 gb per min

So, 6 times as many computers would work at 18 gb per min.

So no. of M = 6

Answer is C

Bunuel · Answer

Another copied question from Gmat hacks. Original question from GMAT Prep: Discussed here: a-company-has-two-types-of-machines-type-r-and-type-s-130108.html

amgelcer · Answer

M = 1 job in 18 min → 1/18
N = 1 job in 09 min → 1/9

M+N = 1/18 + 1/9 = 3/18 = 1/6

M+N = 1 job in 6 minutes.

To complete the job in 1 min will be necessary 6 M+N.

Ans C

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JeffTargetTestPrep · Answer

We are given that the model M computer can complete a task in 18 minutes; thus the rate of model M is 1/18. We are also given that a model N computer can complete the same task in 9 minutes; thus the rate of model N is 1/9.

We need to determine the number of each model of computer used if the task were completed in 1 minute. If that is the case, then the combined rate of all the computers is 1/1 = 1. We can let n = the number of computers used for each model of computer and create the following equation:

rate of n model M computers + rate of n model N computers = 1

n(1/18) + n(1/9) = 1

Multiplying the entire equation by 18, we have:

n + 2n = 18

3n = 18

n = 6

Answer: C

gracie · Answer

let c=number of pairs
combined rate=1/6 
c*1/6*1 minute=1 task
c=6 pairs=6 model M computers

gmatcafe · Answer

If model M computer can complete a certain task in 18 minutes and a model N computer can complete the same task in 9 minutes, then working together one model M computer and 1 Model N computer complete the same task in 6 minutes:
1/18+1/9=1/6
If the company used the same number of each model of computer to complete the task, then to complete the task in 1 minute, 6 computers of each model were used. C)

bumpbot · Answer

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A company has two models of computers, model M and model N

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