Two models of computers

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metallicafan: Master | Next Rank: 500 Posts; Posts: 142; Joined: Sun Jun 12, 2011 7:55 amFollowed by: 3 members; Thanked: 5 times

by metallicafan » Tue Apr 24, 2012 9:08 am

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: www.gmathacks.com

OA: C

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Source: Beat The GMAT — Problem Solving | Tue Apr 24, 2012 9:08 am

Shalabh's Quants: Master | Next Rank: 500 Posts; Posts: 134; Joined: Fri Apr 06, 2012 3:11 amFollowed by: 5 members; Thanked: 35 times

by Shalabh's Quants » Tue Apr 24, 2012 9:43 am

metallicafan wrote: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: www.gmathacks.com

OA: C

Comp M & N's 1 min. job = 1/18+1/9 = 1/6.

It means to complete a job, they need 6 mins. Or to do it 1 min. M & N should be 6 each.

Last edited by Shalabh's Quants on Tue Apr 24, 2012 11:00 pm, edited 1 time in total.

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tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Tue Apr 24, 2012 9:19 pm

Rate problems that do not give a specific amount for the job can best be solved by picking a number for the job so you don't have to work with fraction. In this case you can pick 36 becuase it divides easily into both 9 and 18.

The rate formula is D=R(t) and you often have to use this formula multiple times for different scenarios within a problem.

The first information we get is that M can do the job in 18 minutes that means that 18(M)=36 - thus the rate of M=2.

Next we get that N can do the job in 9 minutes that means 9(N)=36 - the rate of N=4

Then it asks if you are using the same number of each machine and you finish in one minute how many of each machine.

the task stays at 36 because it hasn't changed and the time we are looking for is 1. when machines work together you have to add their rates within the rate formula but here we have some number of each machine thus the combined rate is going to be the sum of that number times each rate.

This gives you the formula: (x(2)+x(4))(1)=36 - which can be solved to 6x=36 thus x=6 and there are 6 of each type of machine, thus the answer is C.

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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redng: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon Mar 12, 2012 7:08 pmFollowed by: 1 member

by redng » Tue Apr 24, 2012 10:05 pm

M's rate = 1/18
N's rate = 1/9
x = number of machines

(1/18x + 1/9x) * (1min) = 1task
1/6x = 1
x = 6

C

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spartacus1412: Master | Next Rank: 500 Posts; Posts: 110; Joined: Wed Feb 22, 2012 11:28 pmFollowed by: 1 member; Location: India; Thanked: 13 times

by spartacus1412 » Tue Apr 24, 2012 11:12 pm

M's rate = 1/18 in 1 minute
N's rate = 1/9 in 1 minute

lets say x number of each m and n machine were used:
therefore, work done in 1 min is:

X*(1/18 + 1/9)
Since all the work is done in 1 min

X*(1/18 + 1/9) = 1
Solving for X, X = 6, therefore 6 machines of M and N each are used.

Its do or die this time!
Practise, practise and practise.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Tue Apr 24, 2012 11:27 pm

metallicafan wrote: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

Some good solutions posted already; we can also use the basic work formula for two workers:

CT = combined time
A = time for worker 1 to do job on its own
B = time for worker 2 to do job on its own

CT = (A*B)/(A+B)

In this case:

CT = 9*18/(9+18) = 162/27 = 6

Since it takes 6 minutes for 1 of each machine to complete the job, we need 6 of each machine to complete the job in 1 minute: choose (C)!

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Wed Apr 25, 2012 1:43 am

Model M Computer's Rate = 1/18

Model N Computer's Rate = 1/9

Combined they do it in; 1/18 + 1/9

Actually the equation goes to: 1/18X n1 + 1/9 X n2 = 1

where n1 and n2 are the no.of machines or computers being used of each model i.e M and N

It is specifically given in the question, that the number of computers being used for both the models are the same i.e

n1 = n2

so now the equation turns out to be

n1/18 + n1/9 =1

therefore, n1/18 + 2n1/18 = 1

therefore, 3n1 = 18

therefore, n1 = 6

and so is n2

I hope this really helped to solve the works problem effectively...

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