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Machines P and Q are two different machines that cover jars in a facto

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Machines P and Q are two different machines that cover jars in a facto [#permalink]

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Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?

A. m/(m + n)
B. n/(m + n)
C. mn/(m + n)
D. mn/(m – n)
E. mn/(n – m)


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[Reveal] Spoiler: OA

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Machines P and Q are two different machines that cover jars in a facto [#permalink]

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New post 27 Feb 2015, 06:00
Work in one hour to get 1500 parts covered
by P---> 1/m
by P+Q--->1/n
by only Q--->1/n-1/m=(m-n)/mn
Total time= mn/(m-n)
answer D

Last edited by ynaikavde on 28 Feb 2015, 15:44, edited 1 time in total.
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Machines P and Q are two different machines that cover jars in a facto [#permalink]

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New post 27 Feb 2015, 06:48
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Bunuel wrote:
Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?

A. m/(m + n)
B. n/(m + n)
C. mn/(m + n)
D. mn/(m – n)
E. mn/(n – m)


Kudos for a correct solution.


This question seems tricky, but I hope that I have been able to crack it! Here's my solution:

Since we are asked to find the number of hours it takes Machine Q to manufacture 1500 jars, we need to first find the rate at which Machine Q operates. So Machine P has a rate of \(\frac{1500}{m}\) because it can manufacture 1500 jars in m hours. Together, Machine P and Machine Q's combined rate (when working simultaneously) is \(\frac{1500}{n}\), this is because it takes Machine P and Q n hours to manufacture 1500 jars when working together. Therefore Machine Q's rate is \(\frac{1500}{n}\) \(-\) \(\frac{1500}{m}\), which simplifies to \(\frac{1500*(m - n)}{mn}\). We need to find the number of hours it takes Machine Q to produce 1500 jars, so that would equal \(\frac{1500}{(1500*(m - n))/mn}\), which simplifies to \(\frac{mn}{(m - n)}\).

I think the answer is D!

Please consider giving me Kudos, if you found this post helpful. Thanks! :)

Last edited by kdatt1991 on 01 Mar 2015, 11:00, edited 1 time in total.
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Re: Machines P and Q are two different machines that cover jars in a facto [#permalink]

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New post 27 Feb 2015, 08:49
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Time to use SMART numbers.

Rate of p = 1500jars/m hours
Let m = 15 hours.
Therefore rate of p = 100 jars per hour

Rate of p + rate of q = 1500jars/n hours.
Let n = 10 hours. We will assume q has a positive rate of work.

Therefore rate of p + rate of q = 150jars per hour.

Solving for q leads us to rate of q = 50 jars per hour.

1500jars/50jars per hour = 30 hours.

(15*10)/(15-10) = 30 hours.

Answer is D.

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Re: Machines P and Q are two different machines that cover jars in a facto [#permalink]

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New post 27 Feb 2015, 08:50
ynaikavde wrote:
Work in one hour to get 1500 parts covered
by P---> 1/m
by P+Q--->1/n
by only Q--->1/n-1/m=(m-n)/mn
Total time= mn/(m-n)
answer E


You mean D. But yes, that's the right answer.

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Re: Machines P and Q are two different machines that cover jars in a facto [#permalink]

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New post 28 Feb 2015, 10:56
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Answer is D...


with the approach of taking SMART numbers,

lets summarize the given info : Machine p : 1500 jars in M hours

Machine P& Q : 1500 jars in N hours


so lets choose M= 5 and N =3 hours so we have for working rates of p& Q : (1/p + 1/Q ) *3 = 1

so we have : ( 1/5 + 1/Q ) *3 =1 OR : ( 5+Q/5Q ) *3 =1 and : 15 +3Q =5Q so, 2Q= 15 Or : Q =15/2

WE obtain Q =15/2 so we plug in M=5 and N=3 in the answer choices and see which answer choice gives us the result 15/2 :

A ) : m/(m+n) = 5/(5+3) = 5/8 : doesn't match , so reject

B ) : n/ (m+n) = 3/ (5+3) = 3/8 : does n't match, so reject

C) : mn/( m+n) = 3*5 /(5+3) = 15/8 : doesn't match, so reject

D) : mn / ( m-n) = 3*5 /(5-3) = 15/2 : THE ANSWER

E) : mn/(n-m) = 3*5 / (3-5) = - 15/2 : doesn't match ,so reject



So, answer is D....
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Re: Machines P and Q are two different machines that cover jars in a facto [#permalink]

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New post 02 Mar 2015, 05:42
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Bunuel wrote:
Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?

A. m/(m + n)
B. n/(m + n)
C. mn/(m + n)
D. mn/(m – n)
E. mn/(n – m)


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

This is a particularly challenging, one because we have variables in the answer choices. I will show an algebraic solution, although a numerical solution (http://magoosh.com/gmat/2012/variables- ... -approach/) is always possible.

“Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars? ”

Since the number “1500 jars” appears over and over, let’s arbitrarily say 1500 jars = 1 lot, and we’ll use units of lots per hour to simplify our calculations.

P’s individual rate is (1 lot)/(m hours) = 1/m. The combined rate of P & Q is (1 lot)/(n hours) = 1/n. We know
(P’s rate alone) + (Q’s rate alone) = (P and Q’s combined rate)
(Q’s rate alone) = (P and Q’s combined rate) – (P’s rate alone)
(Q’s rate alone) = 1/n – 1/m = m/ (nm) – n/ (nm) = (m – n)/(nm)

We now know Q’s rate, and we want the amount of 1 lot, so we use the “art” equation.
1 = [(m – n)/ (nm)]*T
T = (mn)/(m – n)

Answer = D
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Re: Machines P and Q are two different machines that cover jars in a facto [#permalink]

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New post 10 Apr 2015, 06:34
Bunuel wrote:
Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?

A. m/(m + n)
B. n/(m + n)
C. mn/(m + n)
D. mn/(m – n)
E. mn/(n – m)


Kudos for a correct solution.



let 1 jar = 1 unit

let m = 5 and n = 3

P does 300 units/hr
P & Q together do 500 units/hr
so Q does 200 units/hr

hence, Q needs 7.5 hrs to produce 1500 jars

options D satisfies
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Machines P and Q are two different machines that cover jars in a facto [#permalink]

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New post 10 Apr 2015, 07:42
Bunuel wrote:
Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?

A. m/(m + n)
B. n/(m + n)
C. mn/(m + n)
D. mn/(m – n)
E. mn/(n – m)


Kudos for a correct solution.


\(\frac{1}{Q} = \frac{1}{n} -\frac{1}{m}\)

\(Q= \frac{m*n}{(m-n)}\)

answer D
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Re: Machines P and Q are two different machines that cover jars in a facto [#permalink]

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Re: Machines P and Q are two different machines that cover jars in a facto   [#permalink] 01 Mar 2017, 10:42
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