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Math Expert V
Joined: 02 Sep 2009
Posts: 60778
Machines P and Q are two different machines that cover jars in a facto  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 78% (02:06) correct 23% (01:48) wrong based on 160 sessions

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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)

Kudos for a correct solution.

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Joined: 22 Jul 2011
Posts: 73
Machines P and Q are two different machines that cover jars in a facto  [#permalink]

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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)

Originally posted by ynaikavde on 27 Feb 2015, 07:00.
Last edited by ynaikavde on 28 Feb 2015, 16:44, edited 1 time in total.
Intern  Joined: 19 Sep 2014
Posts: 21
Concentration: Finance, Economics
GMAT Date: 05-05-2015
Machines P and Q are two different machines that cover jars in a facto  [#permalink]

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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! Originally posted by kdatt1991 on 27 Feb 2015, 07:48.
Last edited by kdatt1991 on 01 Mar 2015, 12:00, edited 1 time in total.
Manager  B
Joined: 26 May 2013
Posts: 91
Re: Machines P and Q are two different machines that cover jars in a facto  [#permalink]

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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.

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Manager  B
Joined: 26 May 2013
Posts: 91
Re: Machines P and Q are two different machines that cover jars in a facto  [#permalink]

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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)

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

Posted from my mobile device
Manager  Joined: 13 Dec 2013
Posts: 58
Location: Iran (Islamic Republic of)
Re: Machines P and Q are two different machines that cover jars in a facto  [#permalink]

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2

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

Math Expert V
Joined: 02 Sep 2009
Posts: 60778
Re: Machines P and Q are two different machines that cover jars in a facto  [#permalink]

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1
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)

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

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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.

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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Senior Manager  Joined: 07 Aug 2011
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Machines P and Q are two different machines that cover jars in a facto  [#permalink]

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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.

$$\frac{1}{Q} = \frac{1}{n} -\frac{1}{m}$$

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

Non-Human User Joined: 09 Sep 2013
Posts: 14003
Re: Machines P and Q are two different machines that cover jars in a facto  [#permalink]

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