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

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

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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....

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 (https://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

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

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

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

answer D

The rate of machine P is 1500/m.
The combined rate of machines P and Q is 1500/n.

Thus, the rate of machine Q is:

1500/n - 1500/m = 1500m/nm - 1500n/nm = 1500(m - n)/nm

So, the time it takes Machine Q to cover 1500 jars is:

Time = 1500/1500(m - n)/nm

Time = nm/(m - n)

Answer: D

If machine Q doesn't do anything, then m and n would be equal (P alone would take the same time as P and Q together, because Q isn't doing anything). And if Q isn't doing anything, it would take Q an infinite amount of time to do the job, so when m=n, we need to get zero in the denominator of the right answer, and only D or E could be right. But ordinarily n < m (the time for the two machines together is less than the time for either alone), so answer E will usually be negative, which makes no sense, and D is the only answer that could be right.