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Difficulty:
5%
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Question Stats:
91% (01:27) correct
9%
(01:59)
wrong
based on 676
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History
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Working at their respective constant rates, machine A makes 100 copies in 12 minutes and machine B makes 150 copies in 10 minutes. If these machines work simultaneously at their respective rates for 30 minutes, what is the total number of copies that they will produce?
(A) 250
(B) 425
(C) 675
(D) 700
(E) 750
(A) 250
(B) 425
(C) 675
(D) 700
(E) 750
EMPOWERgmatRichC
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Joined: 19 Dec 2014
Last visit: 31 Dec 2023
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Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
Hi All,
This question is essentially just about the two rates involved; as such, the math can be done in a variety of ways (depending on how you want to organize the information).
We're given the rates of 2 machines:
1) Machine A makes 100 copies in 12 minutes
2) Machine B makes 150 copies in 10 minutes.
We're asked for the total number of copies that the two machines will produce in 30 minutes.
30 minutes/12 minutes = 2.5 'sets' of 100 copies
30 minutes/10 minutes = 3 'sets' of 150 copies
(2.5)(100) + 3(150) =
250 + 450 =
700 copies
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This question is essentially just about the two rates involved; as such, the math can be done in a variety of ways (depending on how you want to organize the information).
We're given the rates of 2 machines:
1) Machine A makes 100 copies in 12 minutes
2) Machine B makes 150 copies in 10 minutes.
We're asked for the total number of copies that the two machines will produce in 30 minutes.
30 minutes/12 minutes = 2.5 'sets' of 100 copies
30 minutes/10 minutes = 3 'sets' of 150 copies
(2.5)(100) + 3(150) =
250 + 450 =
700 copies
Final Answer:
GMAT assassins aren't born, they're made,
Rich
General Discussion
rate a= 100/12 copy/min = 25/3 copy/min
rate b = 150/10 copy/min = 15 copy/min
rate a + rate b = rate(ab)
now work done tog = rate(ab) * time ---> (work tog for 30 mins)
work = (25+45)/3 * 30 = 700 copies
rate b = 150/10 copy/min = 15 copy/min
rate a + rate b = rate(ab)
now work done tog = rate(ab) * time ---> (work tog for 30 mins)
work = (25+45)/3 * 30 = 700 copies
Divyadisha
Current Student
Joined: 18 Oct 2014
Last visit: 01 Jun 2018
Posts: 659
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT 1: 660 Q49 V31
Posts: 659
RSOHAL
Machine A can produce 100 *30/12= 250 copies
And, Machine B can produce 150* 30/10= 450 Copies
Total producing 700 Copies.
D is the answer
shuvodip04
Joined: 05 Oct 2017
Last visit: 02 Mar 2022
Posts: 86
Location: India
Concentration: Finance, International Business
Schools: IIMB IIMA ISB'22 (S) IIMA PGPX'22 (I)
GMAT 1: 660 Q48 V33
GMAT 2: 700 Q49 V35 (Online)
GPA: 4
WE:Analyst (Energy)
RSOHAL
A makes in 12 min 100 copies..so in 1 min it makes 25/3 copies
B makes in 10 min 150 copies..so in 1 min it makes 15 copies
So working together A+B in 1 min makes = 25/3+15 = 70/3 copies
So in 30 min they will make = 30*70/3=700 copies so ans is D
GMATWhizTeam
Expert
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Last visit: 25 Jun 2026
Posts: 3,374
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Expert reply
GMAT 2: 760 Q51 V40
Posts: 3,374
This is a simple question on the concept of Rates.
From the first statement in the question, we can find out the respective rates at which the machines work. Then, we can multiply the rate values with the time to obtain the total work done.
So, the only equation/formula that you need to solve this question is the equation,
Work = Rate * Time
Modifying the above can give us the equation for rate as Rate = \(\frac{Work }{ Time}\).
Rate at which machine A copies = \(\frac{100 }{ 12}\) copies per minute
Rate at which machine B copies = \(\frac{150 }{ 10}\) = 15 copies per minute.
Now, we have been told that each of these machines work independently for 30 minutes; therefore, time = 30 minutes. The number of copies produced by each machine will represent the work done by that machine.
Number of copies produced by machine A = Rate of machine A * Time = \(\frac{100 }{ 12 }\)* 30 = 250
Number of copies produced by machine B = Rate of machine B * Time = 15 * 30 = 450
Therefore, total copies produced by the two machines = 250 + 450 = 700.
The correct answer option is D.
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From the first statement in the question, we can find out the respective rates at which the machines work. Then, we can multiply the rate values with the time to obtain the total work done.
So, the only equation/formula that you need to solve this question is the equation,
Work = Rate * Time
Modifying the above can give us the equation for rate as Rate = \(\frac{Work }{ Time}\).
Rate at which machine A copies = \(\frac{100 }{ 12}\) copies per minute
Rate at which machine B copies = \(\frac{150 }{ 10}\) = 15 copies per minute.
Now, we have been told that each of these machines work independently for 30 minutes; therefore, time = 30 minutes. The number of copies produced by each machine will represent the work done by that machine.
Number of copies produced by machine A = Rate of machine A * Time = \(\frac{100 }{ 12 }\)* 30 = 250
Number of copies produced by machine B = Rate of machine B * Time = 15 * 30 = 450
Therefore, total copies produced by the two machines = 250 + 450 = 700.
The correct answer option is D.
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12 mins 100 copies i.e 60 mins 500 copies
10 mins 150 copies i.e 60 mins 900 copies
i.e 60 mins 1400 copies
i.e 30 mins 700 copies
Option E
10 mins 150 copies i.e 60 mins 900 copies
i.e 60 mins 1400 copies
i.e 30 mins 700 copies
Option E
Posts: 1,070
RSOHAL
I don't like fractional rates and prefer working with easy time parts.
A makes 100 in 12 minutes, so 500 per hour.
B makes 150 in 10 minutes, so 900 per hour.
Together they make 1400 per hour.
So in a half hour, they make 700.
Answer choice D.
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