A company uses 2 machines to fill an order for 3,360 bottle caps.

Question

A company uses 2 machines to fill an order for 3,360 bottle caps. Machine A can produce 72 bottle caps every 24 minutes, and it can run for 4 hours before it must undergo a 3-hour recalibration procedure. Machine B can produce 48 bottle caps every 12 minutes, and it can run for 4 hours before it must undergo a 2-hour recalibration procedure. If both machines begin working at the same time, and are working whenever they are not being recalibrated, then how many of the 3,360 bottle caps are made by machine B ?

A. 1,440
B. 1,620
C. 1,680
D. 1,920
E. 2,160

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A. 1,440
B. 1,620
C. 1,680
D. 1,920
E. 2,160

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Vi06 · Accepted Answer

Machine A: 72 caps in 24 min --> 3 cap in 1 min (72/24)
Caps by Machine A in n hours (n*60 min)= 3*n*60

Machine B: 48 caps in 12 min --> 4 cap in 1 min (48/12)
Caps by Machine B in n hours (n*60 min)= 4*n*60

4 hours  
  Next 2 hours   
  Next 1 hour   
  Next 3 hours   
  Next 1 hour   
 
  Machine A  
 720  
  3-hour recalibration procedure   
 0  
  540   
  180   
 
  Machine B  
 960  
  2-hour recalibration procedure   
  240   
  720   
  2-hour recalibration procedure

1680  
  
 1920  
 3180 
 3360

Work done by B: 960+240+720= 1920

purse1234 · Answer

Machine A: 72 caps in 24 minutes; the rate per hour is 72*60/24 = 180 caps/hour
Machine B: 48 caps in 12 minutes; the rate per hour is 48*60/12 = 240 caps/hour

The rate of machine A to machine B is 180/240 = 3/4

Therefore, 3,360 bottle caps are made by machine B = (3,360*4)/(3+4) = 1,920 caps

Choice D.

ioannispar · Answer

I have calculated that D is the correct answer. I took a convntional approach of calculating the production per hour for each machine and found out that after two cycles of production and repair 3360 caps would have produced and that machine B would have contributed 8 (2 cycles * 4 h/cycle) * 240 (caps/hour) = 1920 caps. After the 8 hour timeframe machine B would stop for maintenance, but machine A would keep working for 1 more hour, because it requires one hour longer maintenance, totaling also 8 hours of work. So, its contribution would be 8 * 180 = 1640. And the total production in 9 hours would be 3360.

AVMachine · Answer

For Machine A:
72 Caps in 24 min; 1 min -> 72/24 Caps; 1 Hour -> 72*60/24 = 180 Caps:

For Machine B:
48 Caps in 12 min; 1 min -> 48/12 Caps; 1 Hour -> 48*60/12 = 240 Caps:

Combined Output in One Hour (A+B): 420 Caps

At starting both can work for 4 hours: Output= 420*4 = 1680

Remaining: 3360-1680 = 1680 (Both working together will require 4 hours as previous)

Now, A will be Calibrated for 3 hours, and B will Calibrated for 2 Hours;

After calibration B will have to work for 4 Hours to complete the work;

So the caps made by B would be: 240 * 8 = 1920

onlymalapink · Answer

I dont get it so machine b will sit on its hutt and not work a extra hour until a is fixed where is this mentioned? all calculations are wrong otherwise.

Dereno · Answer

If both machines begin working at the same time, and are working whenever they are not being recalibrated

this is what is mentioned in the question. And I assume u are aware of the machines A and B have different recalibration hours - 3 hrs and 2 hrs respectively. And both work for 4 hrs continuously, with the difference being their hours of idle state (recalibrating time). So B starts to work the third hour , when A was idle.

Hope this answers ur doubt.

I would suggest u to take a look at the most favourable reply.

Edoua · Answer

Machine A produce 72 caps in 24 min -- rate is 3caps /min and works for 4 hours before recalibration means in 4 hours A produce 3*4*60 =720 caps before a 3-hour recalibration

Machine B produces 48 caps in every 12 mins --- rate is 4 caps/min then works for 4hours means it produces in 4 hours 4*4*60= 960 caps before a 2-hour recalibration

Both starts working together

Time; 0--1--2--3--4--5--6--7--8--9--10--11--12--13--14--15

mA /------720---/-stop---/-------720----/--stop------/----720----
mB /-----960----/--stop/-----960----/--stop--/---960-----------

A+B /----1680---/---stop/----3360--------/

both start together after 4 hours they produce 1680 then recalibration for them. B will start 1 hour early than A and will produce 240 the total will be 1920 before A join and they work together for 3 hours from 7 to 10 to add (3*60+4*60) *3hours =420*3=1260 for the total to be 3180 and A will continuous 1 hour alone to produce 3*60=180 during this time with B already started it second recalibration to complete the 3360 needed.

total produce by mB is 960*2= 1920 caps

Natansha · Answer

Hi  KarishmaB  , how can we do the below without taking into account the time a machine is working or stopping for recaliberation?

KarishmaB · Answer

You have to take their recalibration time into account. It works here because both ended up working for same time but you cannot know that without checking.

Machine A produces 72 caps every 24 mins. In 1 hour i.e. 60 mins, it produces 72/24 * 60 = 180 caps (when it is working)
Machine B produces 48 caps every 12 mins. In 1 hour i.e. 60 mins it produces 48*5 = 240 caps. (when it is working)
Together they are producing 180 + 240 = 420 caps per hour when both are working.

Say we start at 12 noon. In 4 hours (by 4 pm) they together produce (180 + 240) * 4 = 1680 caps

Next 2 hours, both machines stop. It is 6 pm. Now Machine B starts back and produces 240 caps next. Now we have total 1920 caps and it is 7 pm and we have remaining 3360 - 1920 = 1440 caps.

In next 3 hours, both work and produce 420*3 = 1260 caps so now only 1440 - 1260 = 180 caps are remaining at 10 pm. 
Machine A will still work for another hour so it produces 180 caps till 11 pm and the order is filled.

Machine B produced 8*240 = 1920 caps

Answer (D)

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A company uses 2 machines to fill an order for 3,360 bottle caps.

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	4 hours	Next 2 hours	Next 1 hour	Next 3 hours	Next 1 hour
Machine A	720	3-hour recalibration procedure	0	540	180
Machine B	960	2-hour recalibration procedure	240	720	2-hour recalibration procedure
	1680		1920	3180	3360

GMAT Problem Solving (PS) Questions

A company uses 2 machines to fill an order for 3,360 bottle caps.

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