At 12:00 noon, a machine, operating at a fixed rate, starts processing

Question

At 12:00 noon, a machine, operating at a fixed rate, starts processing a large set of identical items. At 1:45 p.m., the twenty-first item has just been processed, and 15 have not yet been processed. At what time will all 36 items be processed?

A. 2:25 pm
B. 3:00 pm
C. 3:27 pm
D. 4:13 pm
E. 5:15 pm

Kudos for a correct solution.

A. 2:25 pm 
B. 3:00 pm 
C. 3:27 pm 
D. 4:13 pm 
E. 5:15 pm

Bowtye · Accepted Answer

The initial 21 items took 1 hour and 45 minutes to process (which equals 105 mins).

105 mins / 21 items = 5 mins per item

we have 15 items remaining, so 15 items * 5 mins per item = 75 mins (or 1 hour and 15 mins)

Initial start time was 12 noon and we left off at 1:45 pm after the first 21, we add the additional 1 hour and 15 mins for the remaining 15 items and we get 3 pm.

Answer (B) 3:00 pm

iamdp · Answer

Hi

1 hr 45 min = 105 minutes for 21 items

ie 5 min/item

Therefore for 36 items time =5*36 = 180 minutes ie 3hrs from 12 ie 3pm

gmat6nplus1 · Answer

It takes 1h and 45 minutes to complete 21 items.

1h45m=7/4h.

Rate=21/(7/4)=12items/hour. 36 items are ready in 3 hours from noon.

answer B

rdoshi · Answer

1 hr and 45 min => 7/4 hrs for 21 units

therefore, 1/12 hr for 1 unit and hence 3 hrs for 36 units.

3 hrs after noon = 3:00 pm

Thus, answer is (B)

peachfuzz · Answer

let r=rate
r*(7/4)=21
r=12

12*t=36
t=3

starting at 12:00 noon and adding 3 hrs, we get 3:00pm

Answer: B

EMPOWERgmatRichC · Answer

Hi All,

These types of Rate questions can be solved using a number of different math 'methods.' For most Test Takers, figuring out the 'time per item' is probably the easiest concept. Since the machine is working at a constant rate though, we can also use a ratio to get to the correct answer.

We're told that the machine takes 105 minutes to make 21 items. We then have to figure out how long that same machine takes to make another 15 items. The ratio can actually be written in a few different ways....

21 items/15 items = 105 minutes/X minutes

21/15 = 7/5

7/5 = 105/X

X = 75 minutes

So, this means that 75 minutes after 1:45pm, the machine will finish the job. 75 minutes after 1:45pm is 3:00pm (although from the answer choices, you would not have to do all of that math).

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

23a2012 · Answer

theanswer is B

the first 21 items took 105 minutes to processe with fixed rate=1/5
so the 15 items will need to 75 minutes to processe 
total time=105+75=180 
3 hours from 12pm-3pm

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

At 1:45, that is, 105 minutes after starting, the machine has completed 21/36 = 7/12 of the job. Let T be the whole time in minutes. For the total time, set up a proportion
part/whole = 105/T = 7/12.

Remember, with  proportions , we can cancel a common factor in the two numerators; cancel the factor of 7.
15/T = 1/12.

Now, cross-multiply, and use the  doubling & halving  shortcut for multiplying.
T = 15*12 = 30*6 = 180

Now, 180 minutes = 3 hours, so the task finishes 3 hours later, at 3 p.m.

Answer = (B)

ScottTargetTestPrep · Answer

We see that the machine processes 21 items in 1¾ hours, or 105 minutes. Thus, the rate of the machine is:

105/21 = 5 minutes per item

At this rate, the machine will process 36 items in 36 x 5 = 180 minutes, or 3 hours. So it will finish at 3:00 p.m.

Answer: B

bumpbot · Answer

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At 12:00 noon, a machine, operating at a fixed rate, starts processing

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