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# At the post office, a letter must go through a sorting process with fo

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At the post office, a letter must go through a sorting process with fo  [#permalink]

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13 May 2011, 14:21
8
00:00

Difficulty:

95% (hard)

Question Stats:

36% (02:52) correct 64% (02:52) wrong based on 229 sessions

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At the post office, a letter must go through a sorting process with four distinct steps. Step 1: Mail is picked up every half hour, beginning at 6:00 am. Step 2: Mail is dropped off at the sorting center $$\frac{1}{4}$$ hour later. Step 3: Mail is sorted by zip code and stamped every $$1$$ hour, beginning at 7:00 am, and sent to regional sorting centers $$\frac{1}{3}$$ hour later. Step 4: At the regional sorting centers, incoming mail is put into the system every $$30$$ minutes, beginning at 8:00 am, and sent to individual mail carriers $$45$$ minutes later. Assuming that all mail is picked up, sorted, and dropped off on time, what is the least total amount of time that it could take the letter to go through all four steps?

(A) $$2$$ hours $$45$$ minutes

(B) $$2$$ hours $$15$$ minutes

(C) $$1$$ hour $$45$$ minutes

(D) $$1$$ hour $$20$$ minutes

(E) $$1$$ hour $$15$$ minutes

Let's see who comes up with the best way to solve this.

Spoiler: :: Knewton's OE
When faced with a complicated word problem, we must make sure we determine precisely what we are looking for and how all the pieces (or steps, in this case) relate to one another. In this problem, we’re asked to figure out the least amount of time it takes for a letter to go through the entire sorting process.

First, let's convert all of the units to minutes in order to avoid confusion later on. We need to convert $$\frac{1}{4}$$ hour, $$\frac{1}{3}$$ hour, and a half-hour. Since there are $$60$$ minutes in an hour:

$$\frac{1}{4} \hspace{2} hour=\frac{1}{4} *60 \hspace{2} minutes=15 \hspace{2} minutes$$
$$\frac{1}{3} \hspace{2} hour=\frac{1}{3} *60 \hspace{2} minutes=20 \hspace{2} minutes$$
$$\frac{1}{2} \hspace{2} hour=\frac{1}{2} *60 \hspace{2} minutes=30 \hspace{2} minutes$$

Next, let's list each step, the times when it can happen, and the time required in a clear list.

Mail picked up. Every $$30$$ minutes, starting at 6:00 am.
Dropped off. $$15$$ minutes after pick up.
Sorted and stamped. Every $$60$$ minutes, starting at 7:00 am.
Sent to regional center. $$20$$ minutes after stamp.
Put in system. Every $$30$$ minutes, starting at 8:00 am.
Sent to carrier. $$45$$ minutes after put in system.
Since mail is picked up every $$30$$ minutes beginning at 6:00 am, the process can begin either on the hour (e.g., 6:00 am) or on the half hour (e.g., 6:30 am). This is the only thing that can change — all the subsequent steps are dependent only on whether the mail was picked up on the hour or on the half hour. So, we'll try an example of each. We will begin with a time later in the day, so that we are not constrained by the times that the processes begin (for example, we do not want to wait until 8:00 am for mail to be put into the system if we can avoid doing so).

If the mail is picked up at 9:00am, it will be dropped off $$15$$ minutes later, at 9:15 am. It will be stamped and sorted at 10:00 am. It will be sent to the regional center $$20$$ minutes later, at 10:20 am. It will be put in the system at 10:30 am. It will be sent to the carrier minutes later, at 11:15 am. The total time from 9:00 am to 11:15 am is $$2$$ hours $$15$$ minutes.

If the mail is picked up at 9:30am, it will be dropped off $$15$$ minutes later, at 9:45 am. It will be stamped and sorted at 10:00 am. It will be sent to the regional center $$20$$ minutes later, at 10:20 am. It will be put in the system at 10:30 am. It will be sent to the carrier $$45$$ minutes later, at 11:15 am. The total time from 9:30 am to 11:15 am is $$1$$ hour $$45$$ minutes.

The least amount of time the entire process can take is $$1$$ hour $$45$$ minutes, so answer choice C is correct.
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Re: At the post office, a letter must go through a sorting process with fo  [#permalink]

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Updated on: 13 May 2011, 17:37
1
fluke,
I seen a similar Kaplan problem and realized that it can be solved in very efficient way if I start with the last timetable first. I am not sure about the last step whether it is 45 mins later or it can be sent to individual at 8:45 - but the answer is either C or E depending upon when it is sent to the individual. 8:45 or 9:15

7:30 - picked

7:45 - dropped

8:00 - sorted and stamped

8:30 - put into the system

8:45 - sent to individual

total time = 1 hr 15 mins

The trick is to match the time wrt to the last timetable first bcos it is going to take the max amount of time. E.g If you going to plan the trip - plan the last part first. Another example is if I have to reach offfice at 8:00 AM then I will reverse engineer the other times wrt 8:00 AM. The forward planning is not an option.

Originally posted by gmat1220 on 13 May 2011, 17:24.
Last edited by gmat1220 on 13 May 2011, 17:37, edited 1 time in total.
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Re: At the post office, a letter must go through a sorting process with fo  [#permalink]

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13 May 2011, 17:29
gmat1220 wrote:
7:30 - picked

7:45 - dropped

8:00 - sorted

8:30 - put into the system

8:45 - sent to individual

total time = 1 hr 15 mins

The trick is to match the time wrt to the last timetable first bcos it is going to put the plan in jeopardy and take the max amount of time. E.g If you going to plan the trip - plan the last part first. Another example is if I have to reach offfice at 8:00 AM then I will reverse engineer the other times wrt 8:00 AM.

In this problem start with step 5 first. And reverse engineer the other times.

Last step starts at 8:30 and sent to individual mail carriers 45 minutes later.
So ends at 9:15
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Re: At the post office, a letter must go through a sorting process with fo  [#permalink]

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13 May 2011, 17:52
1
least amount of time to finish all 4 steps = > least waiting time between steps.

step1 can start at 7.30
step1/step2 7.30 - 7.45 (15 mins)

wait - (7.45 to 8.00)15 mins

step3 8.00 to 8.20 (20 mins)
wait 10 mins

step4 8.30 to 9.15 (45 mins)

i.e 105 mins = 1hrs 45min

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Re: At the post office, a letter must go through a sorting process with fo  [#permalink]

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13 May 2011, 19:16
2
1
Regular Cycle
--------------

6:00 AM, 6:30 AM, 7:00 AM,7:30 AM - Mail picked up

6:15 AM, 6:30 AM, 6:45 AM. 7:00 AM, 7:15 AM. 7:30 AM, 7:45 AM - Dropped Off at sorting center

7:00 AM, 8:00 AM, 9:00 AM - Sorted and stamped

7:20 AM, 7:40 AM, 8:00 AM, 8:20 AM, 8:40 AM, 9:00 AM - sent to regional sorting center

8:00 AM, 8:30 AM, 9:00 AM, 9:30 AM - Put in system

9:15 AM, 10:00 AM - Sent to individual carrier

So the least time is when -

7:30 AM - Mail picked up

7:45 AM - Dropped Off at sorting center

8:00 AM - Sorted and stamped

8:30 AM - Put in system

9:15 AM - Sent to individual carrier

1 hr 45 min

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Re: At the post office, a letter must go through a sorting process with fo  [#permalink]

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13 May 2011, 20:01
Each step takes 15 + 20 + 45 mint = 1hr 20 min

options D and E are out.

calculating the delays between each steps now

between step 2 and step 3 fixed delay of 15 mint.

Between Step 3 and step 4

step 3 7:00 7:30
process 20min 20min

delay 40 max 10 min

step 4 8:00

thus step3-step4 delay (min) = 10

hence total delay = 15+10 = 25min

adding total = 1:20 min + 25 min = 1:45 mint.

good numerical.
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Re: At the post office, a letter must go through a sorting process with fo  [#permalink]

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13 May 2011, 23:49
fluke wrote:
At the post office, a letter must go through a sorting process with four distinct steps. Step 1: Mail is picked up every half hour, beginning at 6:00 am. Step 2: Mail is dropped off at the sorting center \frac{1}{4} hour later. Step 3: Mail is sorted by zip code and stamped every 1 hour, beginning at 7:00 am, and sent to regional sorting centers \frac{1}{3} hour later. Step 4: At the regional sorting centers, incoming mail is put into the system every 30 minutes, beginning at 8:00 am, and sent to individual mail carriers 45 minutes later. Assuming that all mail is picked up, sorted, and dropped off on time, what is the least total amount of time that it could take the letter to go through all four steps?

(A) 2 hours 45 minutes

(B) 2 hours 15 minutes

(C) 1 hour 45 minutes

(D) 1 hour 20 minutes

(E) 1 hour 15 minutes

Let's start with step 3 and compare time difference between step 3 and step 4.
Step 3:
[cycle1]
Mail sorting and stamp start time: 7
Mail sent: 7:20
Mail sent: 7:40
[cycle2]
Mail sorted and stamped again: 8
Mail sent: 8:20
Mail sent: 8:40.

Step 4:
[cycle1]
Mail put into system start time: 8
Mail sent: 8:45
[cycle2]
Mail put into system again: 8:30
Mail sent: 9:15

Now check the minimum time between step 3 and step 4.
Sent 7:20 --Put into system at 8. Total time difference= 40minutes
Sent 7:40 --Put into system at 8. Total time difference= 20minutes
Sent 8:20 --Put into system at 8:30. Total time difference= 10minutes
Sent 8:40 --Put into system at 9. Total time difference= 20minutes
Sent 9:20 --Put into system at 9:30. Total time difference= 10minutes

10 minutes is the least time taken between step 3 and step 4. Now pick either 8:20 or 9:20 and work backwards.

Step 3
Mail sorted and stamped again: 8------(1)
Mail sent: 8:20--------(2)
[Time difference between 1 and 2=20]
Step 4--
Mail put into system: 8:30 -------(3)
[Time difference between 2 and 3=10]
Mail sent: 9:15--------(4)
[Time difference between 3 and 4=45]
Step 2
Mail dropped off at 7:45------(5)
[Time difference between 5(mail being dropped off) and 1(mail being sorted and stamped)=15]
Step 1
Mail picked up at 7:30----(6)
[Time difference between 5 and 6=15]

Add all time difference. 15+15+20+10+45= 105minutes = 1hour 45 minutes.

OA C.

Thanks fluke for early morning brain exercise
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Re: At the post office, a letter must go through a sorting process with fo  [#permalink]

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14 May 2011, 05:36
is this a GM math? what source did you find this one????
i found the answer's C too
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Re: At the post office, a letter must go through a sorting process with fo  [#permalink]

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03 Jun 2011, 22:48
Is this a verbal (RC/CR) question or a quant question. I am pretty confused!

That being said, there is no confusion that my answer was wrong.
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Re: At the post office, a letter must go through a sorting process with fo  [#permalink]

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10 Oct 2015, 11:53
At the post office, a letter must go through a sorting process with four distinct steps. Step 1: Mail is picked up every half hour, beginning at 6:00 am. Step 2: Mail is dropped off at the sorting center $$\frac{1}{4}$$ hour later. Step 3: Mail is sorted by zip code and stamped every $$1$$ hour, beginning at 7:00 am, and sent to regional sorting centers $$\frac{1}{3}$$ hour later. Step 4: At the regional sorting centers, incoming mail is put into the system every $$30$$ minutes, beginning at 8:00 am, and sent to individual mail carriers $$45$$ minutes later. Assuming that all mail is picked up, sorted, and dropped off on time, what is the least total amount of time that it could take the letter to go through all four steps?

(A) $$2$$ hours $$45$$ minutes
(B) $$2$$ hours $$15$$ minutes
(C) $$1$$ hour $$45$$ minutes
(D) $$1$$ hour $$20$$ minutes
(E) $$1$$ hour $$15$$ minutes

easy to solve by taking example
- case
step 1-----picked up------7:30
step 2-----delivered-------7:45
step 3-------reach--------7:45-----dispatch 8:00
step 4-------reach--------8:20-----dispatch 8:30
sent----------------------9:15

total time 1:45 Answer
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Re: At the post office, a letter must go through a sorting process with fo  [#permalink]

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22 Dec 2017, 11:30
Mail picked up at 7;30 its confusing
what i got from question is Mail is picked up every half hour, beginning at 6:00 am. so it should be 6;30
plz help me out!
Re: At the post office, a letter must go through a sorting process with fo   [#permalink] 22 Dec 2017, 11:30
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