The elevator in an eleven-story office building travels at

Question

The elevator in an eleven-story office building travels at the rate of one floor per 1/4 minute, which allows time for picking up and discharging passengers. At the main floor and at the top floor, the operator stops for 1 minute. How many complete trips will an operator make during a 7-hour period?

A) 88
B) 56
C) 42
D) 60
E) 64

A) 88
B) 56
C) 42
D) 60
E) 64

Bunuel · Accepted Answer

The elevator in an eleven-story office building travels at the rate of one floor per 1/4 minute, which allows time for picking up and discharging passengers. At the main floor and at the top floor, the operator stops for 1 minute. How many complete trips will an operator make during a 7-hour period?

A) 88
B) 56
C) 42
D) 60
E) 64

A) 88
B) 56
C) 42
D) 60
E) 64

Complete trip = 10 floors up and 10 floors down = 20 floors = 20*1/4 = 5 minutes plus 2 minutes = 7 minutes.

7 hour = 420 minutes.

In 420 minutes operator can make 420/7=60 trips.

Answer: D.

Hope it's clear.

Bunuel · Answer

Think below might help:

(1st floor = 1 minute) 
(1/4 minutes to 2nd floor) 1
(1/4 minutes to 3rd floor) 2
(1/4 minutes to 4th floor) 3
(1/4 minutes to 5th floor) 4
(1/4 minutes to 6th floor) 5
(1/4 minutes to 7th floor) 6
(1/4 minutes to 8th floor) 7
(1/4 minutes to 9th floor) 8
(1/4 minutes to 10th floor) 9
(1/4 minutes to 11th floor) 10

(11th floor = 1 minute) 
(1/4 minutes to 10th floor) 1
(1/4 minutes to 9th floor) 2
(1/4 minutes to 8th floor) 3
(1/4 minutes to 7th floor) 4
(1/4 minutes to 6th floor) 5
(1/4 minutes to 5th floor) 6
(1/4 minutes to 4th floor) 7
(1/4 minutes to 3rd floor) 8
(1/4 minutes to 2nd floor) 9
(1/4 minutes to 1st floor) 10

Complete trip = 20 1/4-minute intervals + 2 minutes = 7 minutes.

Does this make sense?

vishal4584 · Answer

The answer is 60 (option D)
1----2-----3----4----5----6----7----8----9----10----11
0 1.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

So the liftman will take 3.5 min for one way, so for complete trip, he will take 7 min.
(1.25 at the start is the lift rate + ome minute wait).

So, In 60 min, 
The liftman will complete (60/7) trips.

therefore, in 7 hours, the number of complete trips will be (60/7)*7 ie 60 trips.

Berbatov · Answer

Ground floor (Main): 1 minute
Floor 1 - 10..........: 0.25 each * 10 floors = 2.5 mins per direction * 2 = 5 mins per round
Floor 11 (Top).......: 1 minute
=======================
..........................: 7 minutes per ride

7 * 60 mins = 420 mins in total

420/7 = 60

Even though it's a bit weird because in the first round, nobody has to leave and in the last round nobody enters

JusTLucK04 · Answer

60*2= Main + 11 Floor
15*9= 135 Sec for 9 Floors

Total= 9+2 = 11 floors

Wat am I missing here..Coz 390 secs per trip does not lead to 60 trips in 7 hrs

JusTLucK04 · Answer

So you included the 15 seconds for the ground floor/top floor too...for 1complete up-down trip?..I am counting it for just 9 floors

JeffTargetTestPrep · Answer

We are given that an elevator takes 1/4 minute to travel between floors and that it stops for one minute at the top floor and also on the main floor. Since the elevator is traveling from the main floor to the 11th floor, it’s traveling 10 total floors.

Thus, the total time it takes for the elevator to go from the bottom floor to the 11th floor and back down is:

20 x 1/4 = 5 minutes

Since the elevator stops for a minute each at the top and main floors, the amount of time to complete a trip is:

5 + 2 = 7 minutes = 7/60 hours

Thus, in 7 hours the elevator can complete 7/(7/60) = 60 trips.

Answer: D

Fdambro294 · Answer

The tricky part with the Elevator problems is realizing that if the building has 11 Stories, the elevator already starts out on the 1st Floor. The elevator does not do any traveling to get to the 1st Floor.

Then when it travels to the 2nd Floor, it has traveled 1 Story

when it travels to the 3rd Floor, it has traveled 2 Stories

....

when it travels to the 11th Floor, it has traveled 10 stories.

1 Complete Trip = Elevator going to the TOP, and then Elevator coming back DOWN

10 Stories traveled UP + 10 Stories traveled DOWN = 20 Stories traveled for a Complete Trip.

At the rate of 1/4th of a minute per Stories, the TIME spent traveling in a Complete Trip is:

20 Stories traveled * 1/4 min. per Story = 5 Minutes per 1 Complete Trip.

However, the elevator is also open for 1 minute on the 1st Floor and 1 minute on the Top Floor.
For Each Complete Trip, need to Add On +2 minutes for the stopping.

Total of 7 minutes per 1 Complete Trip.

7 hours = 420 minutes

How many Complete Trips can we make in 420 minutes when it takes 7 minutes per 1 Complete Trip?

420 / 7 = 60 Complete Trips

Answer D

kpop1234567890 · Answer

I dont know in problems like this cultural context can play a part. In india we start with ground floor - so it means that you have to infact travel to get to even the first floor and you dont directly start at the first floor

Also the Q doesnt specify that it stops for 1 minute each at top and bottom floors

Also the Q doesnt specify that it stops for 1 minute each at top and bottom floors

ic2022 · Answer

Hi, Why are you not considering Ground floor as well, so it makes 22*1/4 + 2 minutes for a single trip - making the answer 56 mins for 7 hours. Any building with n floors will also have a ground floor making the total count for lift as n+1.

Bunuel · Answer

The question clearly states it’s an  eleven-story  building, which already includes the main (ground) floor as one of the stories.

So, going from the  1st to the 11th floor  involves  10 floor-to-floor movements , not 11. Likewise, coming back down is another 10. That's why the total is 20 movements, each taking 1/4 minute.

There’s no need to add an extra floor for the ground floor, it’s already counted as the 1st story. Please review the discussion above for more.

agrotechpepper · Answer

hi, pretty clear explaination. The mistake I was doing that adding another  1 min,  post finally coming to ground (main) floor for discharging. So I was calculating 1min (Main Floor Stop) + 2.5 min (Ascent) + 1 min (Top floor Stop) + 2.5 min (Descent) +1 min (Main floor Stop) = 8 mins. Any tips (any word I missed) where I went wrong? Help, so as to avoid being wrong in future.

Vivek1707 · Answer

While I understand and do not dispute the solution I have two concerns here

First, the solution  assumes  that an  11-story building means the main floor  is  already counted  as the first story, so the elevator travels only  10 floor-to-floor intervals  to reach the top. While this  follows the American convention , it isn't universal. In many countries (including India), people commonly think of an  n-story  building as  Ground + n upper floors , so an international test-taker could reasonably interpret the travel differently. It could be interpretted to mean that 11 story building would mean there are 11 levels and if an elevator starts from the bottom it would need to travel 11 levels and not just 10.

My second concern is the phrase " complete trip ." The question never explicitly defines a complete trip as a  round trip  (main floor → top floor → main floor). In ordinary English, a "complete trip" can also mean a  one-way journey .

I would expect a GMAT question—especially one intended for an international audience—to avoid relying on such implicit conventions and instead say "complete round trip" or explicitly state that the main floor is the first story.

SVaidyaraman · Answer

Key idea: A round trip is one cycle — the same closed-loop structure as a clock hand returning to start or a worker completing one full job. Find the time for one complete cycle, then it's just a rate question: total time ÷ time per cycle. Don't track floors individually; track the period of the loop.

Step 1 — Build one cycle (the conserved unit).
An 11-story building means 10 floor-gaps between bottom and top. A complete trip = up 10 gaps + down 10 gaps = 20 floor-movements
- Travel: 20 × 1⁄4 min = 5 min
- Stops: 1 min at main floor + 1 min at top = 2 min

One cycle = 5 + 2 = 7 minutes.

Step 2 — Apply the rate (total ÷ per-unit).
This is the same move as "distance ÷ speed" or "job ÷ rate" — total resource divided by cost per unit:

7x60/7= 60

Answer: D) 60

The connection: the whole problem is one rate equation — total time ÷ time per cycle = number of cycles — identical in structure to a work problem (jobs ÷ rate) or a circular-motion problem (laps ÷ lap-time). The only setup step is correctly costing one cycle: 10 gaps, not 11 floors, and the two fixed stops added as overhead.

The elevator in an eleven-story office building travels at

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The elevator in an eleven-story office building travels at

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