Question:
The light in a restroom operates with a 15-minute timer that is reset every time the door opens as a person goes in or out of the room. Thus, after someone enters or exits the room, the light remains on for only 15 minutes unless the door opens again and reset the timer for another 15 minutes. If the times listed above are the times at which the door opened from 8:00 to 10:00, approximately how many minutes during this two-hour period was the light off ?
- 10
- 25
- 35
- 40
- 70
“The light in a restroom operates with a 15-minute timer that is reset every time the door opens as a person goes in or out of the room.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2018”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
As per the problem statement, every time the door opens, the light timer is reset for another 15 minutes.
Now, if, during that 15 minutes, the door is opened or closed, the 15 minute OFF period is interrupted.
Let us scan the times quickly
We will be looking for spots where there are more than 15 minutes between times.
There are only three times that the 15-minute period was NOT interrupted and reset: 8:31, 9:11, and 9:31.
So we will calculate how long it took for someone to open the door after each of those times + 15 minutes.
That is the time when the light was off.
Hence,
8:31 + 15 = 8:46. Light is off until someone opens the door.
Door was opened ar 8:54. 8:54 - 8:46 = 8 minutes
So we get, 9:11 + 15 = 9:26
Door was opened at 9:29. 9:29 - 9:26 = 3 minutes
We get, 9:31 + 15 = 9:46.
10:00 - 9:46 = 14 minutes
Total time that light was off: 8 + 3 + 14 = 25 minutes
Correct Answer: B
Approach Solution 2:
As per the question, the light in the restroom gets reset every time the door opens,
and the table contains the timings when the door opens,
We need to identify the times when the light was not started in excess of 15 minutes.
The time periods,
8:31 - 8:54 (gap of 23 mins),
9:11 - 9:29 (gap of 18 mins), and
9:31 - 10:00 (gap of 29 mins)
The first 15 minutes the light will be on,
so the lights will switch off post 15 mins after the restroom is left undisturbed.
From the gaps, we have to reduce 15 mins each and the light remains off
for 8 mins(in period 1), for 3 mins(in period 2) and 14 mins(in period 3)
Therefore, the total time when the light was off is 8+3+14 or 25 min.
Correct Answer: B
Approach Solution 3:
If the light is on for 15 minutes after the door is opened, and that timer resets if the door is opened again, then the only times it will be dark are when there's a greater than 15 minutes interval between openings.
That happens 3 times:
1) between 8:31 and 8:54; If the timer starts at 8:31, the light will go off at 8:46, and will remain off until 8:54, or 8 minutes.
2) between 9:11 and 9:29; If the timer starts at 9:11, the light will go off at 9:26, and will remain off until 9:29, or 3 minutes.
3) between 9:31 and 10; If the timer starts at 9:31, the light will go off at 9:46, and will remain off at least until 10, as there are no more openings, and thus will remain off for another 14 minutes
8 + 3 + 14 = 25
Correct Answer: B
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