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The light in a restroom operates with a 15-minute timer that is reset

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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 ?

A. 10
B. 25
C. 35
D. 40
E. 70

[Reveal] Spoiler:
Attachment:
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x2p9xx.jpg [ 12.16 KiB | Viewed 2382 times ]
[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Jun 2017, 07:29, edited 1 time in total.
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Every time the door opens, the light timer is reset for another 15 minutes. If, during that 15 minutes, the door is opened or closed, the 15 minute OFF period is interrupted.

Scan the times quickly, 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 you have to calculate how long it took for someone to open the door after each of those times + 15 minutes. That's when the light was off.

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

9:11 + 15 = 9:26

Door was opened at 9:29. 9:29 - 9:26 = 3 minutes

9:31 + 15 = 9:46.

10:00 - 9:46 = 14 minutes

Total time that light was off: 8 + 3 + 14 = 25 minutes

Answer B

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Re: The light in a restroom operates with a 15-minute timer that is reset [#permalink]

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Since the light in the restroom gets reset every time the door opens,
and the table contains the timings when the door opens,
we have 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)
have in excess of 15 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 reduce 15 mins each. Hence the light remains off
for 8 mins(in period 1), for 3 mins(in period 2) and 14 mins(in period 3)
Total time when light was off : 8+3+11 = 25 min (Option B)

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Re: The light in a restroom operates with a 15-minute timer that is reset [#permalink]

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New post 15 Nov 2017, 16:21
AbdurRakib wrote:
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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 ?

A. 10
B. 25
C. 35
D. 40
E. 70

[Reveal] Spoiler:
Attachment:
x2p9xx.jpg


We are looking for two consecutive times (when the door opened) with a gap of more than 15 minutes, since only then the light would be off.

Since the door is opened at 8:31, the light shuts off at 8:46 and stays off until 8:54, so the light is off for 8 minutes.

Since the door is opened at 9:11, the light shuts off at 9:26 and stays off until 9:29, so the light is off for 3 minutes.

Finally, since the door is opened at 9:31, the light shuts off at 9:46 and stays off at least until 10:00, so the light is off for 14 minutes (at least until 10:00).

Thus, the light was off for a total of 8 + 3 + 14 = 25 minutes.

Answer: B
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Re: The light in a restroom operates with a 15-minute timer that is reset   [#permalink] 15 Nov 2017, 16:21
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