Problem Solving

AbeNeedsAnswers wrote: ↑

Sat Aug 19, 2017 3:06 pm

GMAT Official Guide 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 ?

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

B

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

Hi All,

This prompt starts us off with a table that includes all of the specific times in which a door is opened between 8:00 and 10:00. We are then told that a light in a restroom automatically turns on for 15 MINUTES every time the door is opened (and if the light is ALREADY ON, then the timer is reset back to 15 minutes). We’re asked for the total number of minutes that the light is OFF during those 2 hours.

The primary work needed to answer this question involves simply keeping track of the timer – which means that some basic Arithmetic and note-taking is all that’s required to answer it.

1) Since the door first opens at 8:00, we know that the light will stay on until at least 8:15. During those first 15 minutes, the door opens another 5 times – the last of which occurs at 8:10. At this point, the timer has reset several times – and we know that the light will STAY ON until 8:25…

During that next ‘window’ of time, the door opens 2 more times – the last of which is at 8:19. This extends the light 15 minutes from that time, to 8:34.

During that time, the door opens 2 more times – the last at 8:31. This extends the light 15 more minutes to 8:46.

-→ Here, the light turns off for the first time (from 8:46 to 8:54): for 8 MINUTES.

2) At 8:54, the door opens and the timer resets for 9:09. During that time, the door opens 2 more times – the last at 9:05. This extends the light 15 more minutes to 9:20. At 9:11 the door opens once again – and extends the light until 9:26

-→ Here, the light turns off for the second time (from 9:26 to 9:29): for 3 MINUTES.

3) At 9:29, the door opens and the timer resets for 9:44. During that time, the door opens 1 more time at 9:31. This extends the light 15 more minutes to 9:46.

-→ The light turns off for the third and final time (from 9:46 – 10:00): for 14 MINUTES

Total time the light is OFF: 8 + 3 + 14 = 25 minutes

Final Answer: B

GMAT Assassins aren’t born, they’re made,
Rich