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

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)
all 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 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(Option B)

Video solution from Quant Reasoning:
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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

Light remains off between 8:31 and 8:54 for 8 minutes
Light remains off between 9:11 and 9:29 for 3 minutes
Light remains off between 9:31 and 10:00 for 14 minutes

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

IMO B

Hi AviGutman - i think one of my mistakes w.r.t this problem was

-- i thought whenever the door opened up (Say 8 am) i stays on till 8.15

and whenever the door opens again (Say 8.03 am) -- the initial time of 8.15 am still is the time for the bulb to switch off

I think i know understand what the verbiage in the problem is when it says timer that is reset every time the door opens as a person goes in or out of the room.

Any suggestions on how to get better at not making these assumptions / getting better at word problems specifically. I think many times, give the text is rather heavy in word problems == I just struggle to even understand what the inference of a sentence is

Is just more practice the only way out in your view ?

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

I am a bit confused on how we were supposed to know how to read the table. After learning of the answer, I understand that you read each column top to the bottom vertically, but how did you know how to do that? I realize this may be a silly question, but the way that the information appears in the box threw me off. Thank you!

Hi woohoo921,

There are a number of 'context' clues in the way this prompt is written and formatted. First, if you're just looking at the table, its title is "Times at Which the Door Opened from 8:00 to 10:00" - so we know that we're dealing with a 2-hour timeframe (starting at 8:00 and ending at 10:00). When thinking in those terms, the logical way to consider that type of data would be chronological order (and we can see that that's how the 4 columns are written). That's actually the second clue - there is an "order" to the times (as they're arranged in columns - so that's probably how we should view them); with just a little bit of looking around, you can see that all 4 of the times in the 1st column are 'earlier' than the first time in the 2nd column (and so on). Finally, the prompt itself tells us that every time the door is opened, a 15-minute timer resets (and keeps on) the bathroom light. Since we're asked to find the times that the light is NOT on, we need to start with the earliest time and work linearly through the 2 hours. A quick scan of the table shows us that the earliest 4 times are all in the 1st column and the 4 latest times (the only ones after 9:00) are all in the 4th column. That would get me thinking that the columns order the 16 times (and with a little review, we see that that's the case).

GMAT assassins aren't born, they're made,
Rich

At first this questions seems very easy, in fact logically also its very simple but somehow the chances of committing error are very high.

IMO : B = 25 Mins Light will be off (08:00 to 10:00)
120 Mins = (light on) - (light off)
Light off = 120 - (light On) = 120 Mins - 95 Mins = 25 Mins
08:00 to 08:31 = 31+15 = 46 Mins (Gap - 11 Mins)
08:54 to 09:11 = 16+15 = 31 Mins (Gap -3 Mins)
09:21 to 09:31 = 3 + 15 = 18 Mins (Gap - 14 Mins)
Total Time Light ON : 95 Mins
Total Time light OFF - 25 Mins

Though this looks like a lengthy word problem, the sequence is Door opens > Light bulb on for 15 min and if there is any entry/exit in the room within the 15 min, the timer resets.
So we need to consider those times where the time gap is greater than 15 min.

(1) 8:31 - 8:54 : The light remains on till 8:46 and then from 8:46 to 8:54,that is 8 min its switched off.

(2) 9:11-9:29 : The light remains on till 9:26 and then from 9:26 to 9:29,that is 3 min, its switched off.

(3)9:31-10:00 : The light remains on till 9:46 and then from 9:46 to 10:00 that is 14 min, its switched off.

Total time the bulb is off is 8 + 3 + 14 =25 min

(option b)

DM
GMAT SME

Question Statement
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 ?


Hi all!

This is a wonderful question to test your abilities of understanding key words in a Question stem and breaking down the stem to simplify the underlying operation!

On GMAT, word problems find a huge test space. Most of them are from the key areas of Arithmetic like Numbers, Percentage, Percentage Application, Ratios, Rates while some of them are also from undefined zones without any defined topic areas.
These questions truly and unapologetically test your logic and reasoning while throwing at you lengthy wordy forms of a 700+ question.
On the face of it they shall appear challenging and difficult to approach but when you break them down, you shall notice that using the core underlying logic your skills helped you to transform the question into a 600 level easy question!

Can we do that here?
Lets check this out!

Breakdown the question stem at each line and map the sequence of events mentioned in the question.
The sequence is Door opens > Light bulb on for 15 min > If there is any entry/exit in the room within the 15 min,the timer resets
So we need to consider those times where the time gap b/w the door opening/closing is greater than 15 min.
At this juncture, lets make use of the table provided.

(1) 8:31 - 8:54 : The light remains on till 8:46 and then from 8:46 to 8:54,that is 8 min its switched off.

(2) 9:11-9:29 : The light remains on till 9:26 and then from 9:26 to 9:29,that is 3 min, its switched off.

(3)9:31-10:00 : The light remains on till 9:46 and then from 9:46 to 10:00 that is 14 min, its switched off.

GMAT Tip of Focus- Most candidates lose focus on this part of the question where they reach the end of the table and do not think of the 2hr period but stop at 9:31.

If you have not done that then Kudos to your ability of not losing the "context" of the question but if you have then lets "together" make it a point that you have the right takeaway from this question.
Question Takeaway- Always go back to the last line of the question before you mark the answer. It would take a couple of seconds but will help you to evade the traps laid.

Thus, total time the bulb is off is 8 + 3 + 14 =25 min

(option b)

We hope that this question now no longer seems to you like a question of 700 level of difficulty. Let us know in the comments if our response has been helpful to breach the difficulty level of this question.

Devmitra Sen
GMAT Quant SME

Just find the times with a +15 minute gap and add up the resulting time gaps:

 
­
When the door opens, the light turns on for 15 mins. At 8, it turned on for 15 mins (so it would have been on till 8:15) but it reset everytime the door oepned at 8:03, 8:04, 8:06 etc and till 8:31, the door opened before 15 mins elapsed from the last door open. 
After 8:31, it stayed on till 8:46 and then switched off. Then it turned on again at 8:54 os it stayed off for 8 mins.

Again it stayed on and kept getting reset till 9:11. After that it stayed on till 9:26 and the stayed off for 3 mins till the door was opened again at 9:29. 
Then it was reset at 9:31 and it stayed on till 9:46 and stayed off till 10:00 i.e. 14 mins

Total time for which it stayed off = 8  + 5 + 14 = 25 mins

Answer (B)