In any twenty-four-hour period, a certain faulty clock gains anywhere

Question

In any twenty-four-hour period, a certain faulty clock gains anywhere from one second to a maximum of three minutes. The clock did not stop or lose time since noon the day before yesterday. At exactly noon today, did the clock show the correct time to an accuracy of five minutes?

(1) The clock was set to the correct time the day before yesterday at exactly noon.

(2) At exactly noon yesterday, the clock was set back by one minute.

GMATCoachBen · Accepted Answer

Video solution here:

https://www.youtube.com/watch?v=1obMGkB-f60

Maheshkv · Answer

From the details provided in question stem,

Per 24 hour period the clocks anything from 1 second to 3 minutes.

We need to evaluate the time gain in a scenario for period of 48 hours (noon day before yesterday to noon today) if it is in range of at most 5 minutes?

Statement-1:  It helps to say the clock was accurate when it started, but we cannot say the gain on 48 hrs.
Max gain= 3+3 = 6 mins
Min gain= 1+1= 2 sec

So St1 Insufficient

Statement-2:  Clock was set back by 1 min.

So max gain would be 3+3 -1= 5 mins but this holds true only when the clock time is accurate when it started day before yesterday

So St2 alone Insufficient

Combining both  would make the scenario clear:
Initial diff=0
Max gain= 3+3 -1=5 mins
Hence C (both statements needed)

Elite097 · Answer

GMATCoachBen  In st 2, why do we subtract from 6 mins to calculate the time gained or lost? 6 mins is the total of two days so we cannot have a third operation performed . If it was set back by 1, means it lost 1 min yest and now max 3 gains is possible today so it should be -1+3= 2 mins which is the max gain

Bunuel · Answer

"(2) At exactly noon yesterday, the clock was set back by one minute," means that the clock was set back by one minute from the time it was showing. However, the clock could have still gained a maximum of 3 minutes that day, making a net maximum gain of 2 minutes.

Gemmie · Answer

Statement 1:  The clock was set to the correct time the day before yesterday at exactly noon.Since the clock gains anywhere from one second to three minutes in a twenty-four-hour period, we need to calculate the possible range of time gain over two days (48 hours).

- Minimum gain in 48 hours: 2×1 second = 2 seconds
- Maximum gain in 48 hours: 2×3 minutes = 6 minutes

Therefore, by exactly noon today (48 hours later), the clock could have gained anywhere between 2 seconds and 6 minutes.

Therefore, statement (1) alone is  not sufficient .

Statement 2:  At exactly noon yesterday, the clock was set back by one minute.

This statement tells us that the clock was adjusted at noon yesterday, but it does not provide information about the clock's initial accuracy at noon the day before yesterday. The clock could have already been gaining time before being set back, and it might still be off by more than five minutes at noon today. Without knowing the starting point, we cannot determine the overall accuracy by noon today.

Therefore, statement (2) alone is  not sufficient .

Combined:

- Statement (1) provides a starting point - the clock was accurate two days ago.
- Statement (2) tells us about an adjustment made yesterday (set back one minute).

By combining this information, we can figure out the maximum possible error
- The clock gains a maximum of 3 minutes in 24 hours.
- Over 48 hours, it could gain a maximum of 6 minutes (2 * 3 minutes).
- If it was set back by 1 minute yesterday (statement (2)), the net error could be up to 5 minutes (6 minutes gained - 1 minute set back).

Therefore, with both statements, we can see the maximum error is 5 minutes, which falls within the accuracy of five minutes mentioned in the question.

Answer is C

HarshavardhanR · Answer

- From noon day before yesterday to noon today, we are looking at a timespan of 2 days.
- In 1 day, 
-> Min gain - 1 seconds
-> Max gain - 3 minutes
-  So, in 2 days, 
-> Min gain - 2 seconds
-> Max gain - 6 minutes

Question:  did the clock show the correct time to an accuracy of five minutes at noon today?

S1:  The clock was set to the correct time the day before yesterday at exactly noon.

The clock can show a time which is anywhere between 2 seconds forward (within an accuracy of up to 5 min) to 6 minutes forward (outside of an accuracy of up to 5 min).

Thus, S1 is not sufficient.

S2: At exactly noon yesterday, the clock was set back by one minute.

Even if this was true, we do not know how far away from accurate the time was 2 days ago at noon?

If the time at noon 2 days ago was accurate, then even in the most extreme case, the clock would show correct time to an accuracy of 5 min (6 min - 1 min adjusted yesterday = 5 min forward)

But we do not know this from S2. Thus, S2 is not sufficient.

S1 and S2 combined -> 
-> S1 tells us that the time was accurate 2 days ago at noon.
-> If no adjustment was done, the most extreme case would show time at noon today as 6 min ahead from actual.
-> But S2 tells us that the clock was set back by 1 min yesterday. In this case, the maximum possible gain in time in these 2 days is 3 + 3 - 1 = 5 min. Whatever happens, the clock will show the correct time to an accuracy of 5 min at noon today.

Thus, S1 and S2 together are sufficient. Choice C.

Hope this helps.

___
Harsha

SpagetBakemono · Answer

I still dont understand why the answer cant be B.

B says the clock displayed 11:59:00 AM yesterday. So if it gains 1 second, it would display 11:58:59 today and if it gains 3 minutes, it would display 11:56:00 today. Both these values lie within 5 minutes from 12:00 PM. And hence the accuracy is within 5 minutes?

playthegame · Answer

Think there is some uncertainty with B. How do we know that when the statement says exatly 12 noon yesterday that it is the correct time, the statement does not confirm that the clock is showing the correct time. Or is the author reading time from another clock?

C is the correct answer.

If we were to make an inequality from the stem, then time gained t is: 1 second =< t && t <= 180 seconds.

Statement 1 is not suffcient because we do not know much about the range from 150 seconds to 180 seconds, if the clock gained 160 seconds then it would not be within the =/- 5mins accuracy limit.

Statement 2 is not sufficient as we do not know what time the clock was showing the day before yesterday and when it was set to the correct time.

Now with both combined, we know the clock was set at the correct time at noon the day before yesterday so then the inequality becomes is 2t >= -300 seconds && less than 300 seconds. or in other words is t greater than zero and less than 150 seconds, so C is correct as you already have set the clock back by 1min yesterday so even if it gained 180 seconds on the first cycle and gained another 180 seconds on the second cycle you will be within the 5min accuracy, close call with some equality nuance as well.

Interesting question it took me 4mins to solve....

anushree01 · Answer

Amazing question that too from OG, bang onn!!

jameswill8520 · Answer

This is always within ±5 minutes (inclusive), so the clock does show the correct time to an accuracy of five minutes.

soumyab12 · Answer

In statement 2, clock was set back means someone has manually made the clock lose 1 minute from the time it was showing at noon yesterday. The reason why I selected B was because I assumed if someone has manually set a time, it is bound to be the correct time, i.e., the clock would've gained 1 min from day before yesterday noon to yesterday noon and that's what the person has rectified. And then from yesterday noon to today noon the gain will be anywhere from 1 second to 3 minutes. Is it not right to assume that if the clock time is being changed, it is now reflecting the correct time?

GMATCoachBen

Video solution here:

Bunuel · Answer

No. “Set back by one minute” only means the clock was moved one minute earlier, not that it was made correct. We don’t know if it was accurate after that, so statement 2 is not sufficient.

ExoticNeko · Answer

Given part of the reasoning to 1, I'm not sure why we're not assuming aliens didn't freeze time with the 24-hour period as well so that they're both not sufficient.

This was the official answer. C

Taken from the book:
Inference

The clock in question gains anywhere from one second to three minutes in any 24-hour period. Given that we know that the clock never stopped or lost time since noon the day before yesterday, we can answer the question if we could know whether the clock was any more than 5 minutes and one second slow at noon yesterday or any more than two minutes fast at noon yesterday.

1. From this statement we only know that the clock could be as much as six minutes fast—in which case the answer to the question is “No.” But nothing rules out that the clock gained only, for instance, two seconds, or that at some point in the past 48 hours someone manually changed the time on the clock; NOT sufficient.

2. Without the information given in (1), (2) does not help determine an answer to the question, because we do not know what time was on the clock immediately prior to its being reset at noon yesterday. If, for instance, the clock was one minute fast just before noon yesterday, then at most the clock would be three minutes fast at noon today, and the answer would be “Yes.” But if the clock at just before noon yesterday was, for instance, four minutes fast, then the clock at noon today could have been as much as six minutes fast, in which case that answer would be “No”; NOT sufficient.

From (1) and (2), we can infer that, as of just before noon yesterday, the clock was at least one second fast and at most three minutes fast. Therefore, when the clock was set back one minute at noon, the clock could have been anywhere from fifty-nine seconds slow to two minutes fast. Therefore, because the clock would have gained a minimum of one second and a maximum of three minutes between noon yesterday and noon today, we can infer that at most the clock was fifty-eight seconds slow and at most five minutes fast at noon today. Given that range, we can infer that at noon today, the clock showed the correct time to an accuracy of five minutes, and thus the answer to the question is “Yes,” which makes both statements together sufficient.

The correct answer is C; both statements together are sufficient.

Puranjaysapra · Answer

Does this part of the stem " The clock did not stop or lose time since noon the day before yesterday" not mean what the first statement is saying?

Gmat860sanskar · Answer

Puranjay, If you notice both statement ( statement 1 and stimulus part you have mentioned) is information about different time, one is about yesterday and another is about day before yesterday.

Puranjaysapra · Answer

Apologies but both do say day before yesterday

Gmat860sanskar · Answer

Sorry, I was pushing myself late at night and ended up overreading it.

Answering your question :

Question Stem :

“The clock did not stop or lose time since noon the day before yesterday”

This sentence tells us that clock never went back and only gained time  (between 1 sec and 3 min per day), However it tells you nothing about whether it was correct at the start.

Statement 1 :

“The clock was set to the correct time at exactly noon”

this statement tells us about the starting point at noon, where time is fixed. i.e : - error = 0 .

Please feel free to ask, if you have any follow-up query

In any twenty-four-hour period, a certain faulty clock gains anywhere

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In any twenty-four-hour period, a certain faulty clock gains anywhere

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