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Question Stats:
51% (02:11) correct 49% (02:14) wrong based on 68 sessions
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An electronic clock shows time in hours and minutes. For example, 08:15 means that it is now a quarter past eight. If one looks at the clock at some time between 6:00 and 9:00, what is the probability that he will see the digit 8 ? A. \(\frac{1}{5}\) B. \(\frac{1}{3}\) C. \(\frac{2}{5}\) D. \(\frac{4}{9}\) E. \(\frac{1}{2}\)
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Re M1912
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16 Sep 2014, 01:05
Official Solution:An electronic clock shows time in hours and minutes. For example, 08:15 means that it is now a quarter past eight. If one looks at the clock at some time between 6:00 and 9:00, what is the probability that he will see the digit 8 ? A. \(\frac{1}{5}\) B. \(\frac{1}{3}\) C. \(\frac{2}{5}\) D. \(\frac{4}{9}\) E. \(\frac{1}{2}\) The period between 6:00 and 9:00 consists of 180 minutes. During 72 minutes of these 180 the clock will display the digit 8: during 60 minutes of the 8:009:00 hour and during 6 minutes of each of the hours 6:007:00 and 7:008:00 (for example, between 6:00 and 7:00 the clock will show digit 8 only at 06:08, 06:18, 06:28, 06:38, 06:48, and 06:58). The required probability \(= \frac{72}{180} = \frac{2}{5}\). Answer: C
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Re M1912
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22 May 2016, 03:17
I think this is a highquality question and I agree with explanation. We need to mention " both inclusive" after 6 to 9 in the question ; else denominator may become less than 180 as 6:00 and 9:00 are not included.



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09 Jul 2016, 08:33
I think this is a highquality question and I agree with explanation. Superb.



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Re: M1912
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21 Jul 2016, 11:57
This question is a good candidate for calculated guessing. From 6:00 to 8:59, at least 1 hour out of the total 3 hours has a 8. So we are looking for a number more than 1/3 or 33%. Hence, options (a) and (b) are out. Options c,d and e translate to 40%, 44% and 50%. Since the number 8 appears very few times in a hour, option (c) must be our best guess.



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Re: M1912
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28 Mar 2017, 00:13
hi brunel,
i am unable to understand the point how digit 8 will appear 60 times from time interval 8:00 to 9:00.As per me 8:08 , 8:18 , 8:28 etc will give 8 6 times + 59 times on the hour digit.
kindly clear where i am going wrong
thanks in advance



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Re: M1912
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28 Mar 2017, 01:26
sidagar wrote: hi brunel,
i am unable to understand the point how digit 8 will appear 60 times from time interval 8:00 to 9:00.As per me 8:08 , 8:18 , 8:28 etc will give 8 6 times + 59 times on the hour digit.
kindly clear where i am going wrong
thanks in advance The probability that he will see the digit 8, does not increase for 8:18, because there are two 8's there. It's still one point in time. Thus 8:18 is still counted once.
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Re: M1912
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10 Aug 2017, 11:57
By my math, there are 179 minutes between 6:00 and 9:00. Anyone else getting caught up on that? Yes, it's technical and relatively immaterial.



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Re: M1912
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24 Aug 2017, 06:43
Well apparently my rushed mind thinks there are 360 minutes in three hours...
Anyway this is a high quality question.



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Re: M1912
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06 Dec 2017, 07:39
The very best approach for this types of questions is an estimation. There are only 3 hours. The probability of seeing 8 is 1/3 plus another 12 cases. Slightly more than 1/3. 2/5 fits best.



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Re: M1912
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12 Jan 2019, 02:32
Bunuel wrote: An electronic clock shows time in hours and minutes. For example, 08:15 means that it is now a quarter past eight. If one looks at the clock at some time between 6:00 and 9:00, what is the probability that he will see the digit 8 ?
A. \(\frac{1}{5}\) B. \(\frac{1}{3}\) C. \(\frac{2}{5}\) D. \(\frac{4}{9}\) E. \(\frac{1}{2}\) Hi Experts If we are calculating something between X and Y, shouldn't we only include items between X and Y. Isn't it understood that X and Y would not be part of the problem. FOr example: How many numbers are between 10 and 15= 4(11,12,13,14) Similarly in the above question: the minutes between 6:00 and 9:00 should be 179 and not 180. Can some expert please clarify? BunuelgmatbustersGladiator59chetan2uVeritasKarishmaGMATPrepNow



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Re: M1912
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12 Jan 2019, 04:18
nitesh50 wrote: Bunuel wrote: An electronic clock shows time in hours and minutes. For example, 08:15 means that it is now a quarter past eight. If one looks at the clock at some time between 6:00 and 9:00, what is the probability that he will see the digit 8 ?
A. \(\frac{1}{5}\) B. \(\frac{1}{3}\) C. \(\frac{2}{5}\) D. \(\frac{4}{9}\) E. \(\frac{1}{2}\) Hi Experts If we are calculating something between X and Y, shouldn't we only include items between X and Y. Isn't it understood that X and Y would not be part of the problem. FOr example: How many numbers are between 10 and 15= 4(11,12,13,14) Similarly in the above question: the minutes between 6:00 and 9:00 should be 179 and not 180. Can some expert please clarify? BunuelgmatbustersGladiator59chetan2uVeritasKarishmaGMATPrepNowHi... There are 4 integers between 10 and 15 but if I talk of how many hours are there between 10 and 15, they are 5 hrs.. So let us see from 6:00 to 9:00.. So 6:006:01...1 min 6:006:02 .....6:006:01 + 6:016:02...2 Min ...6:006:59...59 mins 6:007:00.....60 mins 7:008:00...60 mins 8:009:00...60 mins So 6:009:00...180 minutes
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Bunuel wrote: An electronic clock shows time in hours and minutes. For example, 08:15 means that it is now a quarter past eight. If one looks at the clock at some time between 6:00 and 9:00, what is the probability that he will see the digit 8 ?
A. \(\frac{1}{5}\) B. \(\frac{1}{3}\) C. \(\frac{2}{5}\) D. \(\frac{4}{9}\) E. \(\frac{1}{2}\) 6 to 7 : 6:08;6:18: 6:28.. 6:58 ; 6 times also similarly 78 ; 6 times 68 : 12 times 89 : 60 times total : 72 mins when 8 would come on display total minutes: (96)hrs * 60 = 180 mins 72/180 = 2/5 IMO C
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Re M1912
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05 Mar 2019, 20:42
As the question is how many times the digit 8 be seen, i believe 8.08, 8.18,8.28,8.38,8.48,8.58 should be counted as well , which means between 8.00 to 9.00 we see 60+6 8's



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Re: M1912
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05 Mar 2019, 21:33
srtdhoni wrote: As the question is how many times the digit 8 be seen, i believe 8.08, 8.18,8.28,8.38,8.48,8.58 should be counted as well , which means between 8.00 to 9.00 we see 60+6 8's Your doubt is addressed above: https://gmatclub.com/forum/m19184192.html#p1828197Hope it helps.
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Re: M1912
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15 May 2019, 10:11
Another way to think about it:
3 hours between 6:00 and 9:00, 1/3 of those hours (from 8:00  8:59) you will definitely see an 8 Of the other two hours, the digit 8 is equally likely out of 10 digits to appear in the last digit.
So 1/3 + 2/3*1/10 = 2/5, Answer C



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Re: M1912
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03 Aug 2019, 06:04
The period between 6:00 and 9:00 consists of 180 minutes. During 72 minutes of these 180 the clock will display the digit 8: during 60 minutes of the 8:009:00 hour and during 6 minutes of each of the hours 6:007:00 and 7:008:00 (for example, between 6:00 and 7:00 the clock will show digit 8 only at 06:08, 06:18, 06:28, 06:38, 06:48, and 06:58). The required probability =72/180=2/5. The correct answer is C










