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M19-12

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:05
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Difficulty:

75% (hard)

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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16 Sep 2014, 01:05
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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 8:00-9:00 hour and during 6 minutes of each of the hours 6:00-7:00 and 7:00-8:00 (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 $$= \frac{72}{180} = \frac{2}{5}$$.

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22 May 2016, 03:17
I think this is a high-quality 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 high-quality question and I agree with explanation. Superb.
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21 Jul 2016, 11:57
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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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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

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28 Mar 2017, 01:26
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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

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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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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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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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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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.

Bunuel
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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.

Bunuel
gmatbusters
chetan2u
GMATPrepNow

Hi...
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 6:00-6:01...1 min
6:00-6:02 .....6:00-6:01 + 6:01-6:02...2 Min
...6:00-6:59...59 mins
6:00-7:00.....60 mins
7:00-8:00...60 mins
8:00-9:00...60 mins

So 6:00-9:00...180 minutes
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12 Jan 2019, 05:49
1
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 7-8 ; 6 times
6-8 : 12 times
8-9 : 60 times
total : 72 mins when 8 would come on display
total minutes: (9-6)hrs * 60 = 180 mins
72/180 = 2/5 IMO C
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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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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

Hope it helps.
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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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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 8:00-9:00 hour and during 6 minutes of each of the hours 6:00-7:00 and 7:00-8:00 (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.
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