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# M19-12

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Math Expert
Joined: 02 Sep 2009
Posts: 44599

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16 Sep 2014, 01:05
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Difficulty:

85% (hard)

Question Stats:

52% (01:23) correct 48% (01:30) wrong based on 82 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. $$\frac{1}{2}$$
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44599

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16 Sep 2014, 01:05
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Expert's post
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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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Joined: 03 May 2015
Posts: 11

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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.
Senior Manager
Joined: 31 Mar 2016
Posts: 404
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

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09 Jul 2016, 08:33
I think this is a high-quality question and I agree with explanation. Superb.
Current Student
Joined: 20 Oct 2014
Posts: 40
GMAT 1: 740 Q49 V42

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21 Jul 2016, 11:57
1
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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.
Intern
Joined: 04 Aug 2014
Posts: 33
GMAT 1: 620 Q44 V31
GMAT 2: 620 Q47 V28
GPA: 3.2

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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

Math Expert
Joined: 02 Sep 2009
Posts: 44599

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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

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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Intern
Joined: 09 Mar 2017
Posts: 1
GMAT 1: 620 Q44 V32

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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.
Manager
Joined: 09 Oct 2016
Posts: 89
Location: United States
GMAT 1: 740 Q49 V42
GPA: 3.49

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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.
Manager
Joined: 31 Oct 2016
Posts: 84

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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.
Re: M19-12   [#permalink] 06 Dec 2017, 07:39
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# M19-12

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