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# M19-12

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Math Expert
Joined: 02 Sep 2009
Posts: 52971

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16 Sep 2014, 00:05
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4
00:00

Difficulty:

85% (hard)

Question Stats:

53% (01:13) correct 47% (01:25) wrong based on 93 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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Math Expert
Joined: 02 Sep 2009
Posts: 52971

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16 Sep 2014, 00:05
1
2
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, 02:17
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: 383
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

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09 Jul 2016, 07:33
I think this is a high-quality question and I agree with explanation. Superb.
Current Student
Joined: 20 Oct 2014
Posts: 38
GMAT 1: 740 Q49 V42

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21 Jul 2016, 10:57
1
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: 29
GMAT 1: 620 Q44 V31
GMAT 2: 620 Q47 V28
GPA: 3.2

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27 Mar 2017, 23:13
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: 52971

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28 Mar 2017, 00:26
1
1
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, 10:57
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.
Current Student
Joined: 09 Oct 2016
Posts: 89
Location: United States
GMAT 1: 740 Q49 V42
GPA: 3.49

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24 Aug 2017, 05:43
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: 106

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06 Dec 2017, 06:39
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.
Manager
Joined: 04 Jun 2018
Posts: 156
GMAT 1: 610 Q48 V25
GMAT 2: 690 Q50 V32
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12 Jan 2019, 01:32
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
gmatbusters
chetan2u
GMATPrepNow
Math Expert
Joined: 02 Aug 2009
Posts: 7334

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12 Jan 2019, 03:18
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Joined: 18 Aug 2017
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Location: India
Concentration: Sustainability, Marketing
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12 Jan 2019, 04:49
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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M19-12   [#permalink] 12 Jan 2019, 04:49
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# M19-12

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