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A particular 12-hour digital clock displays the hour and minute of a

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A particular 12-hour digital clock displays the hour and minute of a  [#permalink]

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New post 29 Mar 2019, 00:49
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A
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E

Difficulty:

  95% (hard)

Question Stats:

17% (04:13) correct 83% (02:57) wrong based on 12 sessions

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A particular 12-hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a 1, it mistakenly displays a 9. For example, when it is 1:16 PM the clock incorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time?

(A) 1/2
(B) 5/8
(C) 3/4
(D) 5/6
(E) 9/10

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Re: A particular 12-hour digital clock displays the hour and minute of a  [#permalink]

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New post 29 Mar 2019, 01:26
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Solution


Given:
    • A particular 12-hour digital clock displays the hour and minute of a day.
    • Unfortunately, whenever it is supposed to display a 1, it mistakenly displays a 9.
      o For example, when it is 1:16 PM the clock incorrectly shows 9:96 PM.

To find:
    • The fraction of the day will the clock show the correct time

Approach and Working:
In a digital clock, the time shown should be in the format ab: cd, where
    • The possible values of ab will be in the range 01 to 12.
    • The possible values of c will be in the range 0 to 5.
    • The possible values of d will be in the range 0 to 9.

Now, the correct value choices of
    • ab = 02, 03, 04, 05, 06, 07, 08, 09 (8 values)
    • c = 0, 2, 3, 4, 5 (5 values)
    • d = 0, 2, 3, 4, 5, 6, 7, 8, 9 (9 values)

Hence, in every 12 hours, the number of correct times shown = 8 x 5 x 9 = 360 minutes
Therefore, the fraction of correct time = \(\frac{360}{720} = \frac{1}{2}\)

Hence, the correct answer is option A.

Answer: A

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Re: A particular 12-hour digital clock displays the hour and minute of a  [#permalink]

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New post 29 Mar 2019, 07:43
Bunuel wrote:
A particular 12-hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a 1, it mistakenly displays a 9. For example, when it is 1:16 PM the clock incorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time?

(A) 1/2
(B) 5/8
(C) 3/4
(D) 5/6
(E) 9/10


total minutes = 12*60 ; 720 mins
so times it will show wrong
complete duration from 1;00 to 1;59 = 60 mins
similarly at 10-12;59 ; 60*3 ; 180 mins
so total 240 mins
also at times 2:01,2:10-2:19, 2:21;2:31;2:41; 2:51 ; 15 times for 2,3,4,5,6,7,8,9 ; 8* 15 ; 120 times
so total times watch will be wrong ; 120+180 ; 360 mins out of 720 mins
i.e 360/720 ; 1/2
IMO A
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Re: A particular 12-hour digital clock displays the hour and minute of a  [#permalink]

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New post 17 May 2019, 08:48
Archit3110 wrote:
Bunuel wrote:
A particular 12-hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a 1, it mistakenly displays a 9. For example, when it is 1:16 PM the clock incorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time?

(A) 1/2
(B) 5/8
(C) 3/4
(D) 5/6
(E) 9/10


total minutes = 12*60 ; 720 mins
so times it will show wrong
complete duration from 1;00 to 1;59 = 60 mins
similarly at 10-12;59 ; 60*3 ; 180 mins
so total 240 mins
also at times 2:01,2:10-2:19, 2:21;2:31;2:41; 2:51 ; 15 times for 2,3,4,5,6,7,8,9 ; 8* 15 ; 120 times
so total times watch will be wrong ; 120+180 ; 360 mins out of 720 mins
i.e 360/720 ; 1/2
IMO A


Hi Archit3110,
Thank you for your solution.
Small correction required in the second last line. It should be 120+240= 360.
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Re: A particular 12-hour digital clock displays the hour and minute of a   [#permalink] 17 May 2019, 08:48
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