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GRE Math Challenge #7-angles formed by the hour hand

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GRE Math Challenge #7-angles formed by the hour hand [#permalink] New post 06 Sep 2014, 12:59
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Question Stats:

41% (00:28) correct 58% (01:06) wrong based on 12 sessions
What is the difference in the degree measures of the angles formed by the hour hand and the minute hand of a clock at 12:35 and 12:36?
A 1
B 5
C 5.5
D 6
E 30
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #7 [#permalink] New post 09 Sep 2014, 17:31
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Refreshing the equivalences, 1 hour=60 mins, 1 min = 60 secs
In a clock the total angle traversed by both hour & minute hands = 360 degrees
In a times period from 12:35 to 12:36 or during 1 minute we have following info:

(i) the minute hand moved in 1 hr = 360 degrees
the minute hand moved in 1 min = 360/60 = 6 degrees
(ii) the hour hand moved in 12 hours = 360 degrees
the hour hand moved in 1 hour = 360/12 = 30 degrees => the hour hand moved in 1 min = 30/60 = 0.5 degrees

Hence, the difference between the 2 hands during that 1 minute = 6 - 0.5 = 5.5 degrees
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Re: GRE Math Challenge #7 [#permalink] New post 23 Jun 2018, 00:01
13divyasha wrote:
Refreshing the equivalences, 1 hour=60 mins, 1 min = 60 secs
In a clock the total angle traversed by both hour & minute hands = 360 degrees
In a times period from 12:35 to 12:36 or during 1 minute we have following info:

(i) the minute hand moved in 1 hr = 360 degrees
the minute hand moved in 1 min = 360/60 = 6 degrees
(ii) the hour hand moved in 12 hours = 360 degrees
the hour hand moved in 1 hour = 360/12 = 30 degrees => the hour hand moved in 1 min = 30/60 = 0.5 degrees

Hence, the difference between the 2 hands during that 1 minute = 6 - 0.5 = 5.5 degrees


I really dont follow this explanation. Can you expatiate further, pleasE?
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Re: GRE Math Challenge #7 [#permalink] New post 27 Jun 2018, 05:06
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Emike56 wrote:

I really dont follow this explanation. Can you expatiate further, pleasE?




We know to make a one complete cycle all the hands need to cover 360°; Now For solving it is useful to know some of the basic

a) Angle covered by the second hand in 1 second = 6°
This is because one complete cycle is 360° and the second hand takes 60 seconds to complete 360°; hence in 1 second it will cover = 360/60 = 6°

b) Angle covered by the minute hand in 1 minute = 6°

Similarly it takes 60 minutes by the minute hand to complete 360°; hence 1 min it will cover = 360/60 =6°

c) Angle covered by the hour hand in 1 hour = 30°

This is because it takes 12 hour by the hour hand to complete 360°; hence 1 hour it will cover = 360/12 =30°

d) Angle covered by the hour hand in 1 minute = 360°/720° = 1/2° =0.5°

Since it will take 720 minutes (12 hour * 60 minutes =720 minutes) to complete 360 degree, so in 1 minute the hour hand will cover = 360/720 = 0.5°

e) The minute and hour hands coincide 22 times in a day or 11 times in 12 hours

Now back to question:-
we are required to find the difference in angle between hour hand and minute hand from 12:35 to 12:36.

For this we have to convert hour to minutes, sinse the difference is of 1 minute

As we know
Angle covered by the minute hand in 1 minute =6°

and angle covered by hour hand in 1 minute = 360°/720° = 0.5°
So the difference of angle between hour hand and minute hand for 1 minute = 6° - 0.5° = 5.5°
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Re: GRE Math Challenge #7-angles formed by the hour hand [#permalink] New post 27 Jun 2018, 09:54
Good explanation thanku :)
Re: GRE Math Challenge #7-angles formed by the hour hand   [#permalink] 27 Jun 2018, 09:54
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GRE Math Challenge #7-angles formed by the hour hand

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