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# What is the difference in the degree measures of the angles formed by

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Math Expert
Joined: 02 Sep 2009
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What is the difference in the degree measures of the angles formed by  [#permalink]

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26 Jun 2018, 04:51
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Difficulty:

75% (hard)

Question Stats:

39% (01:32) correct 61% (01:12) wrong based on 75 sessions

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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

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Joined: 02 Aug 2009
Posts: 6808
What is the difference in the degree measures of the angles formed by  [#permalink]

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26 Jun 2018, 05:04
1
2
Bunuel wrote:
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

So there are two hands moving in this time..
1) minute hand -
Total 60 min and 360° so each minute =$$\frac{360}{60}=6$$°
Since minute hand has moved only one minute, it makes 6°
2) hour hand also moves in this time
It moved 360 in 12h as the hour hand completes 1 circle in 12 hour, so $$\frac{360}{12}=30$$° in 1 hour
If it moves 30° in 1 hour or 60 min, it will move $$\frac{30}{60}$$ or 0.5° in 1 min..

Therefore difference= $$6-0.5=5.5$$

C
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Re: What is the difference in the degree measures of the angles formed by  [#permalink]

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26 Jun 2018, 05:09

Solution

To find:
• 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

Approach and Working:
The minute hand completes a movement of 360° in 60 minutes
• Therefore, in 1 minute, it will cover $$\frac{360°}{60}$$ = 6°

The hour hand completes a movement of 360° in 12 hours or 720 minutes
• Therefore, in 1 minute, it will cover $$\frac{360°}{720}$$ = 0.5°

• Hence, the difference between angles = 6° - 0.5° = 5.5°

Hence, the correct answer is option C.

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What is the difference in the degree measures of the angles formed by  [#permalink]

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26 Jun 2018, 13:51
Bunuel wrote:
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

let x=difference in degrees
x/6=[36-(36/12)]-[35-(35/12)]=11/12 minute
x=6*(11/12)=5.5°
C
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Joined: 08 Oct 2017
Posts: 24
Re: What is the difference in the degree measures of the angles formed by  [#permalink]

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01 Jul 2018, 01:17
Spoiler: Account for hour hand movement as well.

1. Minute hand movement = 360 deg/60 minute = 6 deg/minute
2. Hour hand = 360 deg/12 hour /60 minute = 0.5 deg/minute

Angle change for minute hand = 6 deg
however, hour hand has also move in same direction by 0.5 deg. Hence to be deducted from difference in angle.
Hence, Answer is C; 5.5 deg
Re: What is the difference in the degree measures of the angles formed by &nbs [#permalink] 01 Jul 2018, 01:17
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# What is the difference in the degree measures of the angles formed by

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