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

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Bunuel
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What is the difference in the degree measures of the angles formed by [#permalink] New post   26 Jun 2018, 04:51
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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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C
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What is the difference in the degree measures of the angles formed by [#permalink] New post   26 Jun 2018, 05:04
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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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What is the difference in the degree measures of the angles formed by [#permalink] New post   26 Jun 2018, 13:51
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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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Re: What is the difference in the degree measures of the angles formed by [#permalink] New post   26 Jun 2018, 05:09
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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.

Answer: C
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Re: What is the difference in the degree measures of the angles formed by [#permalink] New post   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
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Re: What is the difference in the degree measures of the angles formed by [#permalink] New post   23 Dec 2019, 18:49
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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


We see that the time difference is 1 minute. In the span of 1 minute, the minute hand moves forward 360/60 = 6 degrees; however, the hour hand also moves forward, but only by 30/60 = 0.5 degree. Therefore, the angles formed by the two times only change by 6 - 0.5 = 5.5 degrees.

Answer: C
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Re: What is the difference in the degree measures of the angles formed by [#permalink]
23 Dec 2019, 18:49
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