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Which of the following is closest to the distance traveled by the tip

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Which of the following is closest to the distance traveled by the tip  [#permalink]

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New post 18 Sep 2018, 22:05
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

33% (01:51) correct 67% (02:04) wrong based on 38 sessions

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Which of the following is closest to the distance traveled by the tip  [#permalink]

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New post 19 Sep 2018, 00:55
Bunuel wrote:
Which of the following is closest to the distance traveled by the tip of a 9-inch hour hand of a clock in 18 minutes?


A. 17 inches
B. 10.8 inches
C. 5.4 inches
D. 3 inches
E. 1.4 inches


In 12 minutes, the hour hand moves by \(\frac{30}{5} = 6\) degree. The hour hand moves 9 degree in 18 minutes.

We can now represent this as a sector with an angle of 9 degrees and the radius of the circle is 9 inch.

Diagrammatic representation
Attachment:
Distance_Clock.png
Distance_Clock.png [ 4.63 KiB | Viewed 386 times ]


Formula used: Length of the sector = \(\frac{A}{360} * 2 * \pi * R\) where A = angle of sector

Length = \(\frac{A}{360} * 2 * \pi * R = \frac{9}{360} * 2 * \pi * 9 = \frac{1}{20} * \frac{22}{7} * 9 = \frac{11*9}{10*7} = \frac{99}{70} = 1.4\) inches

Therefore, the distance travelled by the hour hand is the length of the sector, which is 1.4 inches(Option E)
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Re: Which of the following is closest to the distance traveled by the tip  [#permalink]

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New post 19 Sep 2018, 02:13
according to the given info
we have to find the distance travelled by the minute needle

assume that clock is in the circular shaope and radial measurement is 360
for each minute the radial measurement is 360/60=6
for given 18 minutes = 6* 18= 108
so that 18 minutes part can be taken out of the circle arc part and now the leanth of the minutes needle can be taken as RADIOUS

important formulae is

L = (108/360)*2 PI R

WHERE r= 9,

after solving this we ll get L = 5.4pi
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Re: Which of the following is closest to the distance traveled by the tip  [#permalink]

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New post 19 Sep 2018, 02:58
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Hey karthikpoluri

Welcome to GMATClub!

If you read the question stem carefully - it is asking us to find the distance
travelled by the 9-inch hour hand in 18 minutes.

That's the reason that why you have made the incorrect calculations.

Hope it's clear :)
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Re: Which of the following is closest to the distance traveled by the tip  [#permalink]

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New post 19 Sep 2018, 03:14

Solution


Given:
    • The length of the hour-hand of a clock = 9 inches

To find:
    • The distance covered by the tip of the hour hand in 18 minutes

Approach and Working:
    • The length of hour-hand of a clock = the radius of the circle = 9 inches
    • Hour-hand covers 360 degrees in 12 hours = 12 * 60 minutes
      o So, in 18 minutes it covers, \(360 * \frac{18}{720} = 9\) degrees
    • Thus, the distance covered in 18 minutes = perimeter of the arc, which subtended an angle of 9 degrees at the center = \(2 * ᴨ * r * \frac{9}{360} = 2 * \frac{22}{7} * 9 * \frac{9}{360} = 1.41\)inches

Hence, the correct answer is option E.

Answer: E

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Re: Which of the following is closest to the distance traveled by the tip  [#permalink]

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New post 19 Sep 2018, 08:15
Clock perimeter = 2*π*R = 2*3.14*9 = 56.52

Distance = 56.52*18/60 = 56.52*0.3 = 16.95, which is closest to 17.

Answer A
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Re: Which of the following is closest to the distance traveled by the tip   [#permalink] 19 Sep 2018, 08:15
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