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# The circular clock above shows a time of exactly 3:30. What is the val

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Math Expert
Joined: 02 Sep 2009
Posts: 46302
The circular clock above shows a time of exactly 3:30. What is the val [#permalink]

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31 May 2018, 12:05
00:00

Difficulty:

25% (medium)

Question Stats:

82% (00:59) correct 18% (00:34) wrong based on 55 sessions

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The circular clock above shows a time of exactly 3:30. What is the value of x?

(A) 60
(B) 75
(C) 85
(D) 90
(E) 105

Attachment:

Quant8.jpg [ 9.8 KiB | Viewed 458 times ]

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Re: The circular clock above shows a time of exactly 3:30. What is the val [#permalink]

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31 May 2018, 16:04
Bunuel wrote:

The circular clock above shows a time of exactly 3:30. What is the value of x?

(A) 60
(B) 75
(C) 85
(D) 90
(E) 105

Attachment:
Quant8.jpg

ans: B

at 3:30 hrs needle will be in between/mid 3 and 4 so we will find the angle from there. hour needle runs 360 in 12 hrs means 30 degree in one hour so in half hour it will run only 15 degree. now minutes needle will run for 180 degree in 30 minutes.
now we will get the angle from the 3. hrs needle will run for 15 and minutes needle will run 90 degree.
so the angle between both the needles at 3:30 will be 90-15 =75 degree.
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Re: The circular clock above shows a time of exactly 3:30. What is the val [#permalink]

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01 Jun 2018, 03:59

Solution

Given:
• In the given figure, the circular clock shows a time of exactly 3:30

To find:
• The value of x

Approach and Working:

Method 1: Taking the reference time as 12:00 hrs
• If we consider the movement of the minute hand and hour hand separately, with respect to 12:00 hrs, we can calculate their individual displacement
• The minute hand of a clock covers a distance of 360° in 60 minutes
o Hence, it covers a distance of 6° in every minute
• The hour hand covers a distance of 360° in 12 hrs = 720 minutes
o Hence, it covers a distance of $$\frac{1}{2}$$° in every minute

Now, after the completion of every hour, minute hand comes to 12.
• Hence, at 3:30, the movement of the minute hand = 30 * 6° = 180°
From 12:00 hrs to 3:30, the hour hand moves for a time of 3.5 hrs = 210 minutes
• Hence, at 3:30, the movement of the hour hand = 210 * $$\frac{1}{2}$$° = 105°
• Therefore, the distance in between the minute and the hour hand = x = 180° - 105° = 75°

Method 2: Taking the reference time as 3:00 hrs
At 3:00 hrs, the minute hand will be at 12 and the hour hand will point towards 3, making a gap of 90° in between
• At 3:30 hrs, the minute hand will make a movement from 12 to exact opposite at 6, hence covering a distance of $$\frac{360°}{2}$$ = 180°
o Hence, from 3, the displacement of minute hand = 180° - 90° = 90°
• At 3:30 hrs, the hour hand will move exactly in between 3 and 4, covering a distance of $$\frac{1}{2}$$ * $$\frac{360°}{12}$$ = 15°
• Therefore, the distance between the minute and the hour hand = x = 180° - 105° = 75°

Hence, the correct answer is option B.

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Re: The circular clock above shows a time of exactly 3:30. What is the val [#permalink]

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03 Jun 2018, 18:22
Bunuel wrote:

The circular clock above shows a time of exactly 3:30. What is the value of x?

(A) 60
(B) 75
(C) 85
(D) 90
(E) 105

Attachment:
Quant8.jpg

We see the x is the measure of the angle formed by the minute hand and the hour hand. Since the entire circle is 360 degrees and since there are 12 numbers on the clock, the number of degrees between each pair of consecutive numbers is 360/12 = 30. Also, remember that if the minute hand moves a full rotation, i.e., 60 minutes or 360 degrees, the hour hand moves from one number to next, or 30 degrees. Any fraction of a full rotation of 360 degrees the minute hand moves, the hour hand also moves the same fraction of 30 degrees.

We see that there are 30 degrees between the numbers 6 and 5 and another 30 degrees between 5 and 4. However, since the minute hand moves 30 minutes, half of a full rotation, the hour hand also moves half of the number of degrees from the numbers 3 to 4. That is, there are only 15 degrees between the hour hand and the number 4. So the number of degrees between the minute hand and hour hand is 30 + 30 + 15 = 75 degrees.

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Re: The circular clock above shows a time of exactly 3:30. What is the val [#permalink]

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03 Jun 2018, 22:17
Bunuel wrote:

The circular clock above shows a time of exactly 3:30. What is the value of x?

(A) 60
(B) 75
(C) 85
(D) 90
(E) 105

Attachment:
Quant8.jpg

x/6=30-[15+(30/12)]
x=75°
B
Re: The circular clock above shows a time of exactly 3:30. What is the val   [#permalink] 03 Jun 2018, 22:17
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