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# M21-27

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Math Expert
Joined: 02 Sep 2009
Posts: 50570

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16 Sep 2014, 00:15
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:13) correct 28% (01:05) wrong based on 128 sessions

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Between 10:06 and 12:30 the hour hand of the clock turns by

A. 66 degrees
B. 70 degrees
C. 72 degrees
D. 75 degrees
E. 78 degrees

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Math Expert
Joined: 02 Sep 2009
Posts: 50570

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16 Sep 2014, 00:15
1
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Official Solution:

Between 10:06 and 12:30 the hour hand of the clock turns by

A. 66 degrees
B. 70 degrees
C. 72 degrees
D. 75 degrees
E. 78 degrees

In one hour an hour hand turns by $$\frac{360^{\circ}}{12}=30^{\circ}$$.

Since the difference between 10:06 and 12:30 is $$2\frac{2}{5}$$ hours then in that time the hour hand of the clock turns by $$30^{\circ}*2\frac{2}{5}=72^{\circ}$$.

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Status: Math is psycho-logical
Joined: 07 Apr 2014
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21 Jan 2015, 07:20
Hi Bunuel,

Thank you for this explanaton.
I would like to propose another solution, and you can tell me if it is useful or not and/or perhaps add your comments on it.

So, what I thought and led me to the correct solution is that the hour hand would make 2 full revolutions: one from 10.06 to 11.06 and one from 11.06 to 12.06.

Then, there are some minutes left, but the hour hand would remain at the same hour (even though the degree would change).

So, what I did was 360*2 = 720, and chose ANS C.

Is there some valid reasoning that led me to the correct answer? Because I am definitely missing sth!
Math Expert
Joined: 02 Sep 2009
Posts: 50570

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21 Jan 2015, 07:50
pacifist85 wrote:
Hi Bunuel,

Thank you for this explanaton.
I would like to propose another solution, and you can tell me if it is useful or not and/or perhaps add your comments on it.

So, what I thought and led me to the correct solution is that the hour hand would make 2 full revolutions: one from 10.06 to 11.06 and one from 11.06 to 12.06.

Then, there are some minutes left, but the hour hand would remain at the same hour (even though the degree would change).

So, what I did was 360*2 = 720, and chose ANS C.

Is there some valid reasoning that led me to the correct answer? Because I am definitely missing sth!

Have you read the solution above? The correct answer is 72 degrees, your answer is 720 degrees, which is obviously not correct. In 1 hour the hour hand does NOT make one full revolution, the minute hand does...
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Status: Math is psycho-logical
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21 Jan 2015, 08:06
Hi Bunuel,

Thank you for responding. Yes I did read your solution and I find it very useful, as I said. Thank you.

The reason why I asked whether what I did was reasonable, was exactly because my response was 720 and NOT 72, which is the wrong response obiously, but there could be a connection as 720 is 10*72. I just wanted to see if there was a justification for that or not.

Because only the fact that I got 720, and not 660, 700 or any of the other values in the answer options, or any other random value for that matter, led me to respond C, which happens to be the right answer.. So, I wanted to understand my mistake.
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Joined: 12 Aug 2015
Posts: 287
Concentration: General Management, Operations
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07 Feb 2016, 04:33
The time from 10:06 to 12:30 equals 144 minutes. There are 12 total hours (or 12*60 minutes) on the clock hence 360 degrees. Therefore

144/(12*60) = 1/5 of 360 degrees = 72 degrees
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Joined: 10 May 2017
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10 Jun 2017, 01:06
I solved in a way different manner I suppose.

10:06 to 12:06 - 60 degrees

for next 24 mins the hour hand will move by (24 x 6 x 30)/360=12

So 60+12=72 degrees.

Not sure if this is easy way though.
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08 Dec 2017, 02:37
In one minute the hour hand moves by 0.5 degrees. From 10:06 to 12:30 , the hour hand moves by 144 minutes or 2 hours 24 min. Hence the hour hand will move by 72 degrees between 10:06 and 12:30.

Option C
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Re: M21-27 &nbs [#permalink] 08 Dec 2017, 02:37
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# M21-27

Moderators: chetan2u, Bunuel

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