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Interesting GMATFix Problem-15

by arora007 » Tue Sep 21, 2010 12:54 pm
What is the smaller angle formed by the minutes and hours hand of a 12 hour clock when the time reads 2:40?
a) 180degree
b) 160degree
c) 155degree
d) 140degree
e) 135degree
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by goyalsau » Wed Sep 22, 2010 12:08 am
is it B.
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by arora007 » Wed Sep 22, 2010 2:49 am
you are right, B is the answer.
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by msbinu » Wed Sep 22, 2010 5:26 am
The formula for clock is that

Angle = (60H-11M)/2
=60*2-11*40/2
=160
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by kaushiksin » Wed Sep 22, 2010 6:33 am
What is the smaller angle formed by the minutes and hours hand of a 12 hour clock when the time reads 2:40

angle between the hands = | 1/2 (60H-11M)|

Here H = 2 and
M = 40

therefore, angle = | 1/2 (60*2-11*40)|
= | 1/2 (120-440)|
= | -160| = 160

Hence the answer choice is (B).
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by reply2spg » Wed Sep 22, 2010 7:04 am
Thanks for the same. I was not aware of this formula
msbinu wrote:The formula for clock is that

Angle = (60H-11M)/2
=60*2-11*40/2
=160
Sudhanshu
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by kvcpk » Wed Sep 22, 2010 7:10 am
Good to see formulas for this. But its difficult to remember all formulas. I think even logic would help here.

Assuming that the hour hand doesnt move at all,
at 2:40:
the hour hand is at 2, the minute hand is at 8
Angle formed = (8-2)*30 = 180

Now, Let us see how much the hour hand moves.

For every 1 hour (60 minutes) -> hour hand moves 30 degrees. (360/12)
Hence for 40 minutes -> ?
= 40 * 30/60 = 20 degrees.

Reduce this 20 degrees from total of 180.
= 160 degrees.

Hope this helps!!
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by goyalsau » Wed Sep 22, 2010 7:37 am
kvcpk wrote:Good to see formulas for this. But its difficult to remember all formulas. I think even logic would help here.

Assuming that the hour hand doesnt move at all,
at 2:40:
the hour hand is at 2, the minute hand is at 8
Angle formed = (8-2)*30 = 180

Now, Let us see how much the hour hand moves.

For every 1 hour (60 minutes) -> hour hand moves 30 degrees. (360/12)
Hence for 40 minutes -> ?
= 40 * 30/60 = 20 degrees.

Reduce this 20 degrees from total of 180.
= 160 degrees.

Hope this helps!!
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