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At how many distinct points in a watch do the hour and minute hand me

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At how many distinct points in a watch do the hour and minute hand me  [#permalink]

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New post 06 Jan 2020, 07:10
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Re: At how many distinct points in a watch do the hour and minute hand me  [#permalink]

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New post 06 Jan 2020, 07:45
Bunuel wrote:
At how many distinct points in a watch do the hour and minute hand meet?

A. 10
B. 11
C. 12
D. 13
E. Infinite


LOGICALLY..
1) First time between 12 /0 and 1, both are together at 0/12
2) Next , both will meet sometime between 1 and 2
3) similarly once between 2 and 3, and so on till 10 and 11
4) finally between 11 and 12, they will meet at 12/0
Thus once for every gap, so 12, but between 11 and 12 & between 12 and 1, it is at just one place that is 12/0, so 12-1=11

Arithmetically..
First time at 0 degree
when minute hand travels 360, then hour hand travels 360/12 or 30, thus for every 1 degree of hour hand, minute hand travels 360/12 or 30 degree.
So next time when hour hand is at 1 or 30 degree, let them meet after hour hand moves x degrees => 30+x=0+12*x....11x=30...x=30/11. Thus the point is 30+30/11=30(12/11)..
Similarly when hour hand is at 2 or 60 degree, let them meet after hour hand moves x degrees => \(60+x=0+12*x....11x=60...x=\frac{60}{11}\). Thus the point is \(60+\frac{60}{11}=60(\frac{12}{11})=2*30(\frac{12}{11})\)..
So \(x*30(\frac{12}{11})\leq{360}....x\leq 11\)
Hence 11

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Re: At how many distinct points in a watch do the hour and minute hand me   [#permalink] 06 Jan 2020, 07:45
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At how many distinct points in a watch do the hour and minute hand me

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