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

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Math Expert
Joined: 02 Sep 2009
Posts: 61385
At how many distinct points in a watch do the hour and minute hand me  [#permalink]

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06 Jan 2020, 07:10
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63% (00:46) correct 38% (01:23) wrong based on 15 sessions

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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

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Math Expert
Joined: 02 Aug 2009
Posts: 8250
Re: At how many distinct points in a watch do the hour and minute hand me  [#permalink]

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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

B
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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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