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Question 1037294: Point A is on the edge of a circular disk. Every day at noon, the disk is rotated exactly 150 degrees in a counter-clockwise direction. What day of the week will it be the next time point A is at the same position that it was at l0 am on Saturday?
Answer: Wednesday (How?)
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
To get back to where it started, the disk must have
rotated through a multiple of 360°, and also through a
multiple of 150°. We find the least common multiple
of 150° and 360°
150 = 2∙3∙5²
360 = 2³∙3²∙5
The least common multiple needs
2 as a factor 3 times, 3 as a
factor 2 times, and 5 as a factor
2 times.
So the LCM is 2³∙3²∙5² = 1800°
That means the 150° has been added
1800°/150° = 12 times.
Since we started before noon on a
Saturday, it rotated the first 150°
at noon on Saturday. Heck, let's just
go through the 12 days day by day until the
disk has rotated through 1800° and see what
day we end up on:
1. Saturday noon it had rotated through 150°
2. Sunday noon it had rotated through 300°
3. Monday noon it had rotated through 450°
4. Tuesday noon it had rotated through 600°
5. Wednesday noon it had rotated through 750°
6. Thursday noon it had rotated through 900°
7. Friday noon it had rotated through 1050°
8. Saturday noon it had rotated through 1200°
9. Sunday noon it had rotated through 1350°
10. Monday noon it had rotated through 1500°
11. Tuesday noon it had rotated through 1650°
12. Wednesday noon it had rotated through 1800°,
which is the first time it had rotated through
a multiple of 360°
Edwin
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