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Grades 5-6 Video Solutions 2023
2023_1-2_09
2023_1-2_09
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Video Transcription
Question 9. The gray circle with three holes punched in it is placed on top of the clock face. The gray circle is turned around its center. Which three numbers is it possible to see at the same time? The main thing to recognize is when we have our three holes, for example the ones showing 1, 5, and 7, there is one number in the center that will be four places ahead, and then there will be a number two places ahead of it, like so. 1 plus 4 gives us 5, and then 5 plus 2 gives us 7. Since the holes themselves cannot move away from each other, this will always be true as the gray circle is moved around its center. So we can start off by crossing off B, since 1 and 5 are four apart, but 5 and 10 are five apart. Let's try doing 2, 4, and 9. We see that 2 and 4 are two places apart from each other, but 4 and 9 are five spaces apart, so this will not be the answer. Next, let's try 3, 6, and 9. We notice that each of these is divided by 3, so 3 plus 3 gives us 6, and then 6 plus 3 gives us 9, so this cannot be the answer. Next, if we try 5, 7, and 12, 5 and 7 are apart by 2, but 7 and 12 are apart by 5, so this will not be the answer. And finally, when we try 4, 6, and 12, 4 and 6 are apart by 2, and 6 and 12 are apart by 6. However, since a clock is round, and from 12 it moves to 1, we could move the 12 to the beginning, making the 4 our center. This way, 12 and 4 are four spaces apart, and 4 and 6 are two spaces apart, so the answer will be C.
Video Summary
The question involves aligning numbers on a clock face using a gray circle with three fixed holes. The task is to find which set of three numbers can be seen at the same time when the circle rotates around its center. By examining the distances between numbers, the solution finds that the only set meeting the required spacing, due to the circular nature of the clock, is 4, 6, and 12. The solution involves checking each option against the spacing pattern from the center number, and C (4, 6, 12) satisfies the criteria.
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