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2012 Math Kangaroo

Problem 1

Problem 1 · 2012 Math Kangaroo Easy
Spatial & Visual Reasoning clock-calendar

A clock has three hands of different lengths (for seconds, minutes and hours). We don't know the length of each hand, but we know the clock shows the correct time. At 12:55:30 the hands are in the positions shown on the right. What does the clockface look like at 8:10:00?

Figure for Math Kangaroo 2012 Problem 1
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Answer: A
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Hint 1 of 2
At 8:10:00 the second hand points straight to 12, while the minute hand has barely moved off the top.
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Hint 2 of 2
Decide where each of the three hands sits at 8:10:00, then find the picture that shows all three at once.
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Approach: place each clock hand at 8:10:00 and match the figure
  1. At 8:10:00 the seconds hand is at 0, so it points exactly at 12.
  2. The minute hand sits at 10 minutes, pointing to the 2.
  3. The hour hand is a little past the 8.
  4. Only choice A shows those three directions together.
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