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2014 Math Kangaroo

Problem 7

Problem 7 · 2014 Math Kangaroo Medium
Spatial & Visual Reasoning spatial-reasoning

The kangaroo is inside how many circles?

Figure for Math Kangaroo 2014 Problem 7
Show answer
Answer: C — 3
Show hints
Hint 1 of 3
A circle only counts if the kangaroo is sitting inside its round line, not outside it.
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Hint 2 of 3
Trace each circle's edge with your finger and ask: did I draw a loop around the kangaroo?
Still stuck? Show hint 3 →
Hint 3 of 3
Count one tally for every circle whose loop goes all the way around the kangaroo.
Show solution
Approach: check each circle one at a time and tally the ones that surround the kangaroo
  1. There are four circles, and they overlap, so the kangaroo can be inside more than one.
  2. Go around each circle's edge and check whether the kangaroo is inside that loop.
  3. Three of the circles wrap all the way around the kangaroo; the lowest circle does not.
  4. So the kangaroo is inside 3 circles.
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