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Australian AMC 2016 - Junior Question 19

AMC AUSTRALIA · Australian AMC 2016 - Junior

Question 19

In a packet of spaghetti, one-third of the strands of spaghetti are intact, but the rest have each been snapped into two pieces. Of all the pieces of spaghetti from the packet (broken and whole), what is the largest fraction guaranteed to be at least as long as half an unbroken strand?
  1. $\frac25$
  2. $\frac35$
  3. $\frac23$
  4. $\frac12$
  5. $\frac13$