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1960 AMC 12 Question 19

AMC12 · 1960 AMC 12

Question 19

Consider equation I: $x+y+z=46,$ where $x,$ $y,$ and $z$ are positive integers, and equation II: $x+y+z+w=46,$ where $x,$ $y,$ $z,$ and $w$ are positive integers. Then:
  1. $\mathrm{I}$ can be solved in consecutive integers
  2. $\mathrm{I}$ can be solved in consecutive even integers
  3. $\mathrm{II}$ can be solved in consecutive
    integers
  4. $\mathrm{II}$ can be solved in consecutive even integers
  5. $\mathrm{II}$ can be solved in consecutive odd integers