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1959 AMC 12 Question 14

AMC12 · 1959 AMC 12

Question 14

Given the set $S$ whose elements are zero and the even integers, positive and negative. Of the five operations applied to any pair of elements: $(1)$ addition, $(2)$ subtraction, $(3)$ multiplication, $(4)$ division, $(5)$ finding the arithmetic mean (average), those operations that yield only elements of $S$ are:
  1. all
  2. $1,$ $2,$ $3,$ $4$
  3. $1,$ $2,$ $3,$ $5$
  4. $1,$ $2,$ $3$
  5. $1,$ $3,$ $5$