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MathNet 2023-part-05 — 191 problems (EN–VI) Question 19

Math Olympiad Vault · MathNet 2023-part-05 — 191 problems (EN–VI)

Question 19

The elements of a set $A$ are 13 consecutive positive integers, the elements of a set $B$ are 12 consecutive positive integers, and the elements of the set $A \cup B$ are 15 consecutive integers.
a) Find the number of elements of $A \setminus B$.
b) If, moreover, the sum of the elements of the set $A$ is equal to the sum of the elements of the set $B$, find the two sets.