2023 · Q89
Let X = x | x = 2 + 4k, where k = 0, 1, 2, 3,...24. Let S be a subset of X such that the sum of no two elements of S is 100. What is the maximum possible number of elements in S?
Elementary MathematicsSet Theory
- A10
- B11
- C12
- D13
Explanation
Elements of X pair up as (2 + 4k) + (2 + 4j) = 100 with k + j = 24: twelve pairs, plus the self-pairing element 50. From each pair at most one element can be taken, and 50 may be included since a set contains it only once (no two distinct elements then sum to 100). The maximum is 12 + 1 = 13 (D).