2016 · Q96
Let S be a set of first ten natural numbers. What is the possible number of pairs (a, b) where a,b ∈ S and a ≠ b such that the product ab (>12) leaves remainder 4 when divided by 12 ?
Elementary MathematicsSet Theory
- A4
- B6
- C8
- D10
Explanation
Products ab ≡ 4 (mod 12) with 1 ≤ a≠b ≤ 10: (2,8), (4,7), (4,10), (5,8) — 4 unordered pairs. Since (a,b) is ordered, that doubles to 8 pairs (option C).