2019 · Q3
How many pairs (A, B) are possible in the number 479865AB if the number is divisible by 9 and it is given that the last digit of the number is odd?
Elementary MathematicsNumber System
- A5
- B6
- C9
- D11
Explanation
Digit sum is 4+7+9+8+6+5 = 39 ≡ 3 (mod 9), so divisibility by 9 needs A+B ≡ 6 (mod 9). With B odd, A+B ∈ {6, 15}. For 6: (A,B) = (5,1), (3,3), (1,5) — 3 pairs. For 15: (6,9), (8,7) — 2 pairs. Total 5 pairs.