2024 · Q28
Let N = 12345678AB be a 10-digit number, where A, B are digits. If N is divisible by 9, then which of the following statements is/are correct?
- I(A + B) is divisible by 9
- IIIf A is odd, then B is odd Select the answer using the code given below:
Elementary MathematicsNumber System
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
Digit sum of N is 1+2+…+8+A+B = 36+A+B, so 9 | N forces A+B ∈ {0, 9, 18}, each divisible by 9: statement I is correct. If A is odd, A+B = 9 forces B even (e.g. A=1, B=8), so statement II is false. Only I is correct — option A.