Which one of the following numbers is completely divisible by 99 ?
2023
Which one of the following numbers is completely divisible by 99 ?
- A.
115909
- B.
115919
- C.
115939
- D.
115929
Attempted by 29 students.
Show answer & explanation
Correct answer: D
Answer: 115929
Key idea: 99 = 9 × 11 and 9 and 11 are coprime, so a number is divisible by 99 exactly when it is divisible by both 9 and 11.
115909: Sum of digits = 1+1+5+9+0+9 = 25 → not divisible by 9. Alternating sum = 1-1+5-9+0-9 = -13 → not a multiple of 11. Conclusion: not divisible by 99.
115919: Sum of digits = 1+1+5+9+1+9 = 26 → not divisible by 9. Alternating sum = 1-1+5-9+1-9 = -12 → not a multiple of 11. Conclusion: not divisible by 99.
115939: Sum of digits = 1+1+5+9+3+9 = 28 → not divisible by 9. Alternating sum = 1-1+5-9+3-9 = -10 → not a multiple of 11. Conclusion: not divisible by 99.
115929: Sum of digits = 1+1+5+9+2+9 = 27 → divisible by 9. Alternating sum = 1-1+5-9+2-9 = -11 → a multiple of 11. Conclusion: divisible by both 9 and 11, therefore divisible by 99.
Final conclusion: 115929 is the only number among the given choices that is completely divisible by 99.