X = 101102103104105106107......146147148149150 (From numbers 101-150). Find…
2025
X = 101102103104105106107......146147148149150 (From numbers 101-150). Find out the remainder when this number is divided by 9.
- A.
2
- B.
5
- C.
3
- D.
4
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Key idea: a number modulo 9 equals the sum of its digits modulo 9.
There are 50 numbers from 101 to 150. The hundreds digit is 1 for each, contributing 1 × 50 = 50 to the digit sum.
Tens digits: 0 appears 9 times (101–109), 1–4 appear 10 times each (110–149), and 5 appears once (150). Sum = 0×9 + 1×10 + 2×10 + 3×10 + 4×10 + 5×1 = 105.
Units digits: each digit 0–9 appears exactly 5 times across 101–150, so sum = 5 × (0+1+...+9) = 5 × 45 = 225.
Total sum of digits = 50 + 105 + 225 = 380.
Divide 380 by 9: 380 = 9 × 42 + 2, so the remainder is 2.