Q78. What is the 489th digit in the number 123456789101112...?

To find the 489th digit, we count the number of digits contributed by single-digit, two-digit, and three-digit numbers: 1. **Single-digit numbers (1-9):** There are 9 numbers (1 to 9), each contributing 1 digit.

Total digits = 9 × 1 = 9 digits. 2. **Two-digit numbers (10-99):** There are 90 numbers (from 10 to 99), each contributing 2 digits. Total digits = 90 × 2 = 180 digits. 3. **Total digits up to 99:** 9 (from 1-9) + 180 (from 10-99) = 189 digits.

4. **Remaining digits needed:** We need the 489th digit. So, 489 - 189 = 300 more digits are required. 5. **Three-digit numbers (100 onwards):** These 300 digits must come from three-digit numbers, each contributing 3 digits.

Number of three-digit numbers needed = 300 / 3 = 100 numbers. 6. **Identify the 100th three-digit number:** The three-digit numbers start from 100. The 1st three-digit number is 100, the 2nd is 101, ..., the 100th three-digit number will be 100 + (100 - 1) = 199.

7. **The 489th digit:** The 489th digit will be the last digit of the 100th three-digit number (199), which is 9. This question tests logical reasoning and systematic counting of digits in a concatenated sequence of natural numbers, a common type of problem in CSAT's quantitative aptitude section.