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Q68·CSAT · Prelims 2025

489th digit in concatenated natural numbers

NumericalNumber SequencesNumber theoryMedium

Question

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

Options

a

0

b

3

c

6

d

9

Answer

Explanation

Break the continuous string into blocks of numbers based on digit length: 1-digit numbers (1 to 9): 9 numbers × 1 digit = 9 digits. Remaining digits to find: 489 - 9 = 480 digits. 2-digit numbers (10 to 99): 90 numbers × 2 digits = 180 digits. Remaining digits to find: 480 - 180 = 300 digits. These remaining 300 digits belong exclusively to 3-digit numbers (starting from 100). Number of 3-digit numbers this covers = 300 \div 3 = 100 exact numbers. The 100th 3-digit number starting from 100 is: 100 + 100 - 1 = 199. Since 300 divides perfectly by 3, the 489th digit is the very last digit of the number 199, which is 9.

When finding the Nth digit in a concatenated number string, subtract the total digits consumed by 1-digit (9) and 2-digit (180) numbers first, then divide the remainder by the length of the current tier.

Answer: (d).

Question details

Year

2025

Paper

CSAT

Question

Q68

Section

Numerical Ability

Sub-topic

Number Sequences

Type

Number theory

Difficulty

Medium

Source hint

Number sequence counting

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