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Q29·CSAT · Prelims 2023

Sum of all digits in integers from 10 to 100

NumericalDigit SumsNumber theory● Medium

Question

What is the sum of all digits which appear in all the integers from 10 to 100?

Options

a

855

Answer
b

856

c

910

d

911

Explanation

To sum the individual digits from 10 to 100, break the computation into standard positional blocks.

First, evaluate the clean grid of 2-digit numbers from 10 to 99 (90 total numbers):

Units place distribution: Each digit from 0 to 9 appears exactly once every 10 numbers, so it appears exactly 9 times across the full 90-number range.

Sum of units digits = 9 × (0 + 1 + 2 + \dots + 9) = 9 × 45 = 405.

Tens place distribution: Each digit from 1 to 9 serves as the leading character for an entire decade block of 10 numbers (e.g., 10 to 19).

Sum of tens digits = 10 × (1 + 2 + 3 + \dots + 9) = 10 × 45 = 450.

Now add the final boundary number, 100: Digits are 1, 0, 0, which adds exactly 1 to the total.

Grand Total = 405 + 450 + 1 = 856.

When aggregating digits across numeric blocks, track the units and tens columns independently using the base sum constant of 45 (1+2+\dots+9=45).

Answer: (b).

Question details

Year

2023

Paper

CSAT

Question

Q29

Section

Numerical Ability

Sub-topic

Digit Sums

Type

Number theory

Difficulty

Medium

Source hint

Number theory

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