Quantitative — Integer Digit Frequency

NumericalNumber SystemArithmetic Problem● Easy

Question

All two-digit positive integers contain the digit 5 how many times?

Options

Answer

Explanation

Let us count the occurrences of the digit 5 across all two-digit integers (10 to 99) by separating them into positions:

Case 1: Occurrences in the units place. The digit 5 appears in the units position once every ten numbers:

\{15, 25, 35, 45, 55, 65, 75, 85, 95\} \rightarrow 9 times

Case 2: Occurrences in the tens place. The digit 5 appears in the tens position continuously throughout the 50-series block:

\{50, 51, 52, 53, 54, 55, 56, 57, 58, 59\} \rightarrow 10 times

Total Occurrences Calculation: Add the counts from both cases: 9 + 10 = 19 total times.

Be careful not to double-count the number 55 as a single entry; the question asks how many times the digit 5 appears, meaning it contributes twice to the total count.

When counting digit frequencies across a numeric range, evaluate the units and tens positions separately to ensure numbers like 55 are fully counted.

Answer: (b).

Question details

Year

2026

Paper

CSAT

Question

Q29

Section

Quantitative Aptitude

Sub-topic

Number System

Type

Arithmetic Problem

Difficulty

Easy

Source hint

Digit distribution — systematic combinatorics tracking

Same sub-topic — other years

Number System has appeared in multiple CSAT papers:

Q25

2024

Determining data sufficiency for finding an unknown variable based on divisibility

DI / DSMedium

Q79

2022

Counting two-digit decimal combinations with non-zero constraints

NumericalEasy

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