Explore: All CDS topics · CDS Elementary Mathematics PYQs · CDS hub · Syllabus & pattern · CDS 2026
Answer first
Number System and Simplification PYQs (previous year questions) for CDS: Number System and Simplification (Elementary Mathematics) had 306 questions across the 66 official CDS papers we tagged (2016–2026), and appeared in 22 of them. Asked in 11 of 11 years. The concepts asked in the most papers: HCF and LCM, Remainders, Divisibility.
Year-wise question count
Asked in 11 of 11 years, with 2 papers each year.
| Year | Questions |
|---|---|
| CDS 2026 | 21 |
| CDS 2025 | 34 |
| CDS 2024 | 44 |
| CDS 2023 | 28 |
| CDS 2022 | 17 |
| CDS 2021 | 22 |
| CDS 2020 | 29 |
| CDS 2019 | 34 |
| CDS 2018 | 22 |
| CDS 2017 | 23 |
| CDS 2016 | 32 |
Most-asked concepts
Sorted by the number of papers a concept appeared in.
| Concept | Questions | Papers | Years |
|---|---|---|---|
| HCF and LCM | 39 | 19 | 2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016 |
| Remainders | 35 | 16 | 2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2017, 2016 |
| Divisibility | 33 | 13 | 2026, 2025, 2024, 2023, 2022, 2021, 2020, 2018, 2017, 2016 |
| Number Properties | 28 | 12 | 2024, 2023, 2022, 2021, 2019, 2018, 2016 |
| Prime Numbers | 12 | 8 | 2025, 2024, 2023, 2021, 2020, 2019, 2017 |
| Surds | 9 | 8 | 2024, 2023, 2020, 2019, 2018, 2017 |
| Unit Digit | 8 | 8 | 2026, 2023, 2021, 2020, 2019, 2018, 2016 |
| Logarithms | 14 | 7 | 2025, 2020, 2019, 2018 |
| Simplification | 11 | 7 | 2024, 2022, 2021, 2017, 2016 |
| Factors | 5 | 5 | 2025, 2024, 2023, 2022 |
| Factors and Multiples | 5 | 5 | 2020, 2019, 2018 |
| Perfect Squares | 5 | 5 | 2020, 2019, 2018, 2017 |
| Data Sufficiency | 14 | 4 | 2026, 2025, 2024 |
| Recurring Decimals | 5 | 4 | 2025, 2020, 2019, 2018 |
| Factorials | 4 | 4 | 2025, 2024, 2023, 2018 |
| Fractions | 4 | 4 | 2022, 2021, 2017 |
| Series | 4 | 4 | 2024, 2021, 2016 |
| Sets | 4 | 4 | 2017, 2016 |
| Divisibility Rules | 4 | 3 | 2020, 2019 |
| Integers | 4 | 3 | 2017, 2016 |
| Number Puzzles | 4 | 3 | 2017, 2016 |
| Co-prime Numbers | 3 | 3 | 2026, 2019 |
| Comparison of Numbers | 3 | 3 | 2020, 2018, 2017 |
| Division Algorithm | 3 | 3 | 2026, 2022, 2019 |
| Square Roots | 3 | 3 | 2024, 2022, 2017 |
| Two-digit Numbers | 3 | 3 | 2025, 2020 |
| Surds and Indices | 5 | 2 | 2025 |
| Continued Fractions | 2 | 2 | 2019, 2016 |
| Decimal Expansion | 2 | 2 | 2017, 2016 |
| Digits and Numbers | 2 | 2 | 2016 |
| Prime Factorisation | 2 | 2 | 2021, 2016 |
| Real Numbers | 2 | 2 | 2019, 2016 |
| Digit Problems | 3 | 1 | 2026 |
| Arithmetic Progression | 2 | 1 | 2025 |
| Squares | 2 | 1 | 2019 |
| Digit Puzzles | 1 | 1 | 2019 |
| Digit Sum | 1 | 1 | 2020 |
| Division | 1 | 1 | 2024 |
| Divisors | 1 | 1 | 2026 |
| Indices | 1 | 1 | 2020 |
| Irrational Numbers | 1 | 1 | 2019 |
| Linear Diophantine | 1 | 1 | 2017 |
| Natural Numbers | 1 | 1 | 2025 |
| Number Formation | 1 | 1 | 2024 |
| Number of Divisors | 1 | 1 | 2020 |
| Number Series | 1 | 1 | 2024 |
| Number Theory | 1 | 1 | 2017 |
| Rational and Irrational Numbers | 1 | 1 | 2018 |
| Sets of Numbers | 1 | 1 | 2023 |
| Squares and Cubes | 1 | 1 | 2019 |
| Trailing Zeros | 1 | 1 | 2026 |
| Unit and Last Digits | 1 | 1 | 2025 |
| Units and Conversions | 1 | 1 | 2022 |
How to practise Number System and Simplification PYQs
- Start with the concepts at the top of the table. They have come back the most.
- Solve one year’s Number System and Simplification questions from the official PDF against the clock, then check the answer listed below.
- Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
- Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.
Questions by year
Each line gives the question number and paper, type, concept, our one-line summary and the official answer, with a link to the official PDF.
CDS2026
- Q.5 (CDS (I) Maths) · MCQ · Trailing Zeros: Number of trailing zeros in the sum of two large products PDF
- Q.21 (CDS (I) Maths) · MCQ · Divisibility: Natural numbers below 10 dividing a given large number PDF
- Q.22 (CDS (I) Maths) · MCQ · HCF and LCM: HCF of p with p + q and p - q given HCF of p and q PDF
- Q.23 (CDS (I) Maths) · MCQ · HCF and LCM: Find q from HCF, LCM and division information on p PDF
- Q.24 (CDS (I) Maths) · MCQ · HCF and LCM: Greatest number dividing three numbers with equal remainder PDF
- Q.25 (CDS (I) Maths) · MCQ · HCF and LCM: LCM of three decimal numbers PDF
- Q.26 (CDS (I) Maths) · MCQ · HCF and LCM: Greatest walking speed giving whole-hour times for two distances PDF
- Q.27 (CDS (I) Maths) · MCQ · Divisors: Sum of all divisors of 256 PDF
- Q.28 (CDS (I) Maths) · MCQ · Co-prime Numbers: Statements on consecutive and relatively prime numbers PDF
- Q.30 (CDS (I) Maths) · MCQ · Unit Digit: Unit digit of a product of odd powers PDF
- Q.31 (CDS (I) Maths) · MCQ · Remainders: Remainder when the square of an odd integer is divided by 8 PDF
- Q.76 (CDS (I) Maths) · MCQ · Data Sufficiency: Data sufficiency on whether a power of r is below 1 PDF
- Q.77 (CDS (I) Maths) · MCQ · Data Sufficiency: Data sufficiency on whether p² + q² is composite for primes PDF
- Q.78 (CDS (I) Maths) · MCQ · Data Sufficiency: Data sufficiency on a sum of powers of 0.5 exceeding 2 PDF
- Q.79 (CDS (I) Maths) · MCQ · Data Sufficiency: Data sufficiency for the product of three numbers given HCF and LCM PDF
- Q.80 (CDS (I) Maths) · MCQ · Data Sufficiency: Data sufficiency on digits of the difference of a number and its reverse PDF
- Q.1 (CDS (II) Maths) · MCQ · HCF and LCM: Sum of two integers in ratio 7:19 with a given LCM PDF
- Q.7 (CDS (II) Maths) · MCQ · Digit Problems: Product of digits of a three-digit number with consecutive digits PDF
- Q.17 (CDS (II) Maths) · MCQ · Division Algorithm: Sum of two numbers from their product, quotient and remainder PDF
- Q.23 (CDS (II) Maths) · MCQ · Digit Problems: Product of digits when a number times its reverse is 3627 PDF
- Q.26 (CDS (II) Maths) · MCQ · Digit Problems: Count three-digit numbers with given digit conditions PDF
CDS2025
- Q.2 (CDS (I) Maths) · MCQ · Arithmetic Progression: Sum of all 3-digit numbers leaving remainder 5 when divided by 50 PDF
- Q.5 (CDS (I) Maths) · MCQ · Remainders: Difference of remainders of 7^84 divided by 342 and 344 PDF
- Q.6 (CDS (I) Maths) · MCQ · Remainders: Find n for the smallest 5-digit number leaving remainder 1 on powers of 2 PDF
- Q.7 (CDS (I) Maths) · MCQ · Divisibility: Minimum p making a sum of fractions an integer PDF
- Q.9 (CDS (I) Maths) · MCQ · Two-digit Numbers: Find P + N for a 2-digit number from digit-product conditions PDF
- Q.19 (CDS (I) Maths) · MCQ · Logarithms: Evaluate a sum of base-10 logarithms PDF
- Q.20 (CDS (I) Maths) · MCQ · Logarithms: Solve a logarithmic equation for x PDF
- Q.37 (CDS (I) Maths) · MCQ · Factorials: Largest n with 100! divisible by 100^n PDF
- Q.41 (CDS (I) Maths) · MCQ · Surds and Indices: Simplify a sum of two nested square roots PDF
- Q.42 (CDS (I) Maths) · MCQ · Arithmetic Progression: Maximum sum of a decreasing arithmetic progression PDF
- Q.43 (CDS (I) Maths) · MCQ · Remainders: Remainders of m + n and m - n on division by 12 PDF
- Q.47 (CDS (I) Maths) · MCQ · Remainders: Remainder when 2^p - 1 is divided by prime p PDF
- Q.48 (CDS (I) Maths) · MCQ · Factors: Number of factors of 24^3 - 16^3 - 8^3 PDF
- Q.77 (CDS (I) Maths) · MCQ · Recurring Decimals: Evaluate a quadratic in p for a recurring decimal p PDF
- Q.78 (CDS (I) Maths) · MCQ · Remainders: Remainder when 2^101 is divided by 101 PDF
- Q.85 (CDS (I) Maths) · MCQ · HCF and LCM: Statements on LCM and HCF of two primes PDF
- Q.3 (CDS (II) Maths) · MCQ · Natural Numbers: Largest p such that q^2 - 5p - 4 is negative with q > p (official answer: A) PDF
- Q.4 (CDS (II) Maths) · MCQ · Prime Numbers: Count prime combinations of x, y, x+y, x-y under 20 (official answer: A) PDF
- Q.6 (CDS (II) Maths) · MCQ · Surds and Indices: Evaluate (2+√3)^x - (2-√3)^x given their sum is 2 (official answer: A) PDF
- Q.10 (CDS (II) Maths) · MCQ · Logarithms: Number of digits in a power of 60 using log values (official answer: C) PDF
- Q.11 (CDS (II) Maths) · MCQ · Remainders: Remainder when a sum of two large powers is divided by 18 (official answer: A) PDF
- Q.15 (CDS (II) Maths) · MCQ · HCF and LCM: Count n < 7 for which 12n+2 and 8n+1 are coprime (official answer: A) PDF
- Q.17 (CDS (II) Maths) · MCQ · Divisibility: Divisibility of n(n+1)(n+2) for even n by 48 and 144 (official answer: B) PDF
- Q.19 (CDS (II) Maths) · MCQ · Divisibility: Remainder when difference of a 3-digit number and its reverse is divided by 99 (official answer: A) PDF
- Q.20 (CDS (II) Maths) · MCQ · Divisibility: Least p+q such that (p+q)^(p+q) is divisible by 512 (official answer: C) PDF
- Q.22 (CDS (II) Maths) · MCQ · Surds and Indices: Simplify an exponent expression given a^b = b^a (official answer: A) PDF
- Q.23 (CDS (II) Maths) · MCQ · Surds and Indices: Value of x^2 - 4x - 10 for x = 2 + 2^(1/2) + 2^(3/2) (official answer: C) PDF
- Q.28 (CDS (II) Maths) · MCQ · Surds and Indices: Evaluate p/q + q/p for conjugate surd fractions (official answer: C) PDF
- Q.29 (CDS (II) Maths) · MCQ · Unit and Last Digits: Hundreds digit of 25^10 (official answer: D) PDF
- Q.30 (CDS (II) Maths) · MCQ · HCF and LCM: Smallest 4-digit number leaving remainder 3 on division by 4, 6, 7, 9 (official answer: D) PDF
- Q.37 (CDS (II) Maths) · MCQ · Logarithms: Square of difference of roots of a logarithmic equation (official answer: C) PDF
- Q.38 (CDS (II) Maths) · MCQ · Logarithms: Which log relations follow from x^4 + y^4 = 14x^2y^2 (official answer: C) PDF
- Q.82 (CDS (II) Maths) · MCQ · Data Sufficiency: Data sufficiency: product of a number and its reverse (official answer: A) PDF
- Q.83 (CDS (II) Maths) · MCQ · Data Sufficiency: Data sufficiency: last digit of a factorial-type number (official answer: C) PDF
CDS2024
- Q.16 (CDS (I) Maths) · MCQ · Number Properties: Digit at the hundredth place of a large number (official answer: A) PDF
- Q.17 (CDS (I) Maths) · MCQ · Remainders: Number of possible remainders of a sum of powers divided by 10 (official answer: C) PDF
- Q.18 (CDS (I) Maths) · MCQ · Remainders: Sum of distinct remainders of a sum of powers divided by 10 (official answer: B) PDF
- Q.19 (CDS (I) Maths) · MCQ · Remainders: Remainder when the number formed by writing 1 to 100 is divided (official answer: B) PDF
- Q.22 (CDS (I) Maths) · MCQ · HCF and LCM: Largest equal squares cut from a plank without wastage (official answer: dropped in the final key) PDF
- Q.24 (CDS (I) Maths) · MCQ · HCF and LCM: Value from the HCF of 768 and a product of powers (official answer: A) PDF
- Q.25 (CDS (I) Maths) · MCQ · Factorials: Smallest n for which n! is divisible by 910 (official answer: D) PDF
- Q.26 (CDS (I) Maths) · MCQ · Divisibility: Divisors of 555^777 + 777^555 (official answer: D) PDF
- Q.27 (CDS (I) Maths) · MCQ · Divisibility: Statements on divisibility of algebraic and exponential expressions (official answer: A) PDF
- Q.30 (CDS (I) Maths) · MCQ · Simplification: Range of the value of a continued fraction (official answer: A) PDF
- Q.35 (CDS (I) Maths) · MCQ · Series: Sum of an infinite series of fractions (official answer: A) PDF
- Q.36 (CDS (I) Maths) · MCQ · Simplification: Product of terms of a continued fraction equal to 421/972 (official answer: A) PDF
- Q.61 (CDS (I) Maths) · MCQ · Data Sufficiency: Data sufficiency on the product of four positive integers (official answer: C) PDF
- Q.62 (CDS (I) Maths) · MCQ · Data Sufficiency: Data sufficiency on two primes with a given relation (official answer: A) PDF
- Q.63 (CDS (I) Maths) · MCQ · Data Sufficiency: Data sufficiency on a remainder when p is a positive integer (official answer: A) PDF
- Q.2 (CDS (II) Maths) · MCQ · Number Properties: Pairs of natural numbers whose squares differ by 72 PDF
- Q.3 (CDS (II) Maths) · MCQ · Remainders: Greatest 5-digit number leaving given remainders on division by 6, 12, 15, 24 PDF
- Q.4 (CDS (II) Maths) · MCQ · Remainders: Remainder when a large power expression is divided by 5 PDF
- Q.5 (CDS (II) Maths) · MCQ · Number Properties: Last three digits of the product of two large numbers PDF
- Q.7 (CDS (II) Maths) · MCQ · Remainders: Range of the least multiple of 11 leaving remainder 5 on given divisors PDF
- Q.8 (CDS (II) Maths) · MCQ · Surds: Sum of a telescoping series of reciprocals of root sums PDF
- Q.24 (CDS (II) Maths) · MCQ · Number Formation: Sum of largest and smallest numbers formed from single-digit primes PDF
- Q.25 (CDS (II) Maths) · MCQ · Remainders: Remainder when a power of 3 is divided by 28 PDF
- Q.26 (CDS (II) Maths) · MCQ · Divisibility: Digit x for which an expression is divisible by 9 PDF
- Q.28 (CDS (II) Maths) · MCQ · Divisibility: Statements on a 10-digit number divisible by 9 PDF
- Q.30 (CDS (II) Maths) · MCQ · Prime Numbers: Least x + y when 11x + 5y is prime PDF
- Q.31 (CDS (II) Maths) · MCQ · Factors: Number of divisors of N² when N has 15 divisors PDF
- Q.36 (CDS (II) Maths) · MCQ · HCF and LCM: Number of possible 2-digit LCMs when HCF of n and n+10 is 10 PDF
- Q.45 (CDS (II) Maths) · MCQ · Remainders: Remainder when a product of consecutive numbers is divided by 1000 PDF
- Q.47 (CDS (II) Maths) · MCQ · Division: Quotient of a sum of powers divided by a given expression PDF
- Q.63 (CDS (II) Maths) · MCQ · Data Sufficiency: Data sufficiency on whether a root is prime PDF
- Q.64 (CDS (II) Maths) · MCQ · Data Sufficiency: Data sufficiency on divisibility of a sum of powers by 500 PDF
- Q.68 (CDS (II) Maths) · MCQ · Data Sufficiency: Data sufficiency on three integer weights with a prime sum PDF
- Q.70 (CDS (II) Maths) · MCQ · Data Sufficiency: Data sufficiency on whether p² + pq + q² is odd PDF
- Q.73 (CDS (II) Maths) · MCQ · Remainders: Remainder when a power of 3 is divided PDF
- Q.74 (CDS (II) Maths) · MCQ · Square Roots: Square root of 64% PDF
- Q.75 (CDS (II) Maths) · MCQ · Divisibility: Possible digits p making a difference divisible by 3 PDF
- Q.76 (CDS (II) Maths) · MCQ · Divisibility: Statements on divisibility of sums and differences of powers PDF
- Q.80 (CDS (II) Maths) · MCQ · Number Series: Difference of averages of first 50 even and odd numbers PDF
- Q.89 (CDS (II) Maths) · MCQ · Number Properties: Possible sums of digits when XYZ - YXZ = 90 PDF
- Q.91 (CDS (II) Maths) · MCQ · HCF and LCM: HCF of two numbers of the form 2^n - 1 PDF
- Q.96 (CDS (II) Maths) · MCQ · Number Properties: Writing 199 as a difference of squares PDF
- Q.97 (CDS (II) Maths) · MCQ · Prime Numbers: Count of primes of the form 2^n - 1 below 2000 PDF
- Q.99 (CDS (II) Maths) · MCQ · Remainders: Distinct remainders of a sum of powers divided by 10 PDF
CDS2023
- Q.1 (CDS (I) Maths) · MCQ · HCF and LCM: Largest number dividing two large powers-based expressions (official answer: C) PDF
- Q.2 (CDS (I) Maths) · MCQ · Factorials: Highest power of 10 dividing 29 factorial (official answer: C) PDF
- Q.3 (CDS (I) Maths) · MCQ · Remainders: Remainder of a power of 65 on division (official answer: D) PDF
- Q.7 (CDS (I) Maths) · MCQ · Prime Numbers: How many of three given numbers are prime (official answer: A) PDF
- Q.14 (CDS (I) Maths) · MCQ · Surds: Square root of 8 + 2a for a given surd product (official answer: D) PDF
- Q.15 (CDS (I) Maths) · MCQ · Remainders: Remainder of even powers of odd integers divided by 8 (official answer: C) PDF
- Q.16 (CDS (I) Maths) · MCQ · Divisibility: Statements on integrality of given expressions in n and m (official answer: C) PDF
- Q.17 (CDS (I) Maths) · MCQ · Divisibility: Which expression 5 divides when it divides none of n-1, n, n+1 (official answer: A) PDF
- Q.18 (CDS (I) Maths) · MCQ · HCF and LCM: Largest 5-digit number leaving remainder 7 for 18 and 11 (official answer: C) PDF
- Q.22 (CDS (I) Maths) · MCQ · Factors: Number and sum of factors of 360 (official answer: C) PDF
- Q.23 (CDS (I) Maths) · MCQ · Divisibility: Divisors of every 6-digit number of form XYXYXY (official answer: D) PDF
- Q.24 (CDS (I) Maths) · MCQ · HCF and LCM: HCF of two expressions in powers of 3 (official answer: D) PDF
- Q.25 (CDS (I) Maths) · MCQ · Surds: Value of an infinite nested radical (official answer: B) PDF
- Q.26 (CDS (I) Maths) · MCQ · Divisibility: Minimum m + n so that 33m + 22n is divisible by 121 (official answer: B) PDF
- Q.27 (CDS (I) Maths) · MCQ · HCF and LCM: Mean of two numbers from product, HCF and sum of squares (official answer: C) PDF
- Q.30 (CDS (I) Maths) · MCQ · HCF and LCM: Times four bells ring together in the next 72 hours (official answer: C) PDF
- Q.31 (CDS (I) Maths) · MCQ · Number Properties: Possible values of a sum of powers of -1 over integers summing to 200 (official answer: C) PDF
- Q.32 (CDS (I) Maths) · MCQ · Divisibility: Divisibility of a difference of large powers by 37 and 83 (official answer: C) PDF
- Q.37 (CDS (I) Maths) · MCQ · Divisibility: Divisibility statements for polynomial expressions in n (official answer: D) PDF
- Q.38 (CDS (I) Maths) · MCQ · Unit Digit: Last digit of a sum of two large powers (official answer: B) PDF
- Q.63 (CDS (I) Maths) · MCQ · HCF and LCM: Minimum number of square tiles to pave a hall floor (official answer: D) PDF
- Q.71 (CDS (I) Maths) · MCQ · Divisibility: Data sufficiency: digit X of a number divisible by 25 (official answer: C) PDF
- Q.75 (CDS (I) Maths) · MCQ · Number Properties: Data sufficiency: sum of consecutive odd integers (official answer: C) PDF
- Q.76 (CDS (I) Maths) · MCQ · Number Properties: Data sufficiency: parity of an expression in p and q (official answer: D) PDF
- Q.89 (CDS (I) Maths) · MCQ · Sets of Numbers: Largest subset with no two elements summing to 100 (official answer: D) PDF
- Q.13 (CDS (II) Maths) · MCQ · HCF and LCM: Product of two numbers from LCM:HCF ratio and their sum (official answer: B) PDF
- Q.93 (CDS (II) Maths) · MCQ · Number Properties: Data sufficiency: a 3-digit number divisible by 10 (official answer: C) PDF
- Q.96 (CDS (II) Maths) · MCQ · HCF and LCM: Data sufficiency: sum of two natural numbers (official answer: D) PDF
CDS2022
- Q.2 (CDS (I) Maths) · MCQ · Divisibility: Divisor of 41^43 + 43^43 (official answer: B) PDF
- Q.4 (CDS (I) Maths) · MCQ · Divisibility: Divisor of a sum of consecutive powers of 4 (official answer: D) PDF
- Q.5 (CDS (I) Maths) · MCQ · HCF and LCM: Difference of two numbers from LCM-HCF ratio and product (official answer: D) PDF
- Q.6 (CDS (I) Maths) · MCQ · Simplification: Simplify a decimal cubic expression (official answer: C) PDF
- Q.14 (CDS (I) Maths) · MCQ · Fractions: Product of a, b, c, d from a continued fraction (official answer: A) PDF
- Q.16 (CDS (I) Maths) · MCQ · Number Properties: Least n making a number a fourth power (official answer: A) PDF
- Q.20 (CDS (I) Maths) · MCQ · Square Roots: Least number to subtract for a perfect square (official answer: D) PDF
- Q.21 (CDS (I) Maths) · MCQ · Divisibility: Divisor of 27^5 + 3^13 (official answer: B) PDF
- Q.22 (CDS (I) Maths) · MCQ · Divisibility: Least m making two expressions divisible by 5 (official answer: B) PDF
- Q.29 (CDS (I) Maths) · MCQ · Units and Conversions: Minutes in x weeks and x days (official answer: A) PDF
- Q.34 (CDS (I) Maths) · MCQ · Number Properties: Statements on sums of cubes and odd powers (official answer: C) PDF
- Q.35 (CDS (I) Maths) · MCQ · Factors: Number of divisors of 1000 excluding 1 and itself (official answer: C) PDF
- Q.8 (CDS (II) Maths) · MCQ · Division Algorithm: Difference of two numbers from quotient and remainder data (official answer: B) PDF
- Q.18 (CDS (II) Maths) · MCQ · HCF and LCM: Relation between HCF and LCM of fractions (official answer: D) PDF
- Q.19 (CDS (II) Maths) · MCQ · Remainders: Remainder of x - y divided by 6 (official answer: C) PDF
- Q.20 (CDS (II) Maths) · MCQ · Number Properties: Digit product of a number 5 times its digit sum (official answer: C) PDF
- Q.21 (CDS (II) Maths) · MCQ · Factors: Statements on odd and even factors of a number (official answer: C) PDF
CDS2021
- Q.1 (CDS (I) Maths) · MCQ · Divisibility: Missing digit making a large number divisible by 13 (official answer: D) PDF
- Q.2 (CDS (I) Maths) · MCQ · Remainders: Remainder of a large power of 2 divided by 7 (official answer: B) PDF
- Q.3 (CDS (I) Maths) · MCQ · Number Properties: Pairs from a set satisfying x/y + y/x = 2 (official answer: A) PDF
- Q.4 (CDS (I) Maths) · MCQ · Prime Numbers: Prime pairs between 50 and 100 differing by 6 (official answer: D) PDF
- Q.6 (CDS (I) Maths) · MCQ · Remainders: Remainder of 27^27 - 15^27 divided by 6 (official answer: A) PDF
- Q.9 (CDS (I) Maths) · MCQ · Unit Digit: Unit digit of 67^32 (official answer: A) PDF
- Q.18 (CDS (I) Maths) · MCQ · Simplification: Integer x satisfying a continued fraction equation (official answer: C) PDF
- Q.26 (CDS (I) Maths) · MCQ · Fractions: Fraction least changed when 3 is added to both parts (official answer: D) PDF
- Q.30 (CDS (I) Maths) · MCQ · Series: Value of n for a telescoping series sum (official answer: B) PDF
- Q.43 (CDS (I) Maths) · MCQ · Number Properties: Sum of two alternate numbers from reciprocal sum (official answer: C) PDF
- Q.44 (CDS (I) Maths) · MCQ · Divisibility: Number of divisors always dividing 5^(2n) - 1 (official answer: D) PDF
- Q.1 (CDS (II) Maths) · MCQ · Prime Factorisation: Distinct prime factors of a five-digit number (official answer: D) PDF
- Q.4 (CDS (II) Maths) · MCQ · Remainders: Remainder of 37^1000 divided by 9 (official answer: A) PDF
- Q.5 (CDS (II) Maths) · MCQ · HCF and LCM: Other number from sum and difference of LCM and HCF (official answer: B) PDF
- Q.14 (CDS (II) Maths) · MCQ · HCF and LCM: Difference of two primes from their LCM (official answer: C) PDF
- Q.15 (CDS (II) Maths) · MCQ · HCF and LCM: When three runners next meet at the start (official answer: D) PDF
- Q.17 (CDS (II) Maths) · MCQ · Number Properties: Number of trailing zeros in a product of powers (official answer: A) PDF
- Q.32 (CDS (II) Maths) · MCQ · Number Properties: Two-digit number with digit product 8 and reversal (official answer: D) PDF
- Q.35 (CDS (II) Maths) · MCQ · Fractions: Difference of numerator and denominator of a fraction (official answer: C) PDF
- Q.45 (CDS (II) Maths) · MCQ · Series: Years needed to save a target amount in AP (official answer: B) PDF
- Q.99 (CDS (II) Maths) · MCQ · Number Properties: Sequences of five consecutive integers with product in set (official answer: D) PDF
- Q.100 (CDS (II) Maths) · MCQ · Number Properties: Mean of smallest and largest integers in those sequences (official answer: A) PDF
CDS2020
- Q.1 (CDS (I) Maths) · MCQ · Prime Numbers: Nature of the number formed by a product of primes plus one (official answer: A) PDF
- Q.2 (CDS (I) Maths) · MCQ · HCF and LCM: Mean of means of two number pairs with given product and HCF (official answer: B) PDF
- Q.3 (CDS (I) Maths) · MCQ · Logarithms: Number of digits in a large power using given log values (official answer: B) PDF
- Q.6 (CDS (I) Maths) · MCQ · Digit Sum: Find n from the digit sum of 10 to the n minus 1 (official answer: B) PDF
- Q.7 (CDS (I) Maths) · MCQ · Comparison of Numbers: Largest among numbers built from repeated 2s as powers (official answer: A) PDF
- Q.8 (CDS (I) Maths) · MCQ · Prime Numbers: Difference in counts of primes below 50 and between 50 and 100 (official answer: B) PDF
- Q.10 (CDS (I) Maths) · MCQ · Factors and Multiples: Largest divisor of a sum of consecutive powers of 3 (official answer: C) PDF
- Q.11 (CDS (I) Maths) · MCQ · Two-digit Numbers: Two-digit number from a reversal relation and digit product (official answer: A) PDF
- Q.16 (CDS (I) Maths) · MCQ · Remainders: Largest number leaving equal remainders on three numbers (official answer: C) PDF
- Q.18 (CDS (I) Maths) · MCQ · Indices: Value of (m-1) to the n-1 when m to the n is 1331 (official answer: B) PDF
- Q.20 (CDS (I) Maths) · MCQ · Surds: Order of three surds of different roots (official answer: B) PDF
- Q.21 (CDS (I) Maths) · MCQ · Logarithms: Log of y where y is x raised to log x (official answer: C) PDF
- Q.25 (CDS (I) Maths) · MCQ · Recurring Decimals: Distance between two recurring decimals on the number line (official answer: A) PDF
- Q.41 (CDS (I) Maths) · MCQ · Divisibility Rules: Three-digit numbers divisible by 7 both ways (official answer: C) PDF
- Q.43 (CDS (I) Maths) · MCQ · Divisibility Rules: Divisibility of the sum of cyclic permutations of a 3-digit number (official answer: D) PDF
- Q.47 (CDS (I) Maths) · MCQ · Perfect Squares: Least perfect square divisible by 3, 4, 5, 6 and 7 (official answer: C) PDF
- Q.1 (CDS (II) Maths) · MCQ · Divisibility: Count positive integers x dividing a polynomial expression in x (official answer: C) PDF
- Q.2 (CDS (II) Maths) · MCQ · Factors and Multiples: Number of ordered triples with product 30 (official answer: B) PDF
- Q.6 (CDS (II) Maths) · MCQ · Divisibility Rules: Missing digit for divisibility by the smallest odd composite (official answer: A) PDF
- Q.7 (CDS (II) Maths) · MCQ · Remainders: Remainder of a sum of powers divided by 4 (official answer: B) PDF
- Q.8 (CDS (II) Maths) · MCQ · Unit Digit: Unit digit of a power of 3 (official answer: C) PDF
- Q.9 (CDS (II) Maths) · MCQ · HCF and LCM: Other number from LCM-HCF relation and their sum (official answer: A) PDF
- Q.11 (CDS (II) Maths) · MCQ · Remainders: Remainder when a large power is divided by 18 (official answer: A) PDF
- Q.12 (CDS (II) Maths) · MCQ · Surds: Sum of a telescoping series of surd fractions (official answer: C) PDF
- Q.19 (CDS (II) Maths) · MCQ · Number of Divisors: Statements on the divisor-count function (official answer: B) PDF
- Q.20 (CDS (II) Maths) · MCQ · Prime Numbers: Statements on the product of first n primes plus one (official answer: D) PDF
- Q.36 (CDS (II) Maths) · MCQ · Two-digit Numbers: Product of digits from sum and reversal difference (official answer: B) PDF
- Q.43 (CDS (II) Maths) · MCQ · Logarithms: Range of x in an exponential equation using logs (official answer: B) PDF
- Q.44 (CDS (II) Maths) · MCQ · HCF and LCM: What the Euclidean algorithm computes (official answer: D) PDF
CDS2019
- Q.1 (CDS (I) Maths) · MCQ · Remainders: Remainder when a sum of powers is divided by 18 (official answer: D) PDF
- Q.2 (CDS (I) Maths) · MCQ · Factors and Multiples: Largest power of 10 dividing a given product (official answer: A) PDF
- Q.3 (CDS (I) Maths) · MCQ · Divisibility Rules: Count digit pairs making an eight-digit number divisible by 9 (official answer: A) PDF
- Q.4 (CDS (I) Maths) · MCQ · Digit Puzzles: Find the digits in a multiplication of 999 by a three-digit number (official answer: D) PDF
- Q.6 (CDS (I) Maths) · MCQ · Squares and Cubes: Age that is a cube in the past and a square in the future (official answer: C) PDF
- Q.7 (CDS (I) Maths) · MCQ · Prime Numbers: Pick the false statement about prime numbers (official answer: C) PDF
- Q.13 (CDS (I) Maths) · MCQ · Logarithms: Number of digits in a power using given log values (official answer: C) PDF
- Q.14 (CDS (I) Maths) · MCQ · Prime Numbers: Three primes summing to 100 with two differing by 36 (official answer: C) PDF
- Q.19 (CDS (I) Maths) · MCQ · Unit Digit: A particular digit in the expansion of a power of 7 (official answer: C) PDF
- Q.20 (CDS (I) Maths) · MCQ · Perfect Squares: Count positive integers n making n squared plus 48 a perfect square (official answer: C) PDF
- Q.24 (CDS (I) Maths) · MCQ · Co-prime Numbers: Statements about two relatively prime integers (official answer: D) PDF
- Q.26 (CDS (I) Maths) · MCQ · Real Numbers: Nature of an expression with square roots of real numbers (official answer: C) PDF
- Q.28 (CDS (I) Maths) · MCQ · Recurring Decimals: Sum of two recurring decimals (official answer: A) PDF
- Q.30 (CDS (I) Maths) · MCQ · Irrational Numbers: Identify the irrational number among options (official answer: D) PDF
- Q.33 (CDS (I) Maths) · MCQ · Remainders: Remainder when a power of 3 is divided by 8 (official answer: B) PDF
- Q.34 (CDS (I) Maths) · MCQ · Prime Numbers: Possible unit digits of a prime number (official answer: D) PDF
- Q.13 (CDS (II) Maths) · MCQ · HCF and LCM: Number that cannot be the LCM when HCF is 12 (official answer: A) PDF
- Q.14 (CDS (II) Maths) · MCQ · Number Properties: Statements on unit digits, odd squares and odd products (official answer: C) PDF
- Q.18 (CDS (II) Maths) · MCQ · HCF and LCM: LCM of given fractions (official answer: C) PDF
- Q.24 (CDS (II) Maths) · MCQ · Division Algorithm: Find N from quotient and remainder relation (official answer: C) PDF
- Q.58 (CDS (II) Maths) · MCQ · Logarithms: Log of a small decimal from a given log value (official answer: B) PDF
- Q.60 (CDS (II) Maths) · MCQ · Logarithms: Log of the squared area of an equilateral triangle (official answer: A) PDF
- Q.72 (CDS (II) Maths) · MCQ · Co-prime Numbers: Statements on relatively prime numbers and divisibility (official answer: A) PDF
- Q.76 (CDS (II) Maths) · MCQ · Surds: Square root of a surd expression (official answer: C) PDF
- Q.77 (CDS (II) Maths) · MCQ · Logarithms: Number of digits in three large powers (official answer: C) PDF
- Q.78 (CDS (II) Maths) · MCQ · Remainders: Smallest number with given remainders by 14 and 15 (official answer: B) PDF
- Q.80 (CDS (II) Maths) · MCQ · Number Properties: Statements on irrational and recurring numbers (official answer: D) PDF
- Q.82 (CDS (II) Maths) · MCQ · Continued Fractions: Sum x+y+z from a continued fraction (official answer: A) PDF
- Q.86 (CDS (II) Maths) · MCQ · Factors and Multiples: Largest power of 10 dividing a product (official answer: A) PDF
- Q.87 (CDS (II) Maths) · MCQ · Unit Digit: Unit digit of a difference of powers of 3 (official answer: B) PDF
- Q.88 (CDS (II) Maths) · MCQ · Squares: Sum of four consecutive numbers from sum of squares (official answer: B) PDF
- Q.90 (CDS (II) Maths) · MCQ · Squares: Pairs of natural numbers whose squares differ by 35 (official answer: B) PDF
- Q.95 (CDS (II) Maths) · MCQ · Number Properties: Incorrect statement among number facts (official answer: C) PDF
- Q.96 (CDS (II) Maths) · MCQ · Perfect Squares: Sum of integers n making a quadratic in n a perfect square (official answer: D) PDF
CDS2018
- Q.1 (CDS (I) Maths) · MCQ · Divisibility: Divisor of a sum of four consecutive powers of 5 (official answer: D) PDF
- Q.5 (CDS (I) Maths) · MCQ · Rational and Irrational Numbers: Correct statement on decimal expansions of rationals and irrationals (official answer: D) PDF
- Q.12 (CDS (I) Maths) · MCQ · Perfect Squares: Smallest four-digit perfect square (official answer: B) PDF
- Q.14 (CDS (I) Maths) · MCQ · HCF and LCM: Sum of two numbers from their LCM and HCF (official answer: A) PDF
- Q.18 (CDS (I) Maths) · MCQ · Surds: Simplify a sum of surd fractions with root 5 and root 3 (official answer: A) PDF
- Q.23 (CDS (I) Maths) · MCQ · Recurring Decimals: Difference between 0.9 and 0.9 recurring (official answer: C) PDF
- Q.34 (CDS (I) Maths) · MCQ · Recurring Decimals: Decimal that is a rational number with denominator 37 (official answer: A) PDF
- Q.36 (CDS (I) Maths) · MCQ · Comparison of Numbers: Order of log m, m, m squared and 1/m for 0<m<1 (official answer: A) PDF
- Q.38 (CDS (I) Maths) · MCQ · HCF and LCM: Sum of three co-prime numbers from pairwise products (official answer: D) PDF
- Q.41 (CDS (I) Maths) · MCQ · Unit Digit: Unit digit of product of odd primes up to 110 (official answer: C) PDF
- Q.83 (CDS (I) Maths) · MCQ · Factorials: Largest power of 10 dividing 25 factorial (official answer: D) PDF
- Q.1 (CDS (II) Maths) · MCQ · HCF and LCM: Largest four-digit number divisible by 16, 36, 45 and 48 (official answer: B) PDF
- Q.3 (CDS (II) Maths) · MCQ · Surds: Value of a cubic expression at x = 2 plus cube roots (official answer: A) PDF
- Q.4 (CDS (II) Maths) · MCQ · Divisibility: Count of five-digit XXYXX numbers divisible by 33 (official answer: B) PDF
- Q.5 (CDS (II) Maths) · MCQ · Divisibility: Pairs (X, Y) making XY235 divisible by 3 with X+Y<5 (official answer: C) PDF
- Q.7 (CDS (II) Maths) · MCQ · Factors and Multiples: Number of proper divisors of 38808 (official answer: C) PDF
- Q.12 (CDS (II) Maths) · MCQ · Number Properties: Sum of cubes of three consecutive numbers from sum of squares (official answer: C) PDF
- Q.13 (CDS (II) Maths) · MCQ · HCF and LCM: Sum of two integers from product and HCF (official answer: C) PDF
- Q.14 (CDS (II) Maths) · MCQ · Logarithms: Value of a logarithm of 0.72 using log 2 and log 3 (official answer: B) PDF
- Q.17 (CDS (II) Maths) · MCQ · Divisibility: Statements on the sum of cyclic three-digit numbers (official answer: B) PDF
- Q.18 (CDS (II) Maths) · MCQ · Number Properties: Number of positive integer pairs satisfying a reciprocal equation (official answer: C) PDF
- Q.46 (CDS (II) Maths) · MCQ · Logarithms: Number of zeros after the decimal point in 0.2^25 (official answer: D) PDF
CDS2017
- Q.1 (CDS (I) Maths) · MCQ · Simplification: Square root of a decimal product ratio (official answer: B) PDF
- Q.4 (CDS (I) Maths) · MCQ · HCF and LCM: Statements on HCF and LCM when a=bc (official answer: A) PDF
- Q.5 (CDS (I) Maths) · MCQ · Square Roots: Square root of a decimal expression (official answer: B) PDF
- Q.8 (CDS (I) Maths) · MCQ · Remainders: Remainder of 4444^4444 divided by 9 (official answer: C) PDF
- Q.10 (CDS (I) Maths) · MCQ · Simplification: Evaluate expression with 443 and 547 (official answer: C) PDF
- Q.13 (CDS (I) Maths) · MCQ · Sets: Which set expression is empty (official answer: D) PDF
- Q.21 (CDS (I) Maths) · MCQ · Prime Numbers: Count of primes below 100 (official answer: B) PDF
- Q.25 (CDS (I) Maths) · MCQ · Fractions: Number to subtract to reach a given fraction (official answer: D) PDF
- Q.36 (CDS (I) Maths) · MCQ · Comparison of Numbers: Largest among given numbers (official answer: B) PDF
- Q.40 (CDS (I) Maths) · MCQ · Linear Diophantine: Most sweets for exactly ₹200 (official answer: B) PDF
- Q.43 (CDS (I) Maths) · MCQ · Simplification: Evaluate a numerical expression (official answer: A) PDF
- Q.46 (CDS (I) Maths) · MCQ · Integers: Statements on consecutive and odd integers (official answer: C) PDF
- Q.48 (CDS (I) Maths) · MCQ · Number Theory: Condition for Fermat's little theorem (official answer: A) PDF
- Q.49 (CDS (I) Maths) · MCQ · Number Puzzles: Difference of squares from ratio and product (official answer: C) PDF
- Q.2 (CDS (II) Maths) · MCQ · Divisibility: Numbers to 1000 divisible by 2, 3, 4 and 5 (official answer: A) PDF
- Q.4 (CDS (II) Maths) · MCQ · Simplification: Expression in repunit-type numbers (official answer: B) PDF
- Q.9 (CDS (II) Maths) · MCQ · Decimal Expansion: Distance between two recurring decimals (official answer: B) PDF
- Q.17 (CDS (II) Maths) · MCQ · Perfect Squares: Which numbers are not perfect squares (official answer: D) PDF
- Q.21 (CDS (II) Maths) · MCQ · Divisibility: Divisibility when a and c are coprime (official answer: C) PDF
- Q.24 (CDS (II) Maths) · MCQ · Integers: Property holding for every integer k (official answer: C) PDF
- Q.25 (CDS (II) Maths) · MCQ · Divisibility: Numbers between 500 and 1000 divisible by 13 (official answer: C) PDF
- Q.31 (CDS (II) Maths) · MCQ · Sets: Correct notation for a set statement (official answer: B) PDF
- Q.35 (CDS (II) Maths) · MCQ · Surds: Value of an infinite nested root (official answer: C) PDF
CDS2016
- Q.17 (CDS (I) Maths) · MCQ · Number Properties: Statements on values of a sum expression Sₙ (official answer: A) PDF
- Q.18 (CDS (I) Maths) · MCQ · Integers: Statements comparing p+q and p-q for integers (official answer: A) PDF
- Q.20 (CDS (I) Maths) · MCQ · Number Properties: Evaluate an expression with powers of 10 (official answer: D) PDF
- Q.21 (CDS (I) Maths) · MCQ · Digits and Numbers: Two-digit number as multiple of digit sum after swap (official answer: C) PDF
- Q.28 (CDS (I) Maths) · MCQ · Remainders: Pairs from first 14 numbers with product ≡1 mod 15 (official answer: D) PDF
- Q.29 (CDS (I) Maths) · MCQ · Number Puzzles: Time for a clock to strike 10 (official answer: C) PDF
- Q.32 (CDS (I) Maths) · MCQ · Prime Factorisation: Highest power of 3 dividing a product (official answer: B) PDF
- Q.34 (CDS (I) Maths) · MCQ · Real Numbers: Statements on natural, rational and real numbers (official answer: B) PDF
- Q.36 (CDS (I) Maths) · MCQ · Number Properties: Statements on cos x = 2^m and mn vs m+n (official answer: D) PDF
- Q.41 (CDS (I) Maths) · MCQ · HCF and LCM: Statements on HCF and LCM properties (official answer: C) PDF
- Q.44 (CDS (I) Maths) · MCQ · Sets: People speaking both English and French (official answer: A) PDF
- Q.73 (CDS (I) Maths) · MCQ · Integers: Which expressions in m, n are integers (official answer: B) PDF
- Q.76 (CDS (I) Maths) · MCQ · Continued Fractions: Find z from a continued fraction (official answer: C) PDF
- Q.98 (CDS (I) Maths) · MCQ · Simplification: Evaluate an expression with 243 and 647 (official answer: C) PDF
- Q.3 (CDS (II) Maths) · MCQ · Simplification: Evaluate a ratio of sums of squares (official answer: A) PDF
- Q.5 (CDS (II) Maths) · MCQ · Digits and Numbers: Maximum digit value in a sum of three-digit numbers (official answer: A) PDF
- Q.6 (CDS (II) Maths) · MCQ · Remainders: Integers below 100 leaving remainders 1 to 5 (official answer: B) PDF
- Q.7 (CDS (II) Maths) · MCQ · Number Puzzles: Number multiplied by 8 instead of divided (official answer: B) PDF
- Q.9 (CDS (II) Maths) · MCQ · Number Puzzles: Difference of two integers from squares condition (official answer: C) PDF
- Q.10 (CDS (II) Maths) · MCQ · Sets: Sizes of set differences A-B and B-A (official answer: B) PDF
- Q.11 (CDS (II) Maths) · MCQ · HCF and LCM: Least days to save a whole number of rupees (official answer: B) PDF
- Q.13 (CDS (II) Maths) · MCQ · Decimal Expansion: Rational number with repeating decimal (official answer: D) PDF
- Q.15 (CDS (II) Maths) · MCQ · Remainders: Remainder of a power of 2 divided by 101 (official answer: A) PDF
- Q.22 (CDS (II) Maths) · MCQ · Number Properties: 1729 as a sum of two cubes (official answer: C) PDF
- Q.24 (CDS (II) Maths) · MCQ · HCF and LCM: Statements on co-prime numbers (official answer: D) PDF
- Q.25 (CDS (II) Maths) · MCQ · Simplification: Product of terms like 1-1/n up to 2009 (official answer: A) PDF
- Q.27 (CDS (II) Maths) · MCQ · Number Properties: Statements on squares of odd integers (official answer: A) PDF
- Q.30 (CDS (II) Maths) · MCQ · Divisibility: Divisor of a sum of powers of 2 (official answer: D) PDF
- Q.33 (CDS (II) Maths) · MCQ · Unit Digit: Unit digit of a power of 7 (official answer: D) PDF
- Q.96 (CDS (II) Maths) · MCQ · Remainders: Pairs from 1 to 10 with product ≡4 mod 12 (official answer: C) PDF
- Q.97 (CDS (II) Maths) · MCQ · Remainders: Remainder of a sum of powers divided by 29 (official answer: D) PDF
- Q.98 (CDS (II) Maths) · MCQ · Series: Sum of cubes minus sum of squares to 10 (official answer: B) PDF
Other Elementary Mathematics topics
- Percentage, Ratio, Profit and Interest PYQs
- Time, Speed and Work PYQs
- Algebra PYQs
- Trigonometry PYQs
- Geometry PYQs
- Mensuration PYQs
- Statistics PYQs
FAQ
How many Number System and Simplification questions come in CDS?
In the official papers we tagged: 21 in 2026, 34 in 2025, 44 in 2024, 28 in 2023, 17 in 2022, 22 in 2021, 29 in 2020, 34 in 2019, 22 in 2018, 23 in 2017 and 32 in 2016 (2 papers each year). That is 306 questions in all, about 14% of Elementary Mathematics.
Which Number System and Simplification topics repeat in CDS?
Asked in the most papers: HCF and LCM, Remainders, Divisibility. The concept table lists every one with its count.
Are these official CDS questions?
Yes. Every question is from an official CDS paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.