CAT 2026 Number System: 5-Year Trend, Important PYQs and Shortcuts to Practise

CAT 2026 Number System weightage (2021–2025)

The five-year CAT Quant analysis covers 330 questions across CAT 2021 to 2025. Number System remained remarkably stable during this period.

The important takeaway for CAT 2026 Quantitative Aptitude is consistency, not a guaranteed question count. CAT can change the difficulty or combine two concepts even when the underlying Number System topic remains familiar.

CAT Number System PYQs with answers and solutions

Recent CAT papers show that Number System questions can combine a basic concept with an additional condition. These are more useful for CAT 2026 quant preparation than solving only direct formula-based questions.

Question 1 - CAT 2025, Slot 1

In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is:

Question 2 - CAT 2025, Slot 2

The number of divisors of 26355372, which are of the form (3r+1), where r is a non-negative integer, is

A. 42

B. 36

C. 56

D. 24

Question 3 - CAT 2025, Slot 2

The sum of the digits of the number (625)65(128)36 is:

Question 4 - CAT 2025, Slot 3

For a 4-digit number (greater than 1000), the sum of the digits in the thousands, hundreds, and tens places is 15. The sum of the digits in the hundreds, tens, and units places is 16. Also, the digit in the tens place is 6 more than the digit in the units place. The difference between the largest and smallest possible value of the number is:

A. 811

B. 4078

C. 735

D. 3289

Question 5 - CAT 2025, Slot 3

The sum of all the digits of the number (1050+1025-123) is

A. 324

B. 255

C. 212

D. 221

Question 6 - CAT 2024, Slot 1

When 10100 is divided by 7, the remainder is

A. 3

B. 4

C. 1

D. 6

Question 7 - CAT 2024, Slot 1

For any natural number n, let an be the largest integer not exceeding n. Then the value of a1+a2++a50 is

Question 8 - CAT 2024, Slot 1

The sum of all four-digit numbers that can be formed with the distinct non-zero digits a, b, c, and d, with each digit appearing exactly once in every number, is 153310+n, where n is a single digit natural number. Then, the value of (a+b+c+d+n) is

Question 9 - CAT 2024, Slot 2

A function f maps the set of natural numbers to whole numbers, such that f(xy)=f(x)f(y)+f(x)+f(y) for all x,y and f(p)=1 for every prime number p. Then, the value of f(160000) is

A. 4095

B. 8191

C. 2047

D. 1023

Question 10 - CAT 2024, Slot 2

If m and n are natural numbers such that n>1, and mn=225340, then m-n equals

A. 209932

B. 209937

C. 209942

D. 209947

These CAT PYQs show three different ways CAT can test the same broad area: factor selection, power manipulation and modular cycles.

CAT Number System PYQs PDF download

Practise previous year CAT Number System questions from 2021 to 2025 to understand question trends, difficulty levels, and the types of concepts frequently tested in the Quantitative Aptitude section.

Download Now: CAT Number System PYQs (2021-2025) PDF

Remainder shortcuts

For CAT remainder questions, do not start calculating the full number. First check whether the base or exponent can be reduced.

For example:

${17}^{50}(\mathrm{mod}8)$

Since

$17\equiv 1(\mathrm{mod}8)$,

the answer is immediately 1.

Unit digit tricks

For unit digit tricks, only the final digit of the base matters.

For example: 72026 has a cycle of 4.

Since $2026\equiv 2(\mathrm{mod}4)$, the second value in 7,9,3,1 gives the answer: 9.

Factors and divisibility

The basic factor-counting formula is:

If $N=p^a{q}^b{r}^c$, then

Numberoffactors=(a+1)(b+1)(c+1).

But CAT can add restrictions to this calculation. Practise questions involving:

• Factors divisible by a given number

• Factors satisfying a remainder condition

• Perfect-square factors

• Prime-factor restrictions

• Digit-based divisibility

• HCF and LCM conditions

The CAT 2025 divisor PYQ is a good example because the factor formula alone does not give the answer; the divisor must also satisfy a modular condition.

Get the CAT 2025 slot-wise weightage matrix to understand the topic-wise distribution of questions and identify high-weightage areas for smarter preparation.

Download the CAT 2025 Weightage Matrix

Preparation strategy for CAT 2026

The five-year data should guide what you practise, not dictate a fixed prediction for CAT 2026. Number System has remained present every year, while Arithmetic and Algebra together form the much larger portion of the overall Quant distribution.

For CAT 2026, use a three-level practice cycle:

Level 1: Build the mechanism

Master divisibility, remainders, factorisation, cyclicity, powers and digit properties.

Level 2: Solve CAT Number System PYQs

Start with CAT 2021-2025 and classify each question by the underlying method rather than simply by chapter name.

Level 3: Mix and time the questions

Once comfortable, solve Number System questions alongside Arithmetic and Algebra. This tests whether you can recognise the method without being told that the question is from Number System.

Keep an error log with three labels: concept error, calculation error and approach error. A question solved correctly but taking excessive time should also be recorded.

CAT 2026 Free Mock Test

Prepare for CAT with a free mock test to practise the latest exam pattern, improve time management, and identify your strengths and weak areas.

Attempt the CAT Free Mock Test

Practice with CAT 2026 Mock Test Series - 20 Sets, Questions with Solutions By Experts

Related CAT Quant resources

Explore these useful CAT 2026 Quantitative Aptitude resources and recommended eBooks for formula revision, topic-wise practice, shortcuts, and focused preparation to strengthen your overall QA strategy.