CAT Number System is an important topic in the Quantitative Aptitude (QA) section of the Common Admission Test (CAT). It covers number properties, factors and multiples, remainders, divisibility, digits and base systems, and LCM and HCF. Practising CAT Number System PYQs helps candidates understand question patterns, improve calculation speed, and identify concepts that appear frequently. Based on a five-year analysis of CAT 2021-2025, Number System accounted for 27 out of 330 Quantitative Aptitude questions, or approximately 8.2% of the questions analysed.
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The following guide covers the year-wise weightage trend, question types, topic distribution, difficulty level, and preparation strategy.
This PDF includes:
| 159 Number System questions in the PDF | 8.2% Five-year QA Share (2021-2025) |
| 2025-1990 Years Covered | 27 Exam years in the PDF |
The PDF holds 159 Number System questions from CAT 1990 to 2025, grouped by year and slot. Answer keys and solutions are not included.
CAT Number System PYQ Statistics (2021-2025)
The following figures represent the aggregated number of Number System questions across all three slots of CAT each year, not the count in an individual slot.
| Year | Total Questions (All Slots) | Average per Slot | Weightage in QA | Change in Weightage |
|---|---|---|---|---|
| 2025 | 7 | 2.33 | 10.61% | 0.00% |
| 2024 | 7 | 2.33 | 10.61% | +1.52% |
| 2023 | 6 | 2.00 | 9.09% | +1.52% |
| 2022 | 5 | 1.67 | 7.58% | +4.55% |
| 2021 | 2 | 0.67 | 3.03% | — |
| Total | 27 | 1.80 | 8.18% overall | — |
Weightage is the share of the 66 Quantitative Aptitude questions across the three slots in that year. Change in weightage is the difference in percentage points from the previous year.
CAT Number System PYQ Question-Type Distribution
CAT Number System questions in the Quantitative Aptitude section can appear as Multiple Choice Questions (MCQs) or Type In The Answer (TITA) questions.
Number System questions are few in each slot, so the figures below are totals. Across CAT 2021-2025, 12 of the 27 Number System questions were MCQs and 15 were TITA. In the full PDF of 159 questions, 133 are MCQs and 26 are TITA.
| Question Type | Questions in CAT 2021-2025 | Share | Questions in the full PDF |
|---|---|---|---|
| MCQs (Multiple Choice Questions) | 12 | 44.4% | 133 |
| TITA (Type In The Answer) | 15 | 55.6% | 26 |
| Total | 27 | — | 159 |
CAT Number System Topic-Wise PYQ Distribution
Number System includes several subtopics that test reasoning and the application of mathematical concepts. Number properties are the largest subtopic, with 75 of the 159 questions.
The following areas are covered in the topic-wise PYQ collection, and each has its own PDF.
| Number System subtopic | Concepts to practise | Questions in PDF | Download |
|---|---|---|---|
| Number Properties | Odd and even numbers, primes, squares, factorials and general properties of integers | 75 | Download PDF |
| Divisibility | Divisibility rules and divisibility of expressions | 18 | Download PDF |
| Remainders | Remainder theorems, cyclicity, remainders of large powers | 19 | Download PDF |
| Digits and Base Systems | Unit digits, digit sums, conversion between bases | 17 | Download PDF |
| LCM and HCF | LCM and HCF word problems, relationships between them | 7 | Download PDF |
| Factors and Multiples | Number of factors, sum of factors, multiples | 6 | Download PDF |
| Other Number System questions | Individual questions on more specific sub-topics | 17 | In the full Number System PDF |
Difficulty Level of CAT Number System PYQs
By the difficulty tag in our question bank, 110 of the 159 Number System questions are medium, 42 are hard and 7 are easy.
| Difficulty | Typical question characteristics | Preparation focus | Questions in PDF |
|---|---|---|---|
| Easy | Direct divisibility checks, HCF and LCM, or unit-digit questions | Rule recall and quick checks | 7 |
| Moderate | Remainders of powers, factor counting and base conversions | Pattern spotting and cyclicity | 110 |
| Difficult | Number puzzles with several conditions, or proofs that combine more than one property | Systematic case analysis and constructing examples | 42 |
How to Prepare for CAT Number System Using PYQs
Follow a three-stage preparation plan to get the most out of the question bank.
- Build conceptual clarity: Revise divisibility rules, the factor-count formula, remainder theorems and unit-digit cycles before attempting timed practice.
- Practise topic-wise PYQs: Solve CAT Number System questions grouped by subtopic. Record the year and slot, your accuracy, and the time taken.
- Attempt mixed Number System sets: Once individual concepts are clear, solve questions from different Number System topics together. Review incorrect answers and identify whether the mistake came from concept selection, calculation, or time management.
Because Number System contributed 8.2% of the five-year QA dataset analysed, it needs steady rather than extended preparation. Candidates should prepare Arithmetic, Algebra, Geometry, and Modern Mathematics as well.
CAT QA Formula Sheet PDF
- CAT Number System Formula Sheet: Factors, Remainders and Divisibility
- CAT LCM, HCF and Base Systems Formula Sheet
Related CAT Practice
CAT Number System PYQs FAQs
Ques. How many Number System questions are asked in CAT?
Ans. Based on 2021-2025 analysis, Number System accounts for 27 out of 330 QA questions, representing approximately 8.2%. The number varies across exam years and slots, from 2 to 7 a year across the three slots.
Ques. Which topics are covered in the CAT Number System syllabus?
Ans. The CAT Number System syllabus includes number properties, factors and multiples, remainders, divisibility, digits and base systems, and LCM and HCF.
Ques. How can I practise CAT Number System questions PYQ topic-wise?
Ans. Start with one topic at a time, such as number properties or divisibility. Solve previous-year questions and note the concepts or calculation methods you find difficult. Then practise mixed Number System questions under timed conditions.
Ques. How should I use CAT Number System PYQs for exam preparation?
Ans. Practise questions from different CAT years and slots, and track your accuracy and time per question. Reattempt incorrect questions after revising the relevant concepts. This helps you identify weak areas and improve your problem-solving speed.
Ques. Does the CAT Number System PYQ PDF include solutions?
Ans. No. The PDF contains the 159 questions with their year, slot and source question number, without answer keys or solutions.
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