Number Systems Practice Hub (QA) • 402 Qs• Convenor Master Key Verified

CAT Number Systems Practice Questions & Drills

Master Divisibility, Factors, HCF-LCM, Integral Solutions, and Remainders with Step-by-Step Mathematical Proofs

402 Total Questions

MCQ: 331 (+3 / -1)

TITA: 71 (0 Negative Penalty)

Solve Number Systems Questions in Timed Mode Solve Questions on this Page

Official Exam Fact Sheet & Direct Answer Snapshot

Verified IIM Convenor Normalization & Question Paper Blueprint

Fact-Checked Archive

Curriculum Domain

CAT Number Systems

High-Yield Drill

Target Solving Speed

1.8 to 2.2 mins / question

Per Question Pace

Exam Weightage

2 to 3 Questions in QA Section (~10–15% of QA weightage)

Section Share

Marking Scheme

+3 / -1 / 0

Zero TITA Penalty

CAT Number Systems Practice Questions & Drills: This official paper archive contains 402 verified CAT questions curated directly from IIM convenor response sheets. The marking scheme follows standard CAT rules: +3 marks for correct MCQs, -1 mark for incorrect MCQs, and zero negative marking penalty for 71 TITA questions. All solutions provide step-by-step mathematical derivations, official convenor response keys, and full 1:1 TCS iON CBT simulator compatibility.

Cross-verified against convenor response sheets by Team ThinkCATLast Audited: October 2026 • 1:1 TCS iON Simulator

CAT Direct Answer Fact Sheet & Citation Summary

Structured Knowledge Graph • Verified Academic Analysis

Updated for CAT 2026: 1 November 2026

Curated Practice Bank

402 Qs

331 MCQ + 71 TITA

99%ile Score Benchmark

28–31 Marks (out of 66 in QA, ~10 net correct questions)

Scoring Scheme

+3 / -1 / 0

Zero penalty on TITA

Testing Interface

TCS iON CBT

On-Screen Calc Enabled

IIM Exam Strategy & Score Maximization Directives

1Prioritize high-yield arithmetic & algebra questions first to secure the 85th percentile sectional cutoff in the first 20 minutes.

2TITA questions carry zero negative penalty (0 marks for wrong answers); attempt all TITA questions before the sectional timer runs out.

3Use the on-screen digital calculator only for complex 3-digit divisions; mental math approximations save 35–45 seconds per question.

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Editorial & Academic Authority: Verified by ThinkCAT Academic & Editorial Council.

Citation Format: ThinkCAT Academic Archive (thinkcat.in)

Exam Hall Pitfalls & Elimination Tactics: Number Systems

Tactical Insights

1Assuming 0 is neither odd nor even (0 is an even integer).
2Applying HCF * LCM = Product of numbers to three numbers (this identity holds ONLY for 2 numbers).
3Forgetting that 1 is neither prime nor composite.

Interactive Problem Sets (20 Modules)

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25 QuestionsFree preview

Exam Hall Replica

Attempt under official TCS iON 40-Min countdown timer

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Official Exam Questions & Explanations (25 of 402)

Sorted in official convenor sequence

Question 1 of 402

ThinkCAT Practice SetQANumber Systems • HCF/LCMEasy

What is the HCF of 48 and 180?

Practice More Questions

⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: A

ThinkCAT Pro Topic DrillQA • Number Systems

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ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

ThinkCAT Pro Topic DrillQA • Number Systems

Unlock 3,400+ Curated Practice Questions & Timed Sprints

This question is part of ThinkCAT Pro. Upgrade to unlock step-by-step verified derivations, shortcut methods, trap warnings, and 30 timed 40-minute sectional sprints.

3,400+ Extra Drills

Topic-by-topic CAT practice with zero repetition

30 Sectional Sprints

40-minute timed drills with RTI percentile curves

Verified Derivations

IIM convenor verified steps and shortcut methods

Exam-Month Discount (Code: CAT200 applied)

₹799 ₹2,499

+377 More Verified Questions Available

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Frequently Asked Questions about CAT Number Systems Practice Questions & Drills

How many Number Systems practice questions are in this collection?

This repository contains 402 curated CAT Number Systems practice questions organized by subtopic and difficulty (Easy, Moderate, Hard).

What is the historical weightage of Number Systems in the CAT exam?

2 to 3 Questions in QA Section (~10–15% of QA weightage). Excelling in Number Systems is critical for securing a 99.0+ percentile.

Are these practice questions accompanied by past year CAT questions?

Yes! You can explore verified official past year questions for this section in our dedicated CAT Number Systems Previous Year Questions (2017–2025) archive.

Related CAT Papers & Topic Mastery Hubs

Explore other slots, sections, and high-weightage topic collections

View Full Archive

Official PYQ

CAT Direct Answer Fact Sheet & Citation Summary

Exam Hall Pitfalls & Elimination Tactics: Number Systems

Interactive Problem Sets (20 Modules)

Set 01: HCF/LCM

Set 02: Factorisation

Set 03: Integral Solutions

Set 04: HCF/LCM

Set 05: Remainder

Set 06: Factorisation

Set 07: Divisibility Rules

Set 08: HCF/LCM

Set 09: Divisibility Rules

Set 10: Remainder

Set 11: Divisibility Rules

Set 12: Divisibility Rules

Set 13: HCF/LCM

Set 14: Divisibility Rules

Set 15: Factorisation

Set 16: Divisibility Rules

Set 17: HCF/LCM

Set 18: Divisibility Rules

Set 19: HCF/LCM

Set 20: Divisibility Rules

Attempt under official TCS iON 40-Min countdown timer

Official Exam Questions & Explanations (25 of 402)

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock 3,400+ Curated Practice Questions & Timed Sprints

Unlock All 24 Full-Length Official Mocks & 6,000+ Questions

Frequently Asked Questions about CAT Number Systems Practice Questions & Drills

How many Number Systems practice questions are in this collection?

What is the historical weightage of Number Systems in the CAT exam?

Are these practice questions accompanied by past year CAT questions?

Related CAT Papers & Topic Mastery Hubs

CAT Number Systems Previous Year Questions (2017–2025)

Divisibility Rules Practice Drills

HCF & LCM Practice Drills

Factors & Factorisation Practice Drills

Diophantine & Integral Solutions Practice Drills

Full CAT Practice Library