CAT Number Systems Questions with Solutions; Practice Test & Preparation Guide

Updated on Oct 19, 2026 17:31 IST

By Abhishek Dhawan, Deputy Manager - MBA & BBA Content

Number Systems questions account for nearly 10-15% of direct questions in the entire CAT question paper. A good hold on CAT Number Systems can help candidates obtain a good score in Quant. In each session of the CAT exam, candidates can expect around 3-4 direct questions.

In the CAT exam, apart from the direct Number Systems questions, candidates will find Number System concepts of use while solving DI sets. Candidates find CAT Number Systems questions on Divisibility Rules, HCF/LCM, and Remainder Theorems. A good hold on Number Systems also helps in different types of CAT Number System questions like basic properties of integers to advanced theorems, with questions evaluating logical deduction and pattern recognition. This article hosts some CAT Number Systems questions with solutions PDFs. Candidates can practice these CAT Number Systems questions tier-wise difficulty levels for holistic preparation for the CAT 2026 exam.

Table of contents

Sample CAT Number Systems Questions with Solutions
CAT Number Systems Formulas
CAT Number System Weightage
Explore Topic Wise CAT Practice Questions
FAQs on CAT Number Systems

Sample CAT Number Systems Questions with Solutions

Find CAT Number System questions with solutions below:

Question 1: A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is:

1 : 4
1 : 5
1 : 6
1 : 7

Difficulty Level: Easy

Question 2: Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of $x$ km till then, where $x$ is a whole number and is palindromic, i.e., $x$ remains unchanged when its digits are reversed. At the end of the trip, the car had travelled a total of 26862 km till then, this number again being palindromic. If Brishti never drove at more than 110 km/h, then the greatest possible average speed at which she drove during the trip, in km/h, was:

*(Note: This is a Non-MCQ / Type-In-The-Answer question)*

Difficulty Level: Medium

Question 3: A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is:

Difficulty Level: Medium

Question 4: Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been:

*(Note: This is a Non-MCQ / Type-In-The-Answer question)*

Difficulty Level: Difficult

Read More:

Practice CAT Number System Questions: Master remainders, factors, and high-scoring Quant concepts.

CAT Number System Practice Test

CAT Number Systems Formulas

Most Number System questions in CAT exam will evaluate candidates on clean logical application rather than lengthy calculations. Memorising a few formulas aids solving standard questions in under two minutes.

For any natural number N prime-factorized as N = p^a × q^b × r^c (where p, q, r are distinct primes):

Factor Property	Formula	Quick Example (N = 12 = 2² × 3¹)
Total Number of Factors	(a + 1)(b + 1)(c + 1)	(2 + 1)(1 + 1) = 6 factors
Number of Odd Factors	Ignore power of 2, multiply remaining powers + 1	(1 + 1) = 2 odd factors (1, 3)
Number of Even Factors	Total Factors − Odd Factors	6 − 2 = 4 even factors (2, 4, 6, 12)
Sum of All Factors	(p⁰ + ... + p^a)(q⁰ + ... + q^b)	(1 + 2 + 4)(1 + 3) = 7 × 4 = 28

CAT Number System Weightage

In the modern CAT Quantitative Aptitude (QA) section, candidates get 40 minutes to solve 22 questions. Pure Number System questions usually make up 1 to 3 questions. However, basic number properties, such as factors, divisibility, and prime numbers, appear frequently inside Algebra and Arithmetic questions.

Not all sub-topics carry the same weight. Focusing on high-yield areas saves study time and builds strong basics for other math topics.

Sub-Topic	Usual Questions	Concepts
Factors and Multiples	1 to 2	Total factors, even/odd factors, sum of factors, co-primes
Divisibility and Remainders	1	Divisibility rules, negative remainders, Euler's theorem
Unit and Last Two Digits	0 to 1	Power cyclicity (powers of 2, 3, 7, 8), binomial remainders
Factorials and Trailing Zeros	0 to 1	Highest power of prime in n!, number of zeros in n!
Base Systems	0 to 1	Base conversions (base 10 to base n), operations in other bases

Explore Topic Wise CAT Practice Questions

Check the space below for topic wise practice sets for CAT 2026 preparation:

CAT Topic-Wise Practice Questions

Practice by topic with questions and detailed solutions

📘 VARC Practice 7 Topics ▾

VARC → Para Summary → Verbal Ability → Para Jumbles → Odd One Out → Critical Reasoning → Vocabulary → Idioms →

📊 DILR Practice 5 Topics ▾

DILR→ DI→ LR→ Puzzles→ Seating Arrangement→

📐 Quant Practice 13 Topics ▾

Quant→ Arithmetic→ Algebra→ Geometry→ Percentages→ Profit & Loss→ Averages→ Time & Work→ Probability→ Logarithms→ Trigonometry→ Time, Speed & Distance→

Explore More CAT Preparation Resources →

FAQs on CAT Number Systems

Find some FAQs related to CAT Number Systems below:

Q: Which topics are covered under the Number System in CAT?

The CAT Number System covers topics such as divisibility rules, factors and multiples, prime numbers, HCF and LCM, remainders, unit digits, factorials, integers, rational numbers, and properties of numbers.

Q: Is the Number System important for CAT Quantitative Aptitude?

Yes, the Number System is an important topic for CAT Quantitative Aptitude. Questions may test concepts such as divisibility, remainders, factors, and properties of integers. Candidates should also practise applying these concepts to different question types.

Q: How many questions are asked from the Number System in CAT?

There is no fixed number of questions from the Number System in CAT. The number of questions varies across exam slots and years. Candidates should prepare the topic along with other important areas of Quantitative Aptitude.

Q: How can I prepare for the CAT Number System?

Candidates should first understand basic concepts, including divisibility rules, prime factorisation, HCF and LCM, and remainders. They should then solve topic-wise practice questions and previous years' CAT questions to improve accuracy and problem-solving speed.