What are the key concepts to focus on for CAT Number System questions?

The key concepts include divisibility rules, prime factorization, LCM, GCD, remainder theorem, base conversions, and number of divisors.

Why are base conversion questions tricky in the CAT Number System?

Base conversion problems can be confusing due to the different number systems involved. Regular practice of converting numbers between bases will help build proficiency.

How can I avoid common mistakes in CAT Number System questions?

To avoid mistakes, remember basic rules, simplify problems, practice base conversions, and watch for repeating patterns in remainder problems.

What formulas should I memorize for the CAT Number System section?

Key formulas to memorize include divisibility rules, LCM and GCD formulas, number of divisors, and sum of divisors formulas, along with base conversion methods.

How can I prepare for tough CAT Number System questions?

Focus on practicing multi-step and challenging problems that combine different number system concepts. Regular practice with PDFs and mock tests can help improve speed and accuracy.

What is the importance of understanding divisibility rules for the CAT exam?

Divisibility rules help in quickly identifying whether a number is divisible by certain values, making it easier to solve problems related to factors and multiples in the exam.

Where can I find practice questions and formulas for CAT Number System?

You can download practice PDFs with CAT Number System questions, formulas, and detailed solutions to enhance your preparation.

Most Important Number System Questions For CAT 2025

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Number System Questions for CAT 2025

The Number System is an important topic in the Quantitative Ability section of the CAT exam. It tests your understanding of numbers and how well you can use this knowledge to solve problems quickly. Number system questions often carry a significant weight and are asked regularly in the CAT exam.

For CAT 2025 candidates, it's important to understand the basics of the number system, as it forms the foundation for many other math concepts. Whether it's divisibility rules, remainders, prime factorization, or different number bases, mastering the number system will help you perform better in the exam.

In this blog, we’ll explain why Number System questions matter for CAT 2025 and how mastering them can help you score well. You’ll learn about the types of questions, key formulas, and common mistakes to avoid. We’ll also share PDFs with practice questions and formulas to help you prepare.

CAT Number Systems Questions PDF

Important Formulas for CAT Number System Questions

Knowing the key CAT formulas is important to solve number system questions quickly. Here are the main ones. We’ve also included a PDF with all the formulas for you to download and use.

Download CAT Number System Formula Pdf

Topic	Formula/Concept
Divisibility Rules	- A number is divisible by 2 if its last digit is even.
	- A number is divisible by 3 if the sum of its digits is divisible by 3.
	- A number is divisible by 5 if its last digit is 0 or 5.
	- A number is divisible by 9 if the sum of its digits is divisible by 9.
Prime Factorization	Every number can be expressed as a product of primes.
	Example: 12=22×312 = 2^2 \times 312=22×3.
LCM	- LCM(a,b)=a×bGCD(a,b)\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}LCM(a,b)=GCD(a,b)a×b
GCD	- GCD(a,b)\text{GCD}(a, b)GCD(a,b) is the largest number that divides both aaa and bbb.
Number of Divisors	If N=p1e1×p2e2×⋯×pkekN = p_1^{e_1} \times p_2^{e_2} \times \dots \times p_k^{e_k}N=p1e1×p2e2×⋯×pkek, then number of divisors =(e1+1)(e2+1)…(ek+1)= (e_1 + 1)(e_2 + 1) \dots (e_k + 1)=(e1+1)(e2+1)…(ek+1).
Sum of Divisors	Sum of divisors for N=p1e1×p2e2×⋯×pkekN = p_1^{e_1} \times p_2^{e_2} \times \dots \times p_k^{e_k}N=p1e1×p2e2×⋯×pkek is:
Sum of Divisors	Sum of divisors=(1+p1+p12+⋯+p1e1)(1+p2+p22+⋯+p2e2)…\text{Sum of divisors} = (1 + p_1 + p_1^2 + \dots + p_1^{e_1})(1 + p_2 + p_2^2 + \dots + p_2^{e_2}) \dotsSum of divisors=(1+p1+p12+⋯+p1e1)(1+p2+p22+⋯+p2e2)…
Remainder Theorem	The remainder when aaa is divided by bbb is: Remainder=a−b×⌊ab⌋\text{Remainder} = a - b \times \left\lfloor \frac{a}{b} \right\rfloorRemainder=a−b×⌊ba⌋
Power of a Number (Modulo)	To compute anmod ma^n \mod manmodm, use the fast exponentiation method for large powers.
Number of Digits in a Number	The number of digits in a number NNN is given by Number of digits=⌊log⁡10N⌋+1\text{Number of digits} = \lfloor \log_{10} N \rfloor + 1Number of digits=⌊log10N⌋+1.
Base Conversion	To convert a number from base bbb to base 10, use: N=dk×bk+dk−1×bk−1+⋯+d1×b+d0N = d_k \times b^k + d_{k-1} \times b^{k-1} + \dots + d_1 \times b + d_0N=dk×bk+dk−1×bk−1+⋯+d1×b+d0, where did_idi are the digits.

Common Mistakes to Avoid in CAT Number System Questions:

While preparing for CAT 2025, it’s important to avoid common mistakes in number system questions. Avoiding these mistakes will help you get better results and reduce errors in the exam.

Not Remembering Basic Rules and Formulas: Many students forget basic rules like divisibility and prime factorization. These are key for solving problems quickly. Make sure to practice them often.

Confusing Base Conversions: Questions about base systems can be tricky. Converting numbers between different bases or using non-decimal systems can lead to mistakes. Practice these conversions to avoid errors.

Making Problems Too Complicated: Sometimes students overthink the problem. Try to simplify the question first before doing complex calculations. There’s usually a simpler way to solve it.

Missing Patterns in Remainder Problems: Remainder problems often follow repeating patterns (like powers of numbers modulo 10). Not spotting these patterns can waste time and cause mistakes. Look for these cycles to solve problems faster.

Forgetting Multiple Conditions: Some problems have more than one condition (like a number divisible by several values). Make sure to consider all conditions and apply them correctly.

Not Estimating the Answer: For large number system problems, it helps to estimate the answer first. This will help you avoid mistakes and make sure you’re on the right track.

Not Practicing Hard Problems: CAT often asks harder questions that combine different concepts. Don’t just practice easy problems—make sure to try tough, multi-step problems too.

List of Important CAT Number System Questions

Question 1

Let a, b be any positive integers and x = 0 or 1, then

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Question 2

If 8 + 12 = 2, 7 + 14 = 3 then 10 + 18 = ?

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Question 3

How many five digit numbers can be formed from 1, 2, 3, 4, 5, without repetition, when the digit at the unit’s place must be greater than that in the ten’s place?

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Question 4

If n is any positive integer, then $$n^{3} - n$$ is divisible

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Question 5

A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?

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Question 6

A student instead of finding the value of 7/8 of a number, found the value of 7/18 of the number. If his answer differed from the actual one by 770, find the number.