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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 number system CAT questions, key formulas, and common mistakes to avoid. We’ll also share PDFs with practice questions and formulas to help you prepare.
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=(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=⌊log10N⌋+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
correct answer:- 1
Question 2
If 8 + 12 = 2, 7 + 14 = 3 then 10 + 18 = ?
correct answer:- 1
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?
correct answer:- 2
Question 4
If n is any positive integer, then $$n^{3} - n$$ is divisible
correct answer:- 3
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?
correct answer:- 1
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.
correct answer:- 1
Question 7
What are the last two digits of $$7^{2008}$$?
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correct answer:- 3
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