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Important Number System Formulas for CAT Exam
Number System is one of the most fundamental and concept-driven topics in the CAT Quantitative Aptitude section. It forms the base for advanced topics like Algebra, Arithmetic, and Modern Math. Simply memorizing formulas is not enough — you must understand their application and patterns.
Download Free CAT Number System Formulas PDF
Revise smarter with our concise CAT Number System Formulas PDF, designed for quick and effective preparation before mocks and the final exam. It includes all key formulas and concepts such as divisibility rules, factors, HCF & LCM, remainders, cyclicity, base systems, and solved practice examples all in one place. Perfect for quick revision and last-minute formula recap.
Download CAT Number System Formula PDF
CAT Number System Practice Questions
Question 1
Find out the appropriate next number in the series from the options below :
0, 2, 6, 12, 20, 30, 42, ?
correct answer:- 1
Question 2
The missing numbers in the below series would be
1 : 1, 8 : 4, 9 : 27, 64 : 16, 25 : 125, ? : ?, 49 : 343
correct answer:- 2
Question 3
Which of the following numbers will completely divide (461 + 462 + 463 + 464)?
correct answer:- 2
Question 4
What is the number that is one half of one-quarter of one-tenth of 400?
correct answer:- 2
Question 5
R is a positive number. It is multiplied by 8 and then squared. The square is now divided by 4 and the square root is taken. The result of the square root is Q. What is the value of Q?
correct answer:- 2
Question 6
If n = 1 + x, where x is the product of 4 consecutive positive integers, then which of the following is/are true?
1. n is odd;
2. n is prime
3. n is a perfect square
correct answer:- 1
Question 7
The number 311311311311311311311 is
correct answer:- 4
Question 8
$$\sqrt{110.25} \times \sqrt{0.01} \div \sqrt{0.0025} - \sqrt{420.25}$$ equal to
correct answer:- 2
Question 9
The no. plate of a bus had peculiarity. The bus number was a perfect square. It was also a perfect square when the plate was turned upside down. The bus company had only five hundred buses numbered from 1 to 500. What can be the number?
correct answer:- 3
Question 10
Which is the wrong term in the following sequence?
52, 51, 48, 43, 34, 27, 16
correct answer:- 2
Question 11
P is six times as large as Q. By what per cent is Q less than P?
correct answer:- 3
Question 12
When a heap of pebbles is grouped in 32, 40 or 72 it is left with remainders of 10,
18 or 50 respectively. What is the minimum number of pebbles that the heap contains?
correct answer:- 2
Question 13
Fill in '+' or '-' sign in between these numbers so that they give the correct answer.
$$1 2^3 3^3 1 4^3 = 31$$
correct answer:- 3
Question 14
Symbiosis runs a Corporate Training Programme. At the end of running the first programme its total takings were Rs 38950. There were more than 45 but less than 100 particulars. What was the participant fee the programme?
correct answer:- 1
Question 15
Complete the series 1, 6, 6, 36, 216, .....
correct answer:- 2
Question 16
What year comes next in the sequence 1973, 1979, 1987, 1993, 1997, 1999 ......... ?
correct answer:- 2
Question 17
A difference between two numbers is 1365, when larger number is divided by the
smaller one, the quotient is 6 and the remainder is 15. What is the smaller number?
correct answer:- 3
Question 18
In the following series find the one number that is wrong
2, 3, 13, 37, 86, 167, 288
correct answer:- 2
Question 19
In a row at a bus stop, A is 7th from the left and B is 9th from the right. They both interchange their
positions. A becomes 11th from the left. How many people are there in the row?
correct answer:- 2
Question 20
If N= a*b where a,b are prime numbers, then what are the number of factors of $$N^3/b^2$$
correct answer:- 3
CAT Number System Questions Preparation Strategy
Number System is a concept-driven topic in the CAT Quantitative Aptitude section. Questions are usually logic-based and test your clarity of fundamentals rather than lengthy calculations. A structured preparation approach can help you solve these questions quickly and accurately in the exam.
Build Strong Fundamentals
Start with core concepts like divisibility rules, prime factorization, HCF and LCM, remainders, cyclicity, and base systems. Make sure you understand why formulas work instead of just memorizing them.
Practice Pattern-Based Questions
Most CAT Number System questions follow patterns. Focus on:
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Unit digit and cyclicity of powers
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Remainder theorem and modular arithmetic
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Factor counting and divisor-based problems
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LCM-HCF applications in word problems
Recognizing patterns will significantly improve your speed.
Solve Previous Year CAT Questions
Go through past CAT questions to understand the difficulty level and question framing. PYQs help you identify commonly tested concepts and improve exam confidence.
Take Timed Practice Sets
Since CAT is time-bound, practice solving questions under time pressure. Attempt sectional tests and analyze where you are spending extra time.
Revise Regularly
Keep a short formula sheet or PDF handy and revise weekly. Consistent revision ensures you don’t forget important tricks and shortcuts before the exam.
CAT Number System Formulas with Practice Questions: Conclusion
Number System is a key and concept-based topic in CAT Quantitative Aptitude. A clear understanding of divisibility rules, HCF-LCM, remainders, cyclicity, and base systems helps you solve questions quickly and accurately. Focus on understanding the logic behind formulas instead of just memorizing them.
With regular practice, solving previous year CAT questions, and revising from a short Number System PDF, you can improve speed and confidence. Consistent revision will help you make this topic a strong scoring area in the CAT exam.
