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XAT Formula PDF is a useful tool for daily revision. It helps in avoiding looking for many resources and helps in focusing on a single source. An updated formula PDF helps with time management and boosts confidence when taking the final exam.
XAT Number System Formulas PDF
XAT Number Systems Formula PDF is the foundation of quantitative aptitude section for any entrance exam. Understanding the basics of the number system for the XAT exam can greatly improve aspirants' overall score. Knowing how to use number system formulas is essential in questions of this part of the quant section, not simply memorising them. This article provides detailed information on the important XAT number system formulas and their importance. We've also provided tips to master important Number System questions in the XAT exam.
Importance of XAT Number System Formulas
Number Systems is an important part of the Quantitative Ability section in XAT. Good understanding of these formulas and concepts helps students to solve questions accurately, fast, and with confidence. XAT Number System Formula PDF is important for XAT aspirants. Below are a few points that prove it:
Quick Revision Resource: A Number System formula PDF provides a handy reference to important formulas, making last-minute revision easier.
Supports Basic concepts: Regular practice of formulas and revision helps students master divisibility, remainders, factors, multiples, and other important Number System concepts.
Increases Questions-Solving Speed: Familiarity with formulas reduces calculation time and helps students to solve questions more efficiently during the exam.
Improves Accuracy: Using the correct formula at the right time and on the right questions limits the chances of mistakes and improves the chances of getting the correct answer.
Increases Confidence: A solid understanding of Number System formulas helps students to solve different types of XAT questions, which helps in building confidence and accuracy.
Read Also, XAT Exam Pattern 2027, Negative Marking, Structure, Duration
Complete XAT Number System Formula List
Below is the complete XAT Number System Formula List given. Students can refer to this list to revise the important formulas while solving practice questions.
HCF (Highest Common Factor)
- Euclid's Algorithm: HCF(a, b) = HCF(b, a − b)
- Division Method: HCF(a, b) = HCF(b, a mod b)
- Relation with LCM: HCF × LCM = a × b
LCM (Least Common Multiple)
- Prime Factor Method: LCM = Product of each prime raised to the highest power observed
- Relation with HCF: LCM = (a × b) / HCF
Number of Zeros
- Trailing Zeros in n!: ⌊n/5⌋ + ⌊n/5²⌋ + ⌊n/5³⌋ + ...
- Trailing Zeros in 2ᵃ × 5ᵇ: min(a, b)
Remainder Theorem
- Polynomial Remainder Theorem: Remainder when f(x) is divided by (x − a) = f(a)
- Euler's Reduction: aᵏ mod m = a^(k mod φ(m)) mod m
Unit's Digit
- Cyclicity Method: Unit digit cycles every k powers depending on the base digit.
Factors
- Number of Factors: (e₁ + 1)(e₂ + 1)(e₃ + 1)...
- Number of Odd Factors: (f₁ + 1)(f₂ + 1)...
- Sum of Factors: [(p₁^(e₁+1) − 1)/(p₁ − 1)] × [(p₂^(e₂+1) − 1)/(p₂ − 1)] ...
- Product of Factors: n^(d/2)
Euler's Totient Theorem
- For Prime Powers: φ(pᵏ) = pᵏ − pᵏ⁻¹
- General Formula: φ(n) = n(1 − 1/p₁)(1 − 1/p₂)...
- Euler's Theorem: a^φ(n) ≡ 1 (mod n)
- Fermat's Little Theorem: a^(p−1) ≡ 1 (mod p)
Base Systems
- Base b to Decimal Conversion: Value = ∑dᵢbⁱ
Tips to Master Important Number System Formulas for XAT
A strong base in the Number Systems part of the Quant section is essential for success in the XAT exam. By effectively using a XAT Number Systems Formula PDF, practising regularly, and mastering shortcuts, students can significantly enhance their problem-solving abilities and improve their overall score. Below are a few tips to master Important Number System Formulas for XAT:
- Clarity of Conecpt: Instead of memorising formulas, start by understanding the basic concepts.
- Practice regularly: Constant question-solving is important to building proficiency.
- Focus on the Basic Concepts: Learn the divisibility rules, HCF, LCM, prime numbers, and remainder theorems rather than directly jumping on advanced-level questions.
- Learn from Mistakes: Watch wrong answers to find gaps and improve problem-solving techniques.
- Time Management: Practice answering questions within the time limit to improve speed and accuracy.
Read Also, XAT Syllabus 2027, Section-wise Pattern, Download PDF
Download Cracku's Free XAT Number System Formulas PDF
Cracku has compiled all the important XAT Number System formulas into one complete PDF to help students in passing the XAT Quantitative Ability section and increase their overall score. Download the FREE XAT Number System Formulas PDF to easily revise key formulas from topics such as HCF, LCM, Remainders, Unit Digits, Factors, Trailing Zeros, Euler's Theorem, and Base Systems.
XAT Number System Formulas PDF: Conclusion
The XAT Number System Formulas PDF is an essential resource for candidates preparing for the Quantitative Ability section. Since Number Systems serve as the foundation for many arithmetic and algebraic concepts, mastering formulas related to HCF, LCM, divisibility, remainders, unit digits, factors, and trailing zeros can significantly improve performance in the exam.
Consistent revision using the XAT Number System Formulas PDF, along with regular practice and mock tests, can help aspirants strengthen their conceptual understanding and solve questions more efficiently. A strong grasp of Number Systems not only improves accuracy and speed but also contributes to a higher overall XAT percentile.
