Questions
~4 questions per paper
Difficulty
Medium
Importance
Core - high yield for all PSU exams
Overview
Algebra and Number Systems form the foundation of quantitative aptitude in PSU examinations, testing analytical speed and mathematical precision. Mastering these concepts is essential as they appear frequently and provide high-scoring opportunities through standard procedural methods. The core focus for an aspirant should be on recognizing patterns in series and internalizing the standard forms of algebraic equations.
Number Series
Number series questions evaluate your ability to identify logical patterns within a sequence of integers or decimals. In PSU exams, these usually follow arithmetic progression, squares, cubes, or alternating operations.
- Check for constant differences in AP-based series
- Identify geometric series by constant ratios
- Watch for square or cube shifts (e.g., n^2 + 1)
- Look for prime number sequences
- Apply the two-tier difference method for complex patterns
HCF and LCM
This subtopic relies on prime factorization and the fundamental relationship between numbers and their factors. It is frequently tested in problems involving time intervals and cyclic events.
- Product of two numbers = HCF * LCM
- HCF of fractions = (HCF of numerators) / (LCM of denominators)
- LCM of fractions = (LCM of numerators) / (HCF of denominators)
- Co-prime numbers have an HCF of 1
- Use division method for finding HCF of large numbers
Surds and Indices
Laws of exponents govern these calculations, which are critical for simplifying complex algebraic expressions. Speed in this area is achieved through memorizing standard index identities.
- a^m * a^n = a^(m+n)
- a^m / a^n = a^(m-n)
- (a^m)^n = a^(mn)
- a^0 = 1
- n-th root of a = a^(1/n)
Progressions (AP & GP)
Arithmetic and Geometric Progressions involve finding specific terms or the summation of sequences. These are common in business mathematics and data analysis questions in technical papers.
- AP n-th term: Tn = a + (n-1)d
- AP Sum: Sn = n/2 * [2a + (n-1)d]
- GP n-th term: Tn = a * r^(n-1)
- GP Sum (r < 1): Sn = a(1 - r^n) / (1 - r)
- Sum of infinite GP: S = a / (1 - r)
Formula Sheet
Product of two numbers = HCF * LCM
Tn = a + (n-1)d
Sn = n/2 * (2a + (n-1)d)
Tn = ar^(n-1)
Sn = a(1-r^n)/(1-r)
ax^2 + bx + c = 0 (Quadratic standard form)
Roots of quadratic: x = [-b ± sqrt(b^2 - 4ac)] / 2a
a^m * a^n = a^(m+n)
(a^m)^n = a^(mn)
Exam Tip
In number series, if you cannot spot the pattern within 30 seconds, mark it for review and move on to ensure you do not lose time on potential 'trap' questions.
Common Mistakes
- Confusing the Sum of AP formula with the n-th term formula during time-constrained stress.
- Forgetting to simplify fractions before calculating the LCM or HCF of the total expression.
- Assuming the product rule of HCF and LCM applies to three or more numbers directly without verification.
More Revision Notes
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