Comprehensive Study Guide — Quantitative Reasoning
1. Foundations: Number Sense & Mental Math
The bedrock of fast quantitative performance is strong number sense. This includes quick familiarity with place value, divisibility, prime factors, simple fractional conversions and estimation. Train your mental arithmetic daily — practice multiplying 2-digit numbers, dividing by small integers, and approximating percentages. Over time you will dramatically reduce reliance on scratch work.
2. Arithmetic: Very Common Question Types
Core arithmetic covers addition, subtraction, multiplication, division, fractions, decimals, averages, weighted averages and ratio-based computations. Make a cheat sheet of common conversions (fractions ↔ percentages ↔ decimals), and memorize multiplication tables up to at least 20 × 20.
3. Percentages: Tricks That Save Time
Percentages are ubiquitous. Use these practical shortcuts:
- To compute X% of Y quickly: (X/10 of Y) ± adjustments. For example 12% of 250 = 10% (25) + 2% (5) = 30.
- Use successive approximation for compound percentage changes: 20% off then 10% off is not 30% — compute consecutively.
- For percentage increase/decrease, convert to multiplier: increase 15% → ×1.15; decrease 12% → ×0.88.
4. Ratios & Proportion
Ratios translate many word problems into simple multiplication/division relationships. Common pitfalls include mixing absolute numbers with ratios — always convert ratios to parts, then assign a variable (e.g., let one part = x). Practice age, mixture, and sharing problems which frequently appear in aptitude tests.
5. Algebra: From Linear Equations to Quadratics
Algebraic manipulation, equation solving, inequalities and basic factorization form the algebra syllabus. Key skills:
- Set up equations from word problems — spend more time reading the wording carefully.
- Practice solving linear equations and simple quadratic equations by factoring or completing the square.
- Understand functions, substitution and manipulating algebraic fractions.
6. Geometry: Visual Reasoning and Formulas
Geometry questions test spatial reasoning. Memorize area and perimeter formulas for triangles, rectangles, circles and sectors. Focus on:
- Right triangles — Pythagorean triples (3,4,5; 5,12,13 etc.) are helpful shortcuts.
- Circle theorems (angles, arcs and chords) and properties of parallel lines.
- Coordinate geometry basics: slope, midpoint, distance formula.
7. Statistics & Data Interpretation
Data interpretation problems present charts, tables or graphs and ask for inference. Key concepts include mean, median, mode, range, standard deviation (basic), percentages, ratios and trend interpretation. Train on reading data accurately and checking units carefully.
8. Probability & Counting
Probability problems often involve counting principles: permutations and combinations (basic), complement rules, and conditional probability basics. Practice simple conditional probability cases and common counting formulas (nCr, nPr).
9. Speed & Distance, Time & Work
Speed & Distance and Time & Work are classic aptitude staples. Remember:
- Speed = Distance / Time; Distance = Speed × Time; Time = Distance / Speed.
- When relative speeds are used (two objects moving in opposite or same direction), add or subtract speeds appropriately.
- For Time & Work: work done ∝ time × rate. If A can do a job in x days and B in y days, combined rate = 1/x + 1/y.
10. Problem Solving Strategy (how to attack a question)
1) Read the question fully — underline numbers and keywords. 2) Try a simple estimate first — if the estimate eliminates most options, you save time. 3) Choose the fastest method: algebraic equation or numerical trick. 4) If stuck, skip and return — avoid time-sink traps in timed tests.
11. Common Shortcuts & Tricks
Difference of squares: a^2 - b^2 = (a-b)(a+b).
Percentage to fraction: 12.5% = 1/8, 33.33% ≈ 1/3, 66.67% ≈ 2/3.
LCM/GCD: prime factorization or use (a × b) / GCD = LCM.
12. Sample Study Schedule (8 weeks)
Week 1: Basic arithmetic & number sense (daily 30–45 minutes).
Week 2: Percentages, ratios and averages (practice 3 timed quizzes/week).
Week 3: Algebra fundamentals and equation solving.
Week 4: Geometry basics and coordinate geometry.
Week 5: Probability & statistics, quick formula review.
Week 6: Speed & distance, time & work; practice mixed sets.
Week 7: Data interpretation and advanced problem solving.
Week 8: Full mock tests and revision of weak areas; maintain error log.
13. Mock Tests — When & How Often
After two weeks of focused study, attempt a full-length mock under timed conditions every 5–7 days. Use mocks to calibrate timing and identify topics needing revision. Maintain a log of wrong answers and revisit those topics with targeted practice.
14. How to Use These Quizzes Effectively
- Begin with topic quizzes (the buttons above).
- Time yourself for each quiz — gradually reduce time to exam levels.
- Review explanations for every wrong answer. Re-attempt that topic after revision.
- Mix topics before the exam — adaptability is crucial.
15. Example Questions (Formats)
MCQ: If 3 men can do a job in 8 days, how many days will 6 men take (assuming same rate)?
Data Interpretation: Given a bar chart of yearly sales, what is the percent increase from 2018 to 2019?
Word Problem: A train covers 150 km in 1.5 hours. What is its average speed in km/h?
16. Resources & Recommended Books
Use standard aptitude guides plus problem collections for practice. For statistics and probability, simple university intro books or Khan Academy videos help. For mental math, practice daily with flashcards or apps.
17. Final Exam Day Tips
- Read every question carefully; do simple estimate first.
- Keep track of time (e.g., 1.5 minutes per question if 60 questions in 90 minutes).
- Answer easy questions first; mark uncertain ones and return later.
- Stay calm — accuracy under speed improves with practice, not panic.