Introduction to Quantitative Reasoning
Original concepts, methods, worked examples, exercises and applied revision.
The Math Hub original resource
Quantitative Reasoning — Volume II Complete Solutions 2026
Individual quantitative reasoning notes with 16 detailed units, worked examples, applications and solutions. Prepared by Rana Ali Hasan and Mehreen Kanwal.
Overview, purpose, benefits and learning outcomes
This independent resource develops quantitative interpretation through formulas, tables, graphs, models, logic, data, probability and applied problem solving. It is not official university material.
Who this resource is for
ADP, BS, BSc, computing, engineering, business and other undergraduate learners where it matches the current scheme of studies.
Complete 16-unit detailed coverage
Contributions of Mathematicians and Statisticians, Especially Muslim Scholars
Original concepts, methods, worked examples, exercises and applied revision.
Types of Standard Numbers
Original concepts, methods, worked examples, exercises and applied revision.
Proportions, Rates, Ratio and Percentages
Original concepts, methods, worked examples, exercises and applied revision.
Odds and Odds Ratio
Original concepts, methods, worked examples, exercises and applied revision.
Scale of Measurements
Original concepts, methods, worked examples, exercises and applied revision.
Number Sequence and Series
Original concepts, methods, worked examples, exercises and applied revision.
Unit Analysis as a Problem-Solving Tool
Original concepts, methods, worked examples, exercises and applied revision.
Data Handling (Small and Large)
Original concepts, methods, worked examples, exercises and applied revision.
Data Errors: Absolute and Relative and Their Applications
Original concepts, methods, worked examples, exercises and applied revision.
Descriptive Statistics
Original concepts, methods, worked examples, exercises and applied revision.
Rules of Counting: Multiplication Rule, Factorial, Permutation and Combination
Original concepts, methods, worked examples, exercises and applied revision.
Probability and Its Application in Real Life
Original concepts, methods, worked examples, exercises and applied revision.
A Graphical Perspective through Venn Diagram
Original concepts, methods, worked examples, exercises and applied revision.
Financial Indicator Analysis and Money Management
Original concepts, methods, worked examples, exercises and applied revision.
Practical Scenarios Involving Algebraic Expressions: Linear and Quadratic
Original concepts, methods, worked examples, exercises and applied revision.
Applications and course connections
Applications include financial reasoning, data interpretation, probability, models, computing and practical quantitative literacy.
Pakistan University / Course Crosswalk
Curriculum discovery context for HEC Pakistan, University of the Punjab, University of Sargodha, COMSATS, UCP, Superior, Minhaj, IBA, Bahria, Habib, Sukkur IBA and other Pakistani institutions. Course placement varies and no endorsement is claimed.
Reference books and further study
Use course-aligned quantitative reasoning, statistics, algebra and problem-solving texts, checking the current university scheme and applicable edition.
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About the Authors
Rana Ali Hasan — MPhil Mathematics and Mehreen Kanwal — MPhil Mathematics.
Related resources
ADP Books, Notes & Solutions · BS Mathematics · Mathematics Library