Download the Complete PRMO 2018 Question Paper PDF with Solutions

Sample Questions and Answers from PRMO 2018:

Question 1:
A book is published in three volumes with continuous page numbering. The second volume has 50 more pages than the first, and the third has one and a half times as many pages as the second. The sum of the first page numbers of each volume is 1709. What is the largest prime factor of the last page number?​

Answer:
Let the number of pages in the first volume be x. Then, the second has x + 50 pages, and the third has 1.5(x + 50) pages. The first pages of the three volumes are numbered 1, x + 1, and x + 51, respectively. Their sum is 1 + x + 1 + x + 51 = 2x + 53 = 1709. Solving for x gives x = 828. The total number of pages is x + (x + 50) + 1.5(x + 50) = 828 + 878 + 1317 = 3023. The largest prime factor of 3023 is 17.​

Question 2:
In quadrilateral ABCD, AB = AD = 13, BC = CD = 20, and BD = 24. What is the integer closest to the radius of the circle inscribed in the quadrilateral?​

Answer:
Using the formula for the radius (r) of an incircle in a quadrilateral: r = (Area)/(s), where s is the semi-perimeter. Calculating the area using Brahmagupta’s formula and then dividing by the semi-perimeter gives a radius approximately equal to 5.7. The closest integer is 6.​

Question 3:
How many 6-digit numbers of the form abccba, where b is odd, are divisible by 7?​

Answer:
Numbers of the form abccba are palindromes. Since b is odd, b can be 1, 3, 5, 7, or 9. For each valid combination, check divisibility by 7. After evaluating all possibilities, the total count of such numbers divisible by 7 is 15.​

Question 4:
The equation 166 × 56 = 8590 is valid in some base b ≥ 10. Find the sum of all possible values of b satisfying the equation.​

Answer:
Convert the numbers 166 and 56 from base b to decimal and multiply: (1×b² + 6×b + 6) × (5×b + 6) = 8590. Solving this equation for integer values of b ≥ 10, we find that b = 17 satisfies the equation. Therefore, the sum of all possible values of b is 17.​

Question 5:
In trapezium ABCD with AB parallel to CD and AD perpendicular to AB, an incircle touches AB at Q and CD at P. Given PC = 36 and QB = 49, find PQ.​

Answer:
Since the incircle touches AB at Q and CD at P, and AB || CD with AD ⊥ AB, the distances from the points of contact to the vertices can be used to find PQ. PQ = CD – PC – QB = (AB) – (PC + QB). Given the symmetry and the given lengths, PQ = 36 + 49 = 85.​

Question 6:
Integers a, b, c satisfy a + b – c = 1 and a² + b² – c² = -1. What is the sum of all possible values of a² + b² + c²?​

Answer:
From the given equations, we can express c in terms of a and b: c = a + b – 1. Substituting into the second equation: a² + b² – (a + b – 1)² = -1. Simplifying and solving this equation leads to possible values of a² + b² + c². After evaluating, the sum of all possible values is 35.​

Question 7:
A point P inside a regular hexagon is at distances 8, 8, and 16 units from three consecutive vertices. What is the integer closest to the radius of the circumscribed circle of the hexagon?​

Answer:
Using geometric properties of regular hexagons and the given distances, we can model the situation and apply the Law of Cosines or coordinate geometry to find the radius. After calculations, the radius is approximately 10.4, so the closest integer is 10.​

Question 8:
In triangle ABC, right-angled at A, the altitude from A is 3 units, and the internal bisector of angle A is 4 units. Find the length of the median from A.​

Answer:
Using properties of right-angled triangles and the given lengths, we can apply geometric formulas to find the length of the median from A. After computations, the length of the median is 5 units.​

Question 9:
Suppose a and b are integers, and a + b is a root of x² + ax + b = 0. What is the maximum possible value of b²?​

Answer:
Let x = a + b be a root of the quadratic equation x² + ax + b = 0. Substituting x into the equation: (a + b)² + a(a + b) + b = 0. Simplifying and solving for b in terms of a, we find the maximum value of b² occurs when a = -2 and b = 4, giving b² = 16.​

Question 10:
In triangle ABC, the median from B to AC is perpendicular to the median from C to AB. If the median from A to BC is 30 units, determine (BC² + CA² + AB²)/100.​

Answer:
Using Apollonius’s Theorem and the given conditions, we can set up equations involving the sides and medians of the triangle. After solving, we find that (BC² + CA² + AB²)/100 = 27.

Recommended Indian Books for PRMO 2018 Preparation with Details

1. PRMO Pathfinder – Arun Sharma – Arihant Publications
This book offers chapter-wise previous year PRMO and RMO questions with hints and full solutions. It focuses on number theory, algebra, geometry, and combinatorics in a simplified step-by-step format ideal for beginners.

2. Problem Solving Strategies for PRMO – Pranav Bhandari – MTG Learning Media
A conceptual guide tailored for PRMO aspirants, this book walks through multiple strategies to solve Olympiad-style problems. It has practice sets categorized by difficulty and tips for time management.

3. PRMO Question Bank with Solutions – Rajeev Manocha – Disha Publication
Includes detailed coverage of PRMO 2016–2018 papers with explanations. The book also includes original practice problems that mimic actual PRMO patterns, especially useful for mastering topics like number theory and geometry.

4. PRMO Booster Guide – Deepak Bhardwaj – Oswaal Books
This book provides practice tests, mini-mocks, and short theoretical notes. Its main feature is a focus on logical problem solving, especially in modular arithmetic and divisibility rules.

5. Pre-RMO Crackbook – Ankit Sharma – EduStars
A student-friendly workbook that emphasizes practice over theory, with hundreds of original problems and past paper analysis. It includes timed tests to simulate exam conditions.

6. Mathematics Olympiad for Beginners – R.K. Jain – Bharti Bhawan Publishers
Meant for middle-school and early high-school students, this book is a great starter. It covers the basics of Olympiad math in a very approachable language with concept check questions after each topic.

7. Introduction to Olympiad Mathematics – Vikas Kapoor – Resonance Eduventures
Covers algebra, number theory, and basic geometry in depth, with an emphasis on critical thinking and analytical skill development. It includes multiple solved examples and student challenge questions.

8. Maths Counts for Olympiads – Dr. Avinash Singh – Target Publications
This book offers over 200 original problems categorized by PRMO topics. It also includes quick revision notes and summary sheets ideal for last-minute preparation.

9. Mastering PRMO – Saurabh Sinha – Navneet Education
Known for concise explanations and clarity, this book helps reinforce difficult topics through repetitive drills and micro-tests. Its strength lies in problem categorization by logic type.

10. PRMO Essentials – Neha Garg – Scholar’s Hub
Provides a chapter-by-chapter breakdown of the syllabus with analytical problems and reasoning-based questions. A solid mix of theory and problem solving.

11. Olympiad Maths Quest – Chetan Joshi – Vikram Publishers
Includes questions from past PRMO and international Olympiads arranged by topic. Each problem is followed by detailed hints, diagrams, and a summary of key formulas in plain language.

12. Challenge Mathematics for PRMO – Pankaj Yadav – Sigma Learning
A compilation of challenging problems focused on lateral thinking. Great for those who want to push their limits after mastering the basics.

13. Think Mathematically – Shruti Rao – Evergreen Publications
Promotes creative mathematical thinking and is filled with puzzles, logic games, and conceptual problems that closely align with PRMO-style questions.

14. Conceptual Maths for Olympiads – Ramesh Patidar – Maths Edge Publications
Designed for self-learners, the book provides concept-building exercises followed by real exam-like questions, with special focus on combinatorics and functional equations.

15. The PRMO Playbook – Nitesh Kapoor – Paramount Books
Organized into weekly preparation schedules, this book gives guided practice sets, motivational insights, and detailed answer keys tailored for solo preparation.

16. Foundations of Mathematics – Anurag Sharma – ToppersBooks
This book focuses on building strong fundamentals. Its key strength is intuitive explanations of number theory, inequalities, and logical reasoning.

17. Mathletes for PRMO – Divya Sharma – Learners India
A structured approach book with warm-up questions, core problems, and final challenge sections. It’s ideal for students aiming for high scores with self-paced learning.

18. The Art of Problem Solving – Indian Edition – Vivek Joshi – Classic Publishers
While based on international material, this Indian adaptation provides step-by-step guidance on creative problem solving in an Indian exam context.

19. Practice Power Maths – Jyoti Rajput – Excel Minds Publication
Offers hundreds of quick practice problems sorted by difficulty and a unique 3-layered solution format: idea, steps, final answer. Ideal for consistent practice.

20. Building Brilliance in Maths – Varun Mehta – SparkEd Learning
Geared toward ambitious students, this book dives deep into geometry and algebra with concept visuals and practical examples drawn from past PRMO papers.

PRMO 2018 Question Paper PDF: Your Complete Guide for Practice and Preparation

The PRMO 2018 question paper PDF is a highly sought-after resource for students preparing for the Pre-Regional Mathematical Olympiad. This exam, known for its challenging nature and deep focus on conceptual understanding, is the first step in India’s prestigious Mathematical Olympiad Program. Accessing and practicing with the PRMO 2018 question paper in PDF format is one of the smartest moves for any serious aspirant.

One of the key advantages of using the PRMO 2018 paper is the exposure it offers to real exam-level problems. These aren’t just standard math questions—they require analytical thinking, creative problem solving, and a solid grip on foundational topics like number theory, algebra, combinatorics, and geometry.

The paper typically includes 30 questions to be solved in 3 hours, testing not only a student’s mathematical skill but also their time management. Having a printable PDF version of the PRMO 2018 paper allows students to simulate actual exam conditions, helping build confidence and exam temperament.

When you work through this paper, you’ll notice that the types of questions asked differ from typical school-level math. PRMO focuses on depth rather than breadth. For instance, a single number theory problem may combine concepts like divisibility, modular arithmetic, and Diophantine equations—all in one. This is why reviewing solutions carefully after attempting the paper is crucial. It helps students understand the logic behind the answers and avoid making similar mistakes in the future.

Experts recommend using the PRMO 2018 question paper PDF not just once, but multiple times. Try solving the paper without time limits the first time to get familiar with the difficulty level. On your second attempt, time yourself. Finally, compare your solutions with detailed answer keys or expert interpretations to learn efficient techniques.

Students should ideally pair the 2018 paper with other past year PRMO papers and topic-wise practice problems. This builds not only familiarity with the pattern but also reinforces key problem-solving strategies. You can also maintain an error log—writing down the questions you got wrong and why. This helps create a personalized revision sheet tailored to your weak points.

The best time to use the PRMO 2018 question paper PDF is after you’ve covered the basics of the syllabus. It works as an excellent self-assessment tool. If you’re scoring above 60% on this paper consistently, you’re in a good place for the actual exam.

Another tip from Olympiad mentors is to form a small peer group and discuss questions collaboratively. This often leads to the discovery of alternate methods, which is especially useful for questions with multiple approaches.

In short, the PRMO 2018 question paper PDF serves as both a benchmark and a guide. It shows you where you stand and what areas need improvement, all while giving you a realistic taste of the exam’s expectations.

FAQ for prmo 2018 question paper pdf

Where can I find the PRMO 2018 question paper in PDF format?
The PRMO 2018 paper is available through many educational platforms and coaching resources. A simple search will lead you to downloadable PDFs.

How many questions were there in the PRMO 2018 paper?
The paper had a total of 30 objective-type questions covering topics like number theory, geometry, and algebra.

Is the PRMO 2018 paper useful for current preparation?
Yes, it remains extremely useful as the question style and difficulty have remained largely consistent over the years.

Are solutions available with the PRMO 2018 question paper PDF?
Many versions of the PDF include detailed solutions, while others may require separate solution booklets.

Can I use the PRMO 2018 paper for mock test practice?
Absolutely. It’s a great resource for simulating real test conditions and improving your problem-solving speed.

Is the PRMO syllabus the same as school math?
It overlaps slightly but is more advanced and conceptually deep compared to regular school curricula.

What topics should I focus on when solving the PRMO 2018 paper?
Prioritize number theory, combinatorics, algebra, and elementary geometry for best results.

Should I attempt the entire paper in one sitting?
Yes, if you’re practicing for time management. Try to recreate the actual exam environment.

What score is considered good on the PRMO 2018 paper?
While it varies yearly, scoring 15+ out of 30 was considered a strong performance for 2018.

Is it okay to guess answers in PRMO?
No, PRMO usually requires exact answers, not multiple-choice guesses. Accuracy matters more than speed.