Maths Olympiad - Number System (9 Mathematics)
IMO and NSO-style challenging problems on number theory, rational and irrational numbers, and algebraic properties. Advanced logical reasoning required.
TL;DR: IMO and NSO-style challenging problems on number theory, rational and irrational numbers, and algebraic properties. Advanced logical reasoning require…
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IMO and NSO-style challenging problems on number theory, rational and irrational numbers, and algebraic properties. Advanced logical reasoning required.
Maths Olympiad - Number System MCQs with Answers & Explanations
Q1. What is the largest prime number less than 100 that when divided by 7 leaves a remainder of 3?
- 73 ✓ (correct)
- 79
- 83
- 97
Q2. If p and q are prime numbers and p^2 + q^2 = 100, what are the values of p and q?
- p=2, q=2
- p=3, q=5
- p=5, q=5 ✓ (correct)
- p=6, q=8
Q3. What is the remainder when 2^100 is divided by 5?
- 0
- 1 ✓ (correct)
- 2
- 4
Q4. Express 0.3333... (repeating) as a fraction in lowest terms.
- 1/2
- 1/3 ✓ (correct)
- 2/3
- 3/10
Q5. Which of these is a rational number?
- sqrt(2)
- pi
- sqrt(3)
- 0.256256256... ✓ (correct)
Q6. If 2^a * 3^b * 5^c = 360, what is a + b + c?
- 3
- 4
- 5 ✓ (correct)
- 6
Q7. What is the GCD of 84 and 126?
- 6
- 12
- 21
- 42 ✓ (correct)
Q8. The LCM of two numbers is 60 and their GCD is 5. If one number is 20, what is the other number?
- 12 ✓ (correct)
- 15
- 25
- 30
Frequently Asked Questions
How do we determine if a number is rational or irrational?
A rational number can be expressed as a fraction p/q where p and q are integers and q is not zero. It either terminates (like 0.5) or repeats as a decimal (like 0.333...). An irrational number cannot be expressed as a simple fraction and its decimal representation never terminates or repeats (like pi = 3.14159...). Examples of irrational numbers include sqrt(2), sqrt(3), pi, and e.
What is the Fundamental Theorem of Arithmetic?
Every integer greater than 1 can be uniquely expressed as a product of prime numbers (ignoring the order of factors). For example, 12 = 2^2 * 3, and no other prime factorization equals 12. This theorem guarantees that prime factorization is unique, making it a fundamental tool in number theory for finding GCD, LCM, and solving divisibility problems.
More 9 Mathematics MCQs
- Coordinate Geometry
- Arithmetic Progressions
- Circles
- Surface Areas and Volumes
- Trigonometry (Applications Case Study)
- Probability (Case Study)
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