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Top 10 Maths Olympiad Questions with Solutions for Classes 6-8
Maths Olympiads are a fantastic way for students in Classes 6 to 8 to develop critical thinking and problem-solving skills beyond the classroom. This article presents ten challenging maths olympiad questions with detailed solutions, designed to sharpen your child's mathematical abilities and boost confidence for upcoming competitions. Each question is carefully selected to cover a variety of topics and difficulty levels, helping students practice and excel.
Top 10 Challenging Maths Olympiad Questions for Classes 6 to 8 with Solutions
Preparing for maths olympiads requires practice with diverse and challenging problems. Below are ten carefully chosen questions that cover topics such as number theory, geometry, algebra, and logical reasoning. Each question is followed by a step-by-step solution to help students understand the approach and methods used.
1. Find the sum of all two-digit numbers that are divisible by 7.
Solution:
The smallest two-digit number divisible by 7 is 14 (7 × 2) and the largest is 98 (7 × 14).
These numbers form an arithmetic progression:
- First term (a) = 14
- Last term (l) = 98
- Common difference (d) = 7
Number of terms, n = ((l - a)/d) + 1 = ((98 - 14)/7) + 1 = (84/7) + 1 = 12 + 1 = 13
Sum of AP = n/2 × (a + l) = 13/2 × (14 + 98) = 6.5 × 112 = 728
Answer: 728
2. If the product of two numbers is 144 and their HCF is 6, find their LCM.
Solution:
We know the relationship:
HCF × LCM = Product of the two numbers
Given HCF = 6, Product = 144
Therefore, LCM = Product / HCF = 144 / 6 = 24
Answer: 24
3. A rectangle has a perimeter of 60 cm. If the length is twice the breadth, find its area.
Solution:
Let breadth = x cm, then length = 2x cm.
Perimeter P = 2(length + breadth) = 60
2(2x + x) = 60
2(3x) = 60 → 6x = 60 → x = 10 cm
Length = 2 × 10 = 20 cm
Area = length × breadth = 20 × 10 = 200 cm²
Answer: 200 cm²
4. Find the value of x if 3x + 7 = 2x + 15.
Solution:
3x + 7 = 2x + 15
3x - 2x = 15 - 7
x = 8
Answer: x = 8
5. How many prime numbers are there between 20 and 50?
Solution:
Prime numbers between 20 and 50 are:
- 23, 29, 31, 37, 41, 43, 47
Total = 7
Answer: 7
6. The sum of the angles of a polygon is 1260°. How many sides does the polygon have?
Solution:
Sum of interior angles of a polygon = (n - 2) × 180°, where n = number of sides.
Given sum = 1260°
(n - 2) × 180 = 1260
n - 2 = 1260 / 180 = 7
n = 7 + 2 = 9
Answer: 9 sides
7. If the average of five numbers is 24, what is their total sum?
Solution:
Average = Sum of numbers / Number of numbers
Sum = Average × Number = 24 × 5 = 120
Answer: 120
8. A train travels 360 km in 4 hours. What is its average speed?
Solution:
Speed = Distance / Time = 360 / 4 = 90 km/h
Answer: 90 km/h
9. Find the next number in the sequence: 2, 6, 12, 20, 30, ...
Solution:
Look at the differences between terms:
- 6 - 2 = 4
- 12 - 6 = 6
- 20 - 12 = 8
- 30 - 20 = 10
The differences increase by 2 each time (4, 6, 8, 10, ...)
Next difference = 12
Next number = 30 + 12 = 42
Answer: 42
10. A bag contains 5 red, 7 blue, and 8 green balls. What is the probability of drawing a blue ball?
Solution:
Total balls = 5 + 7 + 8 = 20
Number of blue balls = 7
Probability = Number of favourable outcomes / Total outcomes = 7 / 20
Answer: 7/20
Practice Section
Try solving these additional questions to sharpen your skills:
- Find the LCM of 12 and 18.
- A triangle has sides 7 cm, 24 cm, and 25 cm. Is it a right-angled triangle?
- What is the sum of the first 15 natural numbers?
- If 5x - 3 = 2x + 12, find x.
- How many even numbers are there between 30 and 60?
Conclusion
These maths olympiad questions with solutions for Classes 6 to 8 cover a range of topics and difficulty levels, helping students build a strong foundation in problem-solving. Regular practice with such problems enhances logical thinking and prepares students for competitive exams. Apps like BeadBop provide interactive learning and practice opportunities tailored to students' needs, making preparation engaging and effective.
Frequently asked questions
What topics are commonly covered in maths olympiads for Classes 6 to 8?
Maths olympiads for Classes 6 to 8 typically cover topics such as number theory, algebra, geometry, arithmetic, probability, and logical reasoning.
How can practising olympiad questions help students?
Practising olympiad questions improves problem-solving skills, enhances logical thinking, and builds confidence to tackle challenging maths problems in exams and competitions.
Are solutions important when practising maths olympiad questions?
Yes, solutions help students understand the problem-solving approach, clarify doubts, and learn different methods to solve similar problems effectively.
How often should students practise maths olympiad questions?
Regular practice, ideally several times a week, helps students retain concepts, improve speed, and develop accuracy essential for maths olympiads.