Getting ready for the Class 8 Math Olympiad can be fun and challenging. This guide has 50 sample questions to help you practice and improve. The questions cover logical reasoning, math concepts, and real-life math applications, just like in the Science Olympiad Foundation (SOF) exams. With this set, you can get familiar with the types of questions you’ll see and build your confidence.
Each question includes an answer and explanation. You can check check your work and understand how to solve it. These questions are designed to help you think through each problem step-by-step, building your skills and confidence for the Olympiad. Jump in and see how much you can grow with a bit of practice!
Prepare for Class 8 Math Olympiad (SOF) with 50 Sample Questions in Logical and Mathematical Reasoning
Section I: Logical Reasoning
Question 1. Choose the odd one out in the series: 3, 10, 15, 20, 27
a) 3
b) 10
c) 15
d) 27
Answer:
d) 27 – All other numbers increase by a pattern, except 27, which doesn’t fit the sequence.
Question 2. In a code language, FRIEND is written as 15. What would “HELP” be?
a) 19
b) 22
c) 24
d) 18
Answer:
b) 22 – Each letter’s alphabetical position is summed to get the total value.
Question 3. If today is Tuesday, what day will it be 15 days from now?
a) Tuesday
b) Wednesday
c) Thursday
d) Friday
Answer:
a) Tuesday – 15 days from Tuesday brings it back to Tuesday, as 15 is a multiple of 7 + 1.
Question 4. Find the missing term in the series: 5, 12, 19, __, 33
a) 21
b) 25
c) 26
d) 28
Answer:
b) 25 – The difference between terms is 7, so 19 + 7 = 26.
Question 5. Ritu walks 40 meters north, then turns right and walks 20 meters, then turns right again and walks 40 meters. How far is she from her starting point?
a) 20 meters
b) 30 meters
c) 40 meters
d) 60 meters
Answer:
a) 20 meters – After her moves, Ritu forms a rectangle with a width of 20 meters.
Question 6. Which number should replace the question mark: 8, 12, 20, 32, ?
a) 40
b) 48
c) 52
d) 56
Answer:
b) 48 – Each term increases by an incrementally increasing even number (4, 8, 12, 16).
Question 7. If CLOCK is coded as DMPDL, how would TABLE be written in the same code?
a) UBQMF
b) UBCMF
c) VBCMF
d) UBCLF
Answer:
a) UBQMF – Each letter is shifted forward by one in the alphabet.
Question 8. Which of these completes the series: 9, 27, 81, __, 729?
a) 162
b) 243
c) 324
d) 512
Answer:
b) 243 – The sequence multiplies each term by 3.
Question 9. In a code, STAR is written as 43. How is MOON written in the same code?
a) 57
b) 64
c) 68
d) 74
Answer:
b) 64 – Each letter’s position value in the alphabet is added to get the code.
Question 10. What is the next term in the pattern: A, C, F, J, __?
a) M
b) N
c) O
d) P
Answer:
a) M – The series progresses by adding incrementally increasing positions (1, 2, 3, etc.).
Question 11. “Pen” is to “Write” as “Key” is to __
a) Open
b) Lock
c) Security
d) Start
Answer:
a) Open – Just as a pen is used for writing, a key is used for opening.
Question 12. If 2 pencils and 5 erasers cost ₹3.10, and 5 pencils and 2 erasers cost ₹4.75, what is the cost of 1 eraser?
a) ₹0.25
b) ₹0.50
c) ₹0.75
d) ₹1.00
Answer:
b) ₹0.50 – Solving the system of equations reveals the cost of an eraser.
Question 13. A word pair has the same relationship as “Cow : Milk”. Select the similar pair:
a) Hen : Egg
b) Tree : Fruit
c) River : Water
d) Farm : Animal
Answer:
a) Hen : Egg – Just as a cow produces milk, a hen produces eggs.
Question 14. Complete the analogy: “Book is to Reading as Spoon is to ___”
a) Fork
b) Food
c) Eating
d) Kitchen
Answer:
c) Eating – A book is used for reading, just as a spoon is used for eating.
Question 15. If 2, 10, and 50 follow a certain rule, which of the following will be the next term?
a) 150
b) 180
c) 250
d) 300
Answer:
c) 250 – The series follows a multiplication pattern (×5 for each subsequent term).
Question 16. Identify the missing number in the sequence: 7, 12, 19, __, 39
a) 24
b) 27
c) 28
d) 31
Answer:
d) 31 – The difference between terms increases by 5 each time.
Question 17. Which of these numbers does not belong to the series: 3, 9, 18, 27, 33, 36?
a) 9
b) 27
c) 33
d) 36
Answer:
c) 33 – The series increases by adding 6, but 33 doesn’t fit the pattern.
Question 18. Aman walks 8 km north, then 6 km east, and finally 8 km south. How far is he from his starting point?
a) 6 km
b) 7 km
c) 8 km
d) 9 km
Answer:
a) 6 km – His total horizontal displacement is 6 km.
Question 19. If January 10th was a Saturday, what day is February 15th in the same year?
a) Tuesday
b) Wednesday
c) Friday
d) Sunday
Answer:
c) Sunday – Calculating the weeks and days difference results in Sunday.
Question 20. Find the missing term in the series: 5, 7, 11, 13, __, 17
a) 14
b) 15
c) 16
d) 19
Answer:
d) 19 – Each term in the series is a prime number.
Section II: Mathematical Reasoning
Question 21. What is the square root of 1225?
a) 25
b) 30
c) 35
d) 40
Answer:
c) 35 – The square root of 1225 is 35.
Question 22. Simplify: (3² × 2³) ÷ 6
a) 8
b) 10
c) 12
d) 9
Answer:
a) 8 – 3² = 9, 2³ = 8; (9 × 8) ÷ 6 = 72 ÷ 6 = 8.
Question 23. If x = 4 and y = -3, evaluate 2x – 3y + 5.
a) 19
b) 20
c) 21
d) 23
Answer:
a) 19 – Substituting the values gives: 2(4) – 3(-3) + 5 = 8 + 9 + 5 = 19.
Question 24. Which of the following is a polynomial?
a) 3x² + 4/x
b) 5x³ – 2x + 1
c) √x + x²
d) 1/x³ + 4
Answer:
b) 5x³ – 2x + 1 – This expression is a polynomial with integer powers of x.
Question 25. What is the value of (4x² + 5x – 6) when x = 2?
a) 16
b) 18
c) 20
d) 22
Answer:
b) 18 – Substituting x = 2, we get 4(2)² + 5(2) – 6 = 16 + 10 – 6 = 18.
Question 26. Solve for x: 3x + 7 = 19
a) 3
b) 4
c) 5
d) 6
Answer:
c) 5 – Solving the equation gives x = 5.
Question 27. If the area of a square is 144 cm², what is the length of one side?
a) 10 cm
b) 11 cm
c) 12 cm
d) 13 cm
Answer:
c) 12 cm – The side length is the square root of the area, √144 = 12 cm.
Question 28. Factorize: x² – 9
a) (x – 3)(x + 3)
b) (x – 9)(x + 9)
c) (x + 3)²
d) x(x – 9)
Answer:
a) (x – 3)(x + 3) – This is a difference of squares.
Question 29. Solve for y: 5y – 3 = 2y + 12
a) y = 3
b) y = 5
c) y = 7
d) y = 9
Answer:
c) y = 7 – Simplifying the equation, we find y = 7.
Question 30. What is the value of 2x – y, if x = 5 and y = 3?
a) 7
b) 8
c) 9
d) 10
Answer:
b) 8 – Substituting the values gives 2(5) – 3 = 10 – 3 = 8.
Question 31. Simplify: (5x – 3x + 4) – (2x – 7)
a) 3x + 3
b) 3x + 4
c) 4x + 4
d) 4x + 3
Answer:
a) 3x + 3 – Simplifying the terms gives 3x + 3.
Question 32. If 3 times a number is 45, what is the number?
a) 10
b) 12
c) 15
d) 18
Answer:
c) 15 – Dividing 45 by 3 gives 15.
Question 33. What is the cube of 7?
a) 243
b) 343
c) 373
d) 513
Answer:
b) 343 – 7 × 7 × 7 = 343.
Question 34. If the sum of a number and 12 is 50, what is the number?
a) 28
b) 30
c) 38
d) 42
Answer:
a) 28 – Subtracting 12 from 50 gives 28.
Question 35. Simplify: (2x² + 3x + 4) – (x² – x + 2)
a) x² + 4x + 2
b) x² + 2x + 2
c) 3x² + 4x + 2
d) x² + 2x
Answer:
a) x² + 4x + 2 – Simplifying the terms gives x² + 4x + 2.
Question 36. The perimeter of a rectangle is 50 cm. If the length is 15 cm, what is the width?
a) 5 cm
b) 10 cm
c) 12 cm
d) 15 cm
Answer:
b) 10 cm – Using the perimeter formula, width = 10 cm.
Question 37. Solve for z: 4z – 3 = 17
a) 4
b) 5
c) 6
d) 7
Answer:
c) 6 – Solving the equation gives z = 6.
Question 38. If x² = 49, what is the value of x?
a) 6
b) 7
c) 8
d) 9
Answer:
b) 7 – The square root of 49 is 7 (or -7).
Question 39. What is the remainder when 101 is divided by 4?
a) 1
b) 2
c) 3
d) 4
Answer:
a) 1 – Dividing 101 by 4 leaves a remainder of 1.
Question 40. If y = 3x + 5 and x = 4, what is the value of y?
a) 14
b) 15
c) 17
d) 18
Answer:
d) 18 – Substituting x = 4, y = 3(4) + 5 = 18.
Section III: Everyday Mathematics
Question 41. A rectangle has a length of 12 m and width of 5 m. What is the area?
a) 50 m²
b) 60 m²
c) 72 m²
d) 75 m²
Answer:
b) 60 m² – Area = length × width = 12 m × 5 m = 60 m².
Question 42. The volume of a cube is 125 cm³. What is the length of one side?
a) 4 cm
b) 5 cm
c) 6 cm
d) 7 cm
Answer:
b) 5 cm – The side length is the cube root of 125, which is 5 cm.
Question 43. A car travels 240 km in 3 hours. What is its speed in km/h?
a) 70 km/h
b) 80 km/h
c) 90 km/h
d) 100 km/h
Answer:
b) 80 km/h – Speed = distance ÷ time = 240 km ÷ 3 hours = 80 km/h.
Question 44. A shopkeeper buys a shirt for ₹80 and sells it for ₹100. What is the profit percentage?
a) 20%
b) 25%
c) 30%
d) 35%
Answer:
b) 25% – Profit = Selling Price – Cost Price = ₹100 – ₹80 = ₹20; Profit % = (20/80) × 100 = 25%.
Question 45. If the circumference of a circle is 31.4 cm, what is the diameter? (Use π ≈ 3.14)
a) 5 cm
b) 8 cm
c) 10 cm
d) 12 cm
Answer:
c) 10 cm – Circumference = π × diameter; 31.4 ÷ 3.14 = 10 cm.
Question 46. A bag contains 8 red balls, 5 blue balls, and 7 green balls. What is the probability of picking a red ball?
a) 1/5
b) 2/5
c) 1/2
d) 3/4
Answer:
b) 2/5 – Total balls = 8 + 5 + 7 = 20; Probability = 8/20 = 2/5.
Question 47. An amount of ₹1500 is invested at a 10% annual interest rate. How much interest will be earned in 2 years?
a) ₹150
b) ₹300
c) ₹400
d) ₹500
Answer:
b) ₹300 – Interest = Principal × Rate × Time = 1500 × 0.10 × 2 = ₹300.
Question 48. The cost of 5 notebooks is ₹15. What is the cost of 8 notebooks?
a) ₹20
b) ₹24
c) ₹28
d) ₹30
Answer:
b) ₹24 – Cost per notebook = ₹15 ÷ 5 = ₹3; 8 notebooks = 8 × ₹3 = ₹24.
Question 49. A triangle has a base of 10 cm and height of 8 cm. What is its area?
a) 20 cm²
b) 30 cm²
c) 40 cm²
d) 50 cm²
Answer:
c) 40 cm² – Area = ½ × base × height = ½ × 10 cm × 8 cm = 40 cm².
Question 50. A train travels 300 km in 5 hours. If it continues at the same speed, how far will it travel in 7 hours?
a) 380 km
b) 400 km
c) 420 km
d) 440 km
Answer:
c) 420 km – Speed = 300 km ÷ 5 hours = 60 km/h; Distance = 60 km/h × 7 hours = 420 km.
