Maths Olympiad Practice Test 1 — IMO-style (Class 8)

Q4. Find the odd one out.

Q5. In a certain code language, PAPER is written as QZQDS. How is MONEY written in that code?

Q6. Sameer walks 6 km towards the north, turns right and walks 8 km, then turns right again and walks 12 km. How far is he from his starting point, and in which direction?

Q7. In a row of 40 students, Riya is 14th from the left end and Aman is 9th from the right end. How many students are there between Riya and Aman?

Q8. Pointing to a girl, Arjun said, "Her father is the only son of my father's father." How is the girl related to Arjun?

Q9. A mirror is held along the line MN. Which option shows the mirror image of the given figure?

Q10. Which option shows the water image of the given figure?

Q11. A square sheet of paper is folded as shown in Steps 1 and 2, and then a round hole and a square hole are punched as in Step 3. Which option shows the sheet when it is unfolded?

Q12. How many triangles are there in the figure below?

Q13. Which figure comes next in the series?

Q14. What is the smaller angle between the hour hand and the minute hand of a clock at 4:40?

Q15. The same rule is used in each row. Find the missing number.
5, 3 → 16
7, 2 → 45
8, 6 → ?

Q16. The value of (−2/3) + 5/6 − 1/4 is

Q17. Solve: (3x − 2)/4 − (2x + 3)/3 = 2/3 − x

Q18. What is the smallest number by which 2352 must be multiplied so that the product is a perfect square?

Q19. √(1 + 27/169) equals

Q20. What is the smallest number by which 1323 must be divided so that the quotient is a perfect cube?

Q21. If 5^{2x − 1} = 125^{x − 2}, then x equals

Q22. 0.000000405 written in standard form is

Q23. If a + 1/a = 5, then a² + 1/a² equals

Q24. The factors of x² − 5x − 24 are

Q25. Using a suitable identity, the value of 103 × 97 is

Q26. The compound interest on ₹8000 for 2 years at 10% per annum, compounded annually, is

Q27. Two successive discounts of 20% and 10% are equal to a single discount of

Q28. 12 workers can build a wall in 15 days. How many workers are needed to build the same wall in 9 days?

Q29. Each interior angle of a regular polygon is 156°. How many sides does it have?

Q30. In parallelogram ABCD, ∠A = (3x + 10)° and ∠B = (2x + 20)°. What is the measure of ∠C?

Q31. The parallel sides of a trapezium are 14 cm and 22 cm, and its area is 252 cm². What is the distance between the parallel sides?

Q32. What is the volume of a cylinder of radius 7 cm and height 10 cm? (Take π = 22/7)

Q33. A bag contains 5 red, 7 blue and 8 green balls. One ball is taken out at random. What is the probability that it is not blue?

Q34. A family's monthly budget of ₹36,000 is shown in a pie chart. The sector for food has a central angle of 120°. How much does the family spend on food each month?

Q35. The four-digit number 52A4 is divisible by 9, where A is a digit. What is the value of A?

Q36. A shopkeeper buys 20 pens at ₹15 each and sells all of them at ₹18 each. What is his profit per cent?

Q37. A train 180 m long passes a signal pole in 12 seconds. What is its speed?

Q38. A film starts at 17:45 and lasts 2 hours 38 minutes. At what time does it end?

Q39. 15 August 2026 is a Saturday. What day of the week is 26 January 2027?

Q40. A rectangular garden is 25 m long and 16 m wide. A path 2 m wide runs all along the inside of its boundary. What is the area of the path?

Q41. A shirt marked ₹1500 is sold at a 20% discount, and then 12% GST is charged on the discounted price. How much does the customer pay?

Q42. 2.5 kg of rice costs ₹150. What is the cost of 7 kg 200 g of the same rice?

Q43. Pipe P alone can fill a tank in 6 hours and pipe Q alone can fill it in 9 hours. If both pipes are opened together, how long will they take to fill the empty tank?

Q44. An electricity company charges ₹5 per unit for the first 100 units and ₹7 per unit for every unit after that, plus a fixed charge of ₹75. What is the bill for 260 units?

Q45. A mother is now three times as old as her daughter. In 12 years she will be twice as old as her daughter. How old is the mother now?

Q46. A cuboid measuring 12 cm × 8 cm × 6 cm is cut into cubes of edge 2 cm. By how much is the total surface area of all the cubes greater than the surface area of the cuboid?

Q47. What is the sum of all two-digit numbers that leave a remainder of 3 when divided by 7?

Q48. A boat goes 30 km downstream in 2 hours and 18 km upstream in 3 hours. What is the speed of the stream?

Q49. If x − 1/x = 3, then x³ − 1/x³ equals

Q50. Meera spends 30% of her monthly salary on rent, 25% of the remaining amount on food and 20% of what is then left on travel. She saves the rest, which is ₹12,600. What is her monthly salary?