Maths Olympiad Practice Test 1 — IMO-style (Class 7)

Q4. Which number is the odd one out?

Q5. In a certain code, TABLE is written as UZCKF. How is CHAIR written in that code?

Q6. Riya walks 10 m towards the north. She turns right and walks 6 m, then turns right again and walks 4 m. Finally she turns left and walks 2 m. How far is she now from her starting point (in a straight line)?

Q7. In a row of 45 students, Aman is 17th from the left end and Bina is 21st from the right end. How many students are standing between Aman and Bina?

Q8. A mirror is placed along the line MN. Which figure is the mirror image of the given figure?

Q9. Which of these is the water image of the letters and numbers shown (the water surface is the line below them)?

Q10. How many triangles are there in the figure below? (The figure is a square with both diagonals drawn and the midpoints of its sides joined.)

Q11. A square sheet of paper is folded in half from left to right (Step 1), then folded in half again from top to bottom (Step 2). A round hole and a triangular hole are then punched through all the layers (Step 3). Which figure shows the sheet when it is opened out?

Q12. Which figure comes next in the series?

Q13. Pointing to a girl in a photograph, Arjun said, "She is the daughter of the only son of my grandfather." How is the girl related to Arjun?

Q14. If the letters of the word NUMBER are arranged in alphabetical order, which letter will be third from the right?

Q15. The faces of a cube are numbered 1 to 6. Three different views of the same cube are shown. Which number is on the face opposite the face showing 3?

Q16. What is the value of (−12) × 5 − (−36) ÷ (−4) + 8?

Q17. Simplify: 2³⁄₄ ÷ 1⁵⁄₆ − ¹⁄₂

Q18. What is the value of 0.25 × 0.4 ÷ 0.05?

Q19. Find the value of (2⁷ × 3⁴) ÷ (6³ × 2²).

Q20. If 3(x − 4) + 5 = 2x + 7, what is the value of x?

Q21. If a = 2 and b = −3, what is the value of a² − 2ab + b²?

Q22. Two supplementary angles are in the ratio 7 : 11. What is the measure of the smaller angle?

Q23. The angles of a triangle are (2x + 10)°, (3x − 5)° and (x + 25)°. What is the largest angle of the triangle?

Q24. A 2.5 m ladder leans against a vertical wall with its foot 0.7 m from the wall. The top of the ladder slips 0.4 m down the wall. How far does the foot of the ladder move away from the wall?

Q25. A rectangular park is 60 m long and 40 m wide. A path 2.5 m wide runs all around it on the outside. What is the area of the path?

Q26. A wheel has a diameter of 70 cm. How many complete turns must it make to travel 1.1 km? (Take π = ²²⁄₇.)

Q27. A circle of radius 7 cm is cut out from a circular sheet of radius 14 cm. What is the area of the remaining sheet? (Take π = ²²⁄₇.)

Q28. The mean of five numbers is 18. When one of the numbers is removed, the mean of the remaining four numbers is 16. Which number was removed?

Q29. What is the median of this data?
7, 3, 9, 3, 5, 8, 3, 9, 6, 4

Q30. If a : b = 2 : 3 and b : c = 4 : 5, then a : b : c is

Q31. A number is first increased by 20% and then the new number is decreased by 20%. What is the overall change?

Q32. A bag has 4 red, 5 blue and 6 green balls. One ball is picked without looking. What is the probability that it is not blue?

Q33. Which of these capital letters has both a vertical line of symmetry and a horizontal line of symmetry?

Q34. Which of these rational numbers is the greatest?

Q35. In triangles ABC and PQR, AB = PQ, BC = QR and ∠B = ∠Q. By which rule are the two triangles congruent?

Q36. Pens cost ₹12 each and notebooks cost ₹35 each. Meera buys 4 pens and 3 notebooks and pays with a ₹500 note. How much change should she get?

Q37. A shirt is marked at ₹1,250. The shop gives a discount of 16%. What price does the customer pay?

Q38. A shopkeeper buys 20 kg of rice at ₹45 per kg and sells all of it at ₹54 per kg. What is his profit per cent?

Q39. Kavya deposits ₹8,000 in a bank at 7.5% per year simple interest. How much money will she have after 2 years 6 months?

Q40. A train leaves Pune at 21:45 and reaches Nagpur at 06:20 the next day. How long is the journey?

Q41. 26 January 2027 is a Tuesday. On which day of the week does 15 August 2027 fall?

Q42. A family drives 120 km to a hill station at 40 km/h and returns by the same road at 60 km/h. What is their average speed for the whole trip?

Q43. An empty water tank is 2 m long, 1.5 m wide and 1 m deep. A pipe fills it at 25 litres per minute. How long will it take to fill the tank completely? (1 m³ = 1000 litres)

Q44. 12 workers can paint a school building in 10 days. Working at the same rate, how many days will 15 workers take?

Q45. A mobile recharge of ₹199 lasts 28 days. Another recharge of ₹549 lasts 84 days. How much does a customer save over 84 days by choosing the ₹549 recharge?

Q46. The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is 27 more than the original number. What is the product of the digits?

Q47. A square has sides of 14 cm. With each corner of the square as centre, a quarter circle of radius 7 cm is drawn, as shown (shaded). What is the area of the part of the square that is not shaded? (Take π = ²²⁄₇.)

Q48. In a school, 60% of the students are girls. 25% of the girls and 40% of the boys play a sport. If 186 students play a sport, how many girls do not play a sport?

Q49. Three bells ring every 12 minutes, 18 minutes and 30 minutes respectively. They all ring together at 8:00 a.m. How many times will all three ring together from 8:00 a.m. to 8:00 p.m. (counting both 8:00 a.m. and 8:00 p.m.)?

Q50. The present ages of a mother and her daughter are in the ratio 7 : 2. After 5 years, their ages will be in the ratio 8 : 3. What will be the sum of their ages 10 years from now?