Maths Olympiad Practice Test 1 — IMO-style (Class 5)
A free Maths, Science, English and Reasoning Olympiads (IMO, NSO, IEO style) practice paper for Grade 5 in the format of the real test: 50 questions in 60 minutes, covering Logical Reasoning; Mathematical Reasoning; Everyday Mathematics; Achievers' Section. 60 minutes, no calculator. Choose one answer (A–D) for each question. Logical Reasoning (15), Mathematical Reasoning (20) and Everyday Mathematics (10) are 1 mark each; the Achievers’ Section (5) is 3 marks each — 60 marks in all. There is no penalty for a wrong answer, so answer every question. The portal counts each answer once. Attempt it online — every question is marked instantly and the correct answers are shown at the end.
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Q1. Which number comes next in the series?
3, 7, 15, 31, 63, ?
Q2. Which letter comes next in the series?
B, E, I, N, ?
Q3. Find the missing number.
36 : 216 :: 49 : ?
Q4. Three of these letter groups follow the same rule. Which one is the odd one out?
Q5. In a certain code, WATER is written as XZUDS. How is PLANT written in that code?
Q6. In a certain code, MOTHER is written as OMHTRE. How is SISTER written in that code?
Q7. 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. In which direction is she now from her starting point?
Q8. In a row of 35 children, Aman is 12th from the left and Bina is 9th from the right. How many children are standing between Aman and Bina?
Q9. The English alphabet is written in reverse order (Z to A). Which letter is 7th to the right of the 10th letter from the left?
Q10. If these words are arranged in dictionary order, which word comes third?
Plant, Planet, Plate, Planning, Plan
Q11. A mirror is placed along the line MN, to the right of the figure. Which option shows the mirror image of the figure?
Q12. Which option shows the water image of the figure (its reflection in the water line below it)?
Q13. A square sheet of paper is folded in half from left to right (Step 1), then folded in half from top to bottom (Step 2). A hole is punched as shown (Step 3). What does the sheet look like when it is unfolded?
Q14. How many triangles are there in the figure?
Q15. Study the pattern. Which figure should come in place of the question mark?
Q16. What is the difference between the place values of the two 7s in 57,03,718?
Q17. Which number is shown by the Roman numeral CDXLIV?
Q18. What is the smallest number greater than 5 which leaves a remainder of 5 when it is divided by 6, by 8 and by 12?
Q19. Two ropes of lengths 84 m and 126 m are cut into pieces that are all of the same length, and as long as possible. How many pieces are there in all?
Q20. Which of these fractions is the greatest?
Q21. 3 1/4 + 2 5/6 − 1 2/3 = ?
Q22. 12.5 × 0.4 + 3.75 ÷ 0.25 = ?
Q23. 3 tenths + 5 thousandths + 12 hundredths = ?
Q24. 48 ÷ 6 × 2 + 15 − 3 × 4 = ?
Q25. How many prime numbers are there between 40 and 70?
Q26. The five-digit number 6□184 is divisible by 9. Which digit is in the box?
Q27. 3 km 45 m − 1 km 870 m = ?
Q28. What is the smaller angle between the hour hand and the minute hand of a clock at 8 o’clock?
Q29. A rectangle has a length of 18 cm and a perimeter of 60 cm. What is its area?
Q30. What is the area of the shape shown? (All corners are right angles.)
Q31. How many cubes of edge 2 cm can be packed into a box that measures 10 cm × 8 cm × 6 cm on the inside?
Q32. The bar graph shows the number of books read by five children in a year. What is the average number of books read per child?
Q33. How many lines of symmetry does a regular hexagon have?
Q34. Three circles, each of radius 7 cm, are placed in a row so that each touches the next one and all of them fit exactly inside a rectangle. What is the perimeter of the rectangle?
Q35. What is the smallest five-digit number that can be made using each of the digits 0, 3, 5, 7 and 9 exactly once?
Q36. Meera buys 3 notebooks at ₹45.50 each and a pen for ₹28.75. She pays with a ₹200 note. How much change should she get?
Q37. A train leaves Pune at 9:45 p.m. and the journey takes 7 hours 35 minutes. At what time does it reach?
Q38. In a certain year, 15 August falls on a Saturday. On which day of the week does 2 October fall in the same year?
Q39. A water tank can hold 2,400 litres. It already has 450 litres in it. A tap fills 25 litres every minute. How long will it take to fill the tank completely?
Q40. A bus travels at a steady 45 km every hour. How far does it travel in 2 hours 20 minutes?
Q41. 12 pencils cost ₹84. What is the cost of 20 such pencils?
Q42. A shopkeeper buys 20 kg of rice at ₹48 per kg. 2 kg gets spoilt, and he sells the rest at ₹55 per kg. What is his profit?
Q43. A bag has 5 kg 250 g of sugar. It is packed into small packets of 350 g each. How many packets are filled?
Q44. A film show starts at 2:50 p.m. The film runs for 2 hours 45 minutes and there is a 15-minute interval in between. When does the show end?
Q45. An auto-rickshaw charges ₹30 for the first 2 km and ₹14 for every kilometre after that. What is the fare for a 9 km ride?
Q46. When a number is divided by 7, the quotient is 52 and the remainder is 6. What is the remainder when the same number is divided by 9?
Q47. What is the smaller angle between the hands of a clock at 3:40?
Q48. Anil spent 1/4 of his money on books and then 2/5 of the remaining money on clothes. He was left with ₹540. How much money did he have at first?
Q49. How many times is the digit 7 written when all the numbers from 1 to 100 are written down?
Q50. A square garden of side 30 m has a path 2 m wide all around it on the outside. What is the area of the path?
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