Maths Olympiad Practice Test 1 — IMO-style (Class 6)
A free Maths, Science, English and Reasoning Olympiads (IMO, NSO, IEO style) practice paper for Grade 6 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. Logical Reasoning, Mathematical Reasoning and Everyday Mathematics are worth 1 mark per question; the Achievers' Section is worth 3 marks per question (60 marks in all). On this portal each answer counts once. Answer every question — there is no penalty for a wrong answer. 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?
A, C, F, J, O, ?
Q3. Find the missing number.
7 : 50 :: 9 : ?
Q4. Which number is the odd one out?
Q5. In a certain code, CLOUD is written as FWQNE. How is PLANT written in the same code?
Q6. Riya walks 6 km towards the north. She turns right and walks 4 km. She turns right again and walks 9 km. Then she turns right and walks 8 km. How far is she from her starting point, and in which direction?
Q7. In a row of 40 students, Aman is 12th from the left end and Bela is 15th from the right end. How many students are standing between Aman and Bela?
Q8. Pointing to a boy, Neha said, 'He is the only son of the only son of my paternal grandfather.' How is the boy related to Neha?
Q9. Which of the figures A, B, C or D is the correct mirror image of the given figure, when the mirror is placed along the line MN?
Q10. A square sheet of paper is folded and punched as shown (first the top half is folded down onto the bottom half, then the left half is folded onto the right half). How will the sheet look when it is unfolded?
Q11. How many triangles are there in the figure below?
Q12. Which figure comes next in the series?
Q13. Which letter group is the odd one out?
Q14. Study the pattern in the first two rows and find the missing number.
4, 5, 41
3, 6, 45
2, 7, ?
Q15. If the letters of the word NUMBERS are arranged in alphabetical order, which letter will be exactly in the middle?
Q16. What is the difference between the place values of the two 7s in 5,72,375?
Q17. Which of these is forty-two lakh six thousand nine written in numerals?
Q18. The product of two numbers is 1080 and their HCF is 6. What is their LCM?
Q19. Which digit should replace * so that the number 67*458 is divisible by 11?
Q20. How many prime numbers are there between 50 and 80?
Q21. What is the value of (−15) + 8 − (−12) − 20?
Q22. Which of these fractions is the greatest?
Q23. 3.5 + 0.35 + 0.035 + 35 = ?
Q24. If 3x − 7 = 2x + 5, what is the value of 2x + 1?
Q25. The breadth of a rectangle is 4 cm less than its length l cm. Which expression gives its perimeter in cm?
Q26. The ratio of boys to girls in a class is 5 : 7. There are 84 students in all. How many more girls than boys are there?
Q27. Find x if 15 : x = x : 60.
Q28. 40% of a number is 72. What is 65% of the same number?
Q29. What is the smaller angle between the hour hand and the minute hand of a clock at 4:20?
Q30. An angle is 24° more than its complement. What is the angle?
Q31. How many diagonals does an octagon (8-sided polygon) have?
Q32. A square has the same perimeter as a rectangle measuring 18 cm by 12 cm. What is the area of the square?
Q33. A rectangular garden is 30 m long and 20 m wide. A path 2 m wide runs all around it, just inside its edges. What is the area of the path?
Q34. The bar graph shows the number of books borrowed from a school library from Monday to Friday. The librarian had hoped for an average of 40 books a day. Which statement is correct?
Q35. Which number is written in Roman numerals as CDXLIV?
Q36. Riya buys 3 notebooks at ₹ 45.50 each and a pen for ₹ 18.75. She pays with a ₹ 200 note. How much change should she get?
Q37. A night train leaves Pune at 10:45 p.m. and reaches its destination at 6:20 a.m. the next day. How long is the journey?
Q38. 5 March of a certain year is a Monday. On which day of the week is 30 April of the same year?
Q39. A jug holds 2 L 250 mL of lemonade. How many glasses of 150 mL each can be filled from it?
Q40. A cyclist rides 18 km in 1 hour 30 minutes. At the same speed, how far will she ride in 40 minutes?
Q41. 12 notebooks cost ₹ 324. What will 20 such notebooks cost?
Q42. A shopkeeper buys 20 pens for ₹ 240 and sells each pen for ₹ 15. What is his total profit?
Q43. A carton holding 24 identical books weighs 13.6 kg. The empty carton weighs 1.6 kg. What is the weight of one book?
Q44. Three friends share a restaurant bill of ₹ 1,350 in the ratio 2 : 3 : 4. What is the largest share?
Q45. A mother is 3 times as old as her daughter. In 12 years' time, she will be twice as old as her daughter. What is the mother's present age?
Q46. How many numbers from 1 to 300 are divisible by 3 or by 5, but not by 15?
Q47. A book has 250 pages, numbered 1 to 250. How many digits are used in printing all the page numbers?
Q48. What is the smallest number that leaves a remainder of 7 when divided by 12, by 15 and by 20, and is also exactly divisible by 11?
Q49. A square of side 5 cm is cut from each corner of a rectangular card 40 cm long and 30 cm wide. What are the perimeter and the area of the card that is left?
Q50. A rectangle 5 cm long and 4 cm wide is divided into 1 cm × 1 cm squares by lines drawn parallel to its sides. How many squares of all sizes are there in the figure?
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