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Maths Olympiad Sample Paper (Practice)

Maths Olympiad topic 20: Maths Olympiad mock test · Set 85 · 40 questions
TalentJR

How to solve it (Spot the topic first): Read the question and name the topic: HCF/LCM, fractions, calendar, ratio, percentage, interest, average, equation or number theory. Use that lesson’s method; write small working on rough paper. Look at the options: rule out answers that are too big, too small or the wrong kind. Check your answer by working backwards when you can.

NameDateTime takenScore ___ / 40
  1. 1.What is the units digit of 2^34? (a) 8 (b) 4 (c) 6 (d) 2
  2. 2.A batter has an average of 57 runs in 5 matches. How many runs are needed in the next match to raise the average to 59? (a) 59 (b) 12 (c) 61 (d) 69
  3. 3.Which of these numbers is divisible by 6? (a) 1352 (b) 1349 (c) 1344 (d) 1342
  4. 4.If 21 May is a Thursday, what day of the week is 1 June? (a) Sunday (b) Tuesday (c) Monday (d) Wednesday
  5. 5.What is the average of 49, 22, 36, 21, 41 and 47? (a) 35 (b) 37 (c) 36 (d) 38
  6. 6.A rectangle has an area of 30 sq cm and a length of 15 cm. What is its width? (a) 2 cm (b) 3 cm (c) 4 cm (d) 15 cm
  7. 7.If 5x − 69 = 1, what is x? (a) 14 (b) 15 (c) 70 (d) 13
  8. 8.If 5 notebooks cost ₹125, how much do 3 notebooks cost? (a) ₹75 (b) ₹123 (c) ₹375 (d) ₹100
  9. 9.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 20 days (c) 21 days (d) 11 days
  10. 10.What is the smallest number you must add to 191 to make it divisible by 5? (a) 2 (b) 1 (c) 3 (d) 4
  11. 11.What is the average of 64, 50, 41, 53 and 42? (a) 52 (b) 51 (c) 49 (d) 50
  12. 12.What is the simple interest on ₹5000 at 10% per year for 5 years? (a) ₹7500 (b) ₹3000 (c) ₹500 (d) ₹2500
  13. 13.What is the smallest number you must add to 451 to make it divisible by 7? (a) 3 (b) 5 (c) 4 (d) 6
  14. 14.A batter has an average of 57 runs in 7 matches. How many runs are needed in the next match to raise the average to 63? (a) 69 (b) 48 (c) 63 (d) 105
  15. 15.What is the units digit of 9^16? (a) 0 (b) 2 (c) 9 (d) 1
  16. 16.₹6500 is invested at 12% per year simple interest. What is the amount after 4 years? (a) ₹7280 (b) ₹10400 (c) ₹9620 (d) ₹3120
  17. 17.2/3 + 1/2 = ? (a) 1 (b) 7/6 (c) 3/5 (d) 4/3
  18. 18.What is the average of all the whole numbers from 57 to 85? (a) 14 (b) 72 (c) 28 (d) 71
  19. 19.What is 60% of 580? (a) 696 (b) 348 (c) 232 (d) 3480
  20. 20.If 10 March is a Saturday, what day of the week is 21 March? (a) Friday (b) Tuesday (c) Wednesday (d) Thursday
  21. 21.What is the units digit of 7^15? (a) 7 (b) 9 (c) 3 (d) 1
  22. 22.Which is the smallest: 0.87, 0.763, 0.8, 0.086? (a) 0.87 (b) 0.763 (c) 0.8 (d) 0.086
  23. 23.If 8x + 12 = 108, what is x? (a) 15 (b) 12 (c) 96 (d) 13
  24. 24.If 6x + 10 = 88, what is x? (a) 78 (b) 13 (c) 14 (d) 12
  25. 25.A teacher has 4 pencils and 10 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 4 (c) 6 (d) 2
  26. 26.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 20 days (d) 5 days
  27. 27.₹117 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹78 (b) ₹39 (c) ₹117 (d) ₹79
  28. 28.A rectangle has an area of 136 sq cm and a length of 17 cm. What is its width? (a) 119 cm (b) 9 cm (c) 16 cm (d) 8 cm
  29. 29.What is the value of the digit 9 in 17.296? (a) 0.9 (b) 0.009 (c) 0.09 (d) 9
  30. 30.Which is the smallest: 0.057, 0.68, 0.6, 0.557? (a) 0.057 (b) 0.68 (c) 0.6 (d) 0.557
  31. 31.What is the value of the digit 4 in 15.492? (a) 0.04 (b) 4 (c) 0.4 (d) 0.004
  32. 32.If 3x + 3 = 2x + 8, what is x? (a) 1 (b) 6 (c) 5 (d) 11
  33. 33.What is the average of 57, 56, 33, 62, 32 and 42? (a) 49 (b) 46 (c) 47 (d) 48
  34. 34.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 14 days (d) 24 days
  35. 35.What is the remainder when 223 is divided by 3? (a) 0 (b) 2 (c) 1
  36. 36.What is the smallest number of sweets that can be shared equally among 8 children or among 14 children, with none left over? (a) 22 (b) 57 (c) 56 (d) 112
  37. 37.Every pair follows the same rule: 4 : 24, 5 : 33, 9 : 89. What is 6 : ? (a) 26 (b) 44 (c) 36 (d) 47
  38. 38.Which is the greatest: 0.082, 0.135, 0.2, 0.28? (a) 0.082 (b) 0.135 (c) 0.2 (d) 0.28
  39. 39.Every pair follows the same rule: 1 : 1, 3 : 27, 6 : 216. What is 4 : ? (a) 90 (b) 4 (c) 65 (d) 64
  40. 40.2/3 + 1/7 = ? (a) 3/10 (b) 17/21 (c) 16/21 (d) 6/7

Answer key

  1. 4
  2. 69
  3. 1344
  4. Monday
  5. 36
  6. 2 cm
  7. 14
  8. ₹75
  9. 20 days
  10. 4
  11. 50
  12. ₹2500
  13. 4
  14. 105
  15. 1
  16. ₹9620
  17. 7/6
  18. 71
  19. 348
  20. Wednesday
  21. 3
  22. 0.086
  23. 12
  24. 13
  25. 2
  26. 5 days
  27. ₹78
  28. 8 cm
  29. 0.09
  30. 0.057
  31. 0.4
  32. 5
  33. 47
  34. 24 days
  35. 1
  36. 56
  37. 44
  38. 0.28
  39. 64
  40. 17/21

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