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Maths Olympiad Sample Paper (Practice)

Maths Olympiad topic 20: Maths Olympiad mock test · Set 699 · 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.A teacher has 63 pencils and 81 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 63 (b) 3 (c) 18 (d) 9
  2. 2.The average of 7 numbers is 45. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 45 (b) 88 (c) 57 (d) 14
  3. 3.Every pair follows the same rule: 2 : 5, 6 : 25, 8 : 35. What is 7 : ? (a) 30 (b) 10 (c) 29 (d) 31
  4. 4.2/3 + 1/7 = ? (a) 17/21 (b) 6/7 (c) 3/10 (d) 16/21
  5. 5.The average of 5 numbers is 45. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 25 (b) 85 (c) 65 (d) 45
  6. 6.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹34 (b) ₹68 (c) ₹85 (d) ₹102
  7. 7.What is the units digit of 8^14? (a) 6 (b) 8 (c) 2 (d) 4
  8. 8.1/2 + 4/7 = ? (a) 8/7 (b) 5/9 (c) 1 (d) 15/14
  9. 9.A rectangle has an area of 44 sq cm and a length of 11 cm. What is its width? (a) 8 cm (b) 5 cm (c) 4 cm (d) 33 cm
  10. 10.What is the average of 48, 25, 35, 25, 32 and 33? (a) 35 (b) 32 (c) 33 (d) 34
  11. 11.Every pair follows the same rule: 2 : 13, 4 : 25, 5 : 34. What is 9 : ? (a) 20 (b) 91 (c) 90 (d) 70
  12. 12.A shopkeeper buys a toy for ₹460 and sells it for ₹529. What is his profit percent? (a) 20% (b) 10% (c) 69% (d) 15%
  13. 13.Every pair follows the same rule: 2 : 4, 7 : 49, 9 : 81. What is 6 : ? (a) 33 (b) 36 (c) 12 (d) 8
  14. 14.If 3x − 12 = 33, what is x? (a) 45 (b) 15 (c) 16 (d) 7
  15. 15.₹546 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹39 (b) ₹351 (c) ₹273 (d) ₹195
  16. 16.9.83 + 1.8 = ? (a) 10.01 (b) 11.53 (c) 11.73 (d) 11.63
  17. 17.If 3x + 15 = x + 35, what is x? (a) 5 (b) 11 (c) 25 (d) 10
  18. 18.Two ribbons are 18 cm and 27 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 18 cm (b) 54 cm (c) 3 cm (d) 9 cm
  19. 19.Every pair follows the same rule: 2 : 20, 4 : 22, 8 : 26. What is 3 : ? (a) 22 (b) 20 (c) 30 (d) 21
  20. 20.Which is the greatest: 0.8, 0.774, 0.016, 0.81? (a) 0.8 (b) 0.774 (c) 0.016 (d) 0.81
  21. 21.Every pair follows the same rule: 3 : 27, 5 : 125, 6 : 216. What is 1 : ? (a) 25 (b) 1 (c) 2 (d) 9
  22. 22.2/6 + 1/2 = ? (a) 5/6 (b) 3/8 (c) 2/3 (d) 1
  23. 23.3/7 + 1/5 = ? (a) 22/35 (b) 1/3 (c) 3/5 (d) 23/35
  24. 24.What is 3/7 of 14? (a) 6 (b) 2 (c) 8 (d) 7
  25. 25.Which is the smallest: 0.5, 0.076, 0.51, 0.417? (a) 0.5 (b) 0.076 (c) 0.51 (d) 0.417
  26. 26.A shopkeeper buys a toy for ₹360 and sells it for ₹342. What is his loss percent? (a) 6% (b) 5% (c) 10% (d) 18%
  27. 27.What is the average of 62, 59, 47 and 40? (a) 51 (b) 53 (c) 54 (d) 52
  28. 28.A teacher has 16 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 16 (c) 4 (d) 2
  29. 29.If 3x − 6 = 6, what is x? (a) 4 (b) 3 (c) 12 (d) 5
  30. 30.Which fraction is greater: 5/6 or 1/5? (a) They are equal (b) 5/6 (c) 1/5
  31. 31.Which fraction is greater: 7/8 or 2/11? (a) 7/8 (b) They are equal (c) 2/11
  32. 32.If 7x − 25 = 52, what is x? (a) 11 (b) 12 (c) 10 (d) 77
  33. 33.If 4 mangoes cost ₹36, how much do 8 mangoes cost? (a) ₹40 (b) ₹72 (c) ₹288 (d) ₹81
  34. 34.What is 1/7 of 28? (a) 24 (b) 5 (c) 8 (d) 4
  35. 35.What is the smallest number you must add to 410 to make it divisible by 6? (a) 2 (b) 4 (c) 3 (d) 5
  36. 36.If 9 July is a Monday, what day of the week is 18 July? (a) Thursday (b) Friday (c) Tuesday (d) Wednesday
  37. 37.2/3 + 5/8 = ? (a) 4/3 (b) 5/4 (c) 7/11 (d) 31/24
  38. 38.In how many years will ₹2500 earn ₹150 simple interest at 3% per year? (a) 3 years (b) 4 years (c) 2 years (d) 1 year
  39. 39.A batter has an average of 57 runs in 6 matches. How many runs are needed in the next match to raise the average to 60? (a) 21 (b) 78 (c) 63 (d) 60
  40. 40.A square has a perimeter of 32 cm. What is its area? (a) 81 sq cm (b) 16 sq cm (c) 64 sq cm (d) 32 sq cm

Answer key

  1. 9
  2. 57
  3. 30
  4. 17/21
  5. 65
  6. ₹102
  7. 4
  8. 15/14
  9. 4 cm
  10. 33
  11. 90
  12. 15%
  13. 36
  14. 15
  15. ₹351
  16. 11.63
  17. 10
  18. 9 cm
  19. 21
  20. 0.81
  21. 1
  22. 5/6
  23. 22/35
  24. 6
  25. 0.076
  26. 5%
  27. 52
  28. 4
  29. 4
  30. 5/6
  31. 7/8
  32. 11
  33. ₹72
  34. 4
  35. 4
  36. Wednesday
  37. 31/24
  38. 2 years
  39. 78
  40. 64 sq cm

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