Maths Olympiad Sample Paper (Practice)

Maths Olympiad topic 20: Maths Olympiad mock test · Set 935 · 40 questions

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.

1. 1.₹69 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹46 (b) ₹47 (c) ₹23 (d) ₹69
2. 2.A shopkeeper buys a toy for ₹760 and sells it for ₹456. What is his loss percent? (a) 40% (b) 41% (c) 45% (d) 35%
3. 3.₹91 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹56 (d) ₹63
4. 4.Every pair follows the same rule: 3 : 9, 4 : 14, 6 : 24. What is 2 : ? (a) 5 (b) 8 (c) 6 (d) 4
5. 5.If 3 kites cost ₹72, how much do 7 kites cost? (a) ₹504 (b) ₹192 (c) ₹76 (d) ₹168
6. 6.Which of these numbers is divisible by 8? (a) 5666 (b) 5653 (c) 5656 (d) 5658
7. 7.Every pair follows the same rule: 3 : 9, 5 : 25, 8 : 64. What is 7 : ? (a) 49 (b) 51 (c) 21 (d) 13
8. 8.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 14 days (c) 9 days (d) 15 days
9. 9.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) 54 cm (b) 3 cm (c) 18 cm (d) 9 cm
10. 10.If 14 January is a Wednesday, what day of the week is 30 January? (a) Saturday (b) Friday (c) Thursday (d) Sunday
11. 11.What is the smallest number of sweets that can be shared equally among 12 children or among 14 children, with none left over? (a) 85 (b) 84 (c) 168 (d) 26
12. 12.If 11 October is a Sunday, what day of the week is 24 October? (a) Sunday (b) Monday (c) Friday (d) Saturday
13. 13.4/6 + 1/6 = ? (a) 5/6 (b) 1 (c) 2/3 (d) 5/12
14. 14.₹4000 is invested at 12% per year simple interest. What is the amount after 3 years? (a) ₹1440 (b) ₹5920 (c) ₹4480 (d) ₹5440
15. 15.1.21 + 5.4 = ? (a) 6.71 (b) 6.51 (c) 1.75 (d) 6.61
16. 16.Which is the smallest: 0.056, 0.6, 0.61, 0.535? (a) 0.056 (b) 0.6 (c) 0.61 (d) 0.535
17. 17.If 6x − 4 = 8, what is x? (a) 12 (b) 2 (c) 1 (d) 3
18. 18.What is the simple interest on ₹4500 at 7% per year for 5 years? (a) ₹1575 (b) ₹315 (c) ₹6075 (d) ₹1890
19. 19.Every pair follows the same rule: 2 : 3, 7 : 48, 8 : 63. What is 3 : ? (a) 8 (b) 4 (c) 7 (d) 9
20. 20.Which fraction is greater: 1/5 or 5/8? (a) 1/5 (b) 5/8 (c) They are equal
21. 21.What is 2/7 of 77? (a) 11 (b) 33 (c) 55 (d) 22
22. 22.What is 25% of 420? (a) 210 (b) 105 (c) 1050 (d) 315
23. 23.What is the average of 37, 60, 64, 61 and 38? (a) 65 (b) 52 (c) 51 (d) 53
24. 24.What is the remainder when 99 is divided by 4? (a) 0 (b) 1 (c) 3 (d) 2
25. 25.If x/4 + 15 = 21, what is x? (a) 144 (b) 69 (c) 6 (d) 24
26. 26.What is the smallest number of sweets that can be shared equally among 12 children or among 15 children, with none left over? (a) 60 (b) 180 (c) 27 (d) 120
27. 27.If 8x + 7 = 127, what is x? (a) 16 (b) 14 (c) 15 (d) 120
28. 28.A shopkeeper buys a toy for ₹280 and sells it for ₹364. What is his profit percent? (a) 35% (b) 84% (c) 30% (d) 25%
29. 29.A shopkeeper buys a toy for ₹340 and sells it for ₹238. What is his loss percent? (a) 35% (b) 30% (c) 25% (d) 31%
30. 30.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
31. 31.2.41 + 7.1 = ? (a) 9.41 (b) 3.12 (c) 9.51 (d) 9.61
32. 32.If x/3 + 13 = 18, what is x? (a) 41 (b) 93 (c) 15 (d) 5
33. 33.The average of 4 numbers is 16. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 16 (b) 31 (c) 4 (d) 19
34. 34.Every pair follows the same rule: 6 : 27, 8 : 35, 9 : 39. What is 7 : ? (a) 30 (b) 31 (c) 28 (d) 32
35. 35.What is the units digit of 7^19? (a) 7 (b) 9 (c) 1 (d) 3
36. 36.A rectangle is 20 cm long and 8 cm wide. What is its area? (a) 28 sq cm (b) 160 sq cm (c) 56 sq cm (d) 180 sq cm
37. 37.If 5 kites cost ₹45, how much do 10 kites cost? (a) ₹90 (b) ₹50 (c) ₹99 (d) ₹450
38. 38.Two ribbons are 14 cm and 63 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 49 cm (b) 1 cm (c) 14 cm (d) 7 cm
39. 39.Two ribbons are 55 cm and 77 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 1 cm (b) 55 cm (c) 22 cm (d) 11 cm
40. 40.What is the units digit of 3^26? (a) 7 (b) 3 (c) 9 (d) 1

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