Maths Olympiad Sample Paper (Practice)

Maths Olympiad topic 20: Maths Olympiad mock test · Set 902 · 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.What is the average of all the whole numbers from 5 to 13? (a) 9 (b) 8 (c) 4 (d) 10
2. 2.What is the units digit of 3^28? (a) 1 (b) 9 (c) 3 (d) 7
3. 3.The simple interest on ₹9500 for 4 years is ₹1900. What is the rate per year? (a) 20% (b) 5% (c) 4% (d) 6%
4. 4.If 11 January is a Friday, what day of the week is 14 February? (a) Friday (b) Thursday (c) Wednesday (d) Saturday
5. 5.What is the smallest number you must add to 235 to make it divisible by 3? (a) 1 (b) 2
6. 6.Every pair follows the same rule: 2 : 15, 3 : 20, 9 : 50. What is 6 : ? (a) 35 (b) 36 (c) 19 (d) 34
7. 7.If x/4 + 12 = 14, what is x? (a) 44 (b) 8 (c) 2 (d) 104
8. 8.If x/3 + 11 = 19, what is x? (a) 46 (b) 90 (c) 24 (d) 8
9. 9.What is the average of 32, 30, 46 and 40? (a) 39 (b) 38 (c) 37 (d) 36
10. 10.What is 2/7 of 42? (a) 18 (b) 6 (c) 30 (d) 12
11. 11.Two ribbons are 24 cm and 54 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 6 cm (b) 30 cm (c) 24 cm (d) 3 cm
12. 12.What is the value of the digit 1 in 24.731? (a) 0.001 (b) 0.01 (c) 1 (d) 0.1
13. 13.Every pair follows the same rule: 4 : 15, 5 : 24, 8 : 63. What is 3 : ? (a) 9 (b) 8 (c) 14 (d) 7
14. 14.What is 75% of 620? (a) 930 (b) 4650 (c) 465 (d) 155
15. 15.If 9x − 64 = 53, what is x? (a) 12 (b) 14 (c) 13 (d) 117
16. 16.If 8x − 15 = 33, what is x? (a) 48 (b) 7 (c) 6 (d) 5
17. 17.If 14 August is a Sunday, what day of the week is 3 September? (a) Friday (b) Sunday (c) Saturday (d) Monday
18. 18.₹9000 is invested at 7% per year simple interest. What is the amount after 4 years? (a) ₹2520 (b) ₹12150 (c) ₹9630 (d) ₹11520
19. 19.What is the remainder when 121 is divided by 12? (a) 11 (b) 2 (c) 1 (d) 0
20. 20.If 5 October is a Tuesday, what day of the week is 19 October? (a) Monday (b) Wednesday (c) Tuesday (d) Thursday
21. 21.If 29 June is a Sunday, what day of the week is 12 July? (a) Friday (b) Sunday (c) Monday (d) Saturday
22. 22.If 3x + 2 = 2x + 13, what is x? (a) 15 (b) 11 (c) 12 (d) 13
23. 23.What is the smallest number of sweets that can be shared equally among 15 children or among 25 children, with none left over? (a) 40 (b) 150 (c) 75 (d) 375
24. 24.Every pair follows the same rule: 2 : 12, 3 : 13, 7 : 17. What is 9 : ? (a) 20 (b) 19 (c) 54 (d) 18
25. 25.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹20 (b) ₹30 (c) ₹10 (d) ₹15
26. 26.Two bells ring every 10 minutes and every 35 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 45 min (b) 70 min (c) 350 min (d) 5 min
27. 27.A batter has an average of 34 runs in 5 matches. How many runs are needed in the next match to raise the average to 36? (a) 36 (b) 46 (c) 38 (d) 12
28. 28.What is the smallest number of sweets that can be shared equally among 6 children or among 9 children, with none left over? (a) 54 (b) 18 (c) 36 (d) 15
29. 29.A batter has an average of 26 runs in 3 matches. How many runs are needed in the next match to raise the average to 32? (a) 24 (b) 38 (c) 50 (d) 32
30. 30.Every pair follows the same rule: 4 : 15, 6 : 23, 8 : 31. What is 7 : ? (a) 18 (b) 26 (c) 28 (d) 27
31. 31.9.66 + 8.8 = ? (a) 18.56 (b) 18.36 (c) 18.46 (d) 10.54
32. 32.₹539 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹49 (b) ₹147 (c) ₹392 (d) ₹441
33. 33.What is the smallest number of sweets that can be shared equally among 16 children or among 20 children, with none left over? (a) 160 (b) 80 (c) 36 (d) 320
34. 34.What is the units digit of 4^13? (a) 6 (b) 4 (c) 5 (d) 3
35. 35.If 8 kites cost ₹176, how much do 2 kites cost? (a) ₹170 (b) ₹44 (c) ₹66 (d) ₹352
36. 36.The simple interest on ₹3500 for 4 years is ₹1680. What is the rate per year? (a) 13% (b) 48% (c) 11% (d) 12%
37. 37.If 13 May is a Sunday, what day of the week is 21 May? (a) Monday (b) Tuesday (c) Sunday (d) Wednesday
38. 38.In how many years will ₹8000 earn ₹2560 simple interest at 8% per year? (a) 8 years (b) 4 years (c) 3 years (d) 5 years
39. 39.What is 7/9 of 18? (a) 16 (b) 2 (c) 4 (d) 14
40. 40.What is the average of all the whole numbers from 36 to 48? (a) 6 (b) 43 (c) 12 (d) 42

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