Maths Olympiad Sample Paper (Practice)

Maths Olympiad topic 20: Maths Olympiad mock test · Set 312 · 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.A shopkeeper buys a toy for ₹520 and sells it for ₹572. What is his profit percent? (a) 10% (b) 52% (c) 5% (d) 15%
2. 2.A rectangle is 13 cm long and 2 cm wide. What is its area? (a) 39 sq cm (b) 30 sq cm (c) 15 sq cm (d) 26 sq cm
3. 3.A square has a perimeter of 60 cm. What is its area? (a) 30 sq cm (b) 60 sq cm (c) 225 sq cm (d) 256 sq cm
4. 4.8/9 + 1/2 = ? (a) 4/3 (b) 25/18 (c) 13/9 (d) 9/11
5. 5.What is the smallest number you must add to 217 to make it divisible by 3? (a) 2 (b) 1
6. 6.A rectangle has an area of 114 sq cm and a length of 19 cm. What is its width? (a) 6 cm (b) 12 cm (c) 95 cm (d) 7 cm
7. 7.Which is the greatest: 0.77, 0.661, 0.025, 0.7? (a) 0.77 (b) 0.661 (c) 0.025 (d) 0.7
8. 8.What is the average of 51, 31, 36 and 66? (a) 47 (b) 45 (c) 48 (d) 46
9. 9.Every pair follows the same rule: 2 : 8, 3 : 27, 4 : 64. What is 1 : ? (a) 7 (b) 1 (c) 4 (d) 2
10. 10.A rectangle has an area of 51 sq cm and a length of 17 cm. What is its width? (a) 6 cm (b) 3 cm (c) 34 cm (d) 4 cm
11. 11.A teacher has 24 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 84 (b) 6 (c) 24 (d) 12
12. 12.In how many years will ₹6000 earn ₹2160 simple interest at 12% per year? (a) 4 years (b) 6 years (c) 2 years (d) 3 years
13. 13.A rectangle is 18 cm long and 7 cm wide. What is its area? (a) 50 sq cm (b) 25 sq cm (c) 126 sq cm (d) 144 sq cm
14. 14.Two ribbons are 15 cm and 20 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 60 cm (b) 15 cm (c) 5 cm (d) 1 cm
15. 15.Two ribbons are 33 cm and 44 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 33 cm (b) 11 cm (c) 1 cm (d) 132 cm
16. 16.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹39 (b) ₹78 (c) ₹26 (d) ₹52
17. 17.What is the units digit of 3^11? (a) 3 (b) 7 (c) 1 (d) 9
18. 18.If 5x − 4 = 21, what is x? (a) 4 (b) 6 (c) 5 (d) 25
19. 19.A batter has an average of 27 runs in 7 matches. How many runs are needed in the next match to raise the average to 29? (a) 43 (b) 29 (c) 31 (d) 16
20. 20.Two bells ring every 12 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 27 min (b) 3 min (c) 180 min (d) 60 min
21. 21.In how many years will ₹10000 earn ₹2400 simple interest at 12% per year? (a) 1 year (b) 3 years (c) 4 years (d) 2 years
22. 22.₹176 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹132 (b) ₹176 (c) ₹88 (d) ₹44
23. 23.A bag marked ₹1220 is sold at a 10% discount. What is its selling price? (a) ₹1342 (b) ₹1210 (c) ₹1098 (d) ₹122
24. 24.A batter has an average of 28 runs in 9 matches. How many runs are needed in the next match to raise the average to 36? (a) 108 (b) 44 (c) 36 (d) 80
25. 25.A rectangle is 7 cm long and 3 cm wide. What is its area? (a) 28 sq cm (b) 21 sq cm (c) 10 sq cm (d) 20 sq cm
26. 26.If 3x + 1 = 37, what is x? (a) 36 (b) 13 (c) 11 (d) 12
27. 27.Two ribbons are 27 cm and 36 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 9 cm (b) 27 cm (c) 3 cm (d) 108 cm
28. 28.Today is Monday. What day of the week will it be after 56 days? (a) Tuesday (b) Sunday (c) Monday (d) Wednesday
29. 29.If 7x + 18 = x + 36, what is x? (a) 4 (b) 3 (c) 5 (d) 9
30. 30.What is the smallest number of sweets that can be shared equally among 4 children or among 6 children, with none left over? (a) 10 (b) 24 (c) 12 (d) 13
31. 31.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) 4 (b) 31 (c) 16 (d) 19
32. 32.Two bells ring every 6 minutes and every 10 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 16 min (b) 60 min (c) 30 min (d) 2 min
33. 33.If x/4 + 8 = 14, what is x? (a) 24 (b) 48 (c) 6 (d) 88
34. 34.If 9 May is a Friday, what day of the week is 21 May? (a) Friday (b) Thursday (c) Tuesday (d) Wednesday
35. 35.9.14 + 5.9 = ? (a) 9.73 (b) 15.14 (c) 14.94 (d) 15.04
36. 36.Which is the smallest: 0.88, 0.014, 0.8, 0.789? (a) 0.88 (b) 0.014 (c) 0.8 (d) 0.789
37. 37.If 7x − 38 = 4, what is x? (a) 6 (b) 42 (c) 5 (d) 7
38. 38.₹2500 is invested at 7% per year simple interest. What is the amount after 3 years? (a) ₹3025 (b) ₹2675 (c) ₹3200 (d) ₹525
39. 39.What is 1/2 of 18? (a) 10 (b) 18 (c) 9 (d) 8
40. 40.What is the value of the digit 3 in 89.317? (a) 0.3 (b) 0.003 (c) 0.03 (d) 3

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