Maths Olympiad Sample Paper (Practice)

Maths Olympiad topic 20: Maths Olympiad mock test · Set 672 · 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 rectangle has an area of 108 sq cm and a length of 12 cm. What is its width? (a) 9 cm (b) 96 cm (c) 10 cm (d) 18 cm
2. 2.What is the units digit of 7^56? (a) 9 (b) 3 (c) 7 (d) 1
3. 3.Every pair follows the same rule: 5 : 25, 6 : 36, 9 : 81. What is 2 : ? (a) 5 (b) 10 (c) 4 (d) 22
4. 4.What is the smallest number of sweets that can be shared equally among 20 children or among 35 children, with none left over? (a) 140 (b) 55 (c) 700 (d) 280
5. 5.Two ribbons are 30 cm and 35 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 5 cm (b) 30 cm (c) 210 cm (d) 1 cm
6. 6.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 11 days (d) 1 day
7. 7.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 11 days (d) 1 day
8. 8.A rectangle has an area of 192 sq cm and a length of 16 cm. What is its width? (a) 13 cm (b) 12 cm (c) 24 cm (d) 176 cm
9. 9.A shopkeeper buys a toy for ₹320 and sells it for ₹192. What is his loss percent? (a) 41% (b) 45% (c) 40% (d) 35%
10. 10.6.61 + 9.1 = ? (a) 15.81 (b) 7.52 (c) 15.61 (d) 15.71
11. 11.Which fraction is greater: 3/5 or 3/8? (a) 3/8 (b) They are equal (c) 3/5
12. 12.What is the units digit of 2^35? (a) 4 (b) 6 (c) 2 (d) 8
13. 13.Two ribbons are 48 cm and 84 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 12 cm (b) 6 cm (c) 36 cm (d) 48 cm
14. 14.What is the average of all the whole numbers from 60 to 66? (a) 63 (b) 3 (c) 64 (d) 6
15. 15.Today is Tuesday. What day of the week will it be after 70 days? (a) Monday (b) Wednesday (c) Thursday (d) Tuesday
16. 16.If 4x − 57 = 3, what is x? (a) 16 (b) 15 (c) 14 (d) 60
17. 17.If 12 January is a Saturday, what day of the week is 23 January? (a) Wednesday (b) Thursday (c) Friday (d) Tuesday
18. 18.Which fraction is greater: 1/3 or 1/8? (a) They are equal (b) 1/8 (c) 1/3
19. 19.A teacher has 20 pencils and 50 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 20 (b) 30 (c) 5 (d) 10
20. 20.2.71 + 6.1 = ? (a) 3.32 (b) 8.71 (c) 8.81 (d) 8.91
21. 21.What is 3/4 of 32? (a) 24 (b) 32 (c) 8 (d) 25
22. 22.What is 1/8 of 40? (a) 10 (b) 35 (c) 6 (d) 5
23. 23.A rectangle is 7 cm long and 3 cm wide. What is its area? (a) 10 sq cm (b) 28 sq cm (c) 21 sq cm (d) 20 sq cm
24. 24.Which of these numbers is divisible by 6? (a) 4237 (b) 4227 (c) 4231 (d) 4230
25. 25.What is 4/5 of 10? (a) 10 (b) 2 (c) 9 (d) 8
26. 26.A rectangle has an area of 32 sq cm and a length of 16 cm. What is its width? (a) 16 cm (b) 4 cm (c) 2 cm (d) 3 cm
27. 27.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 84 (b) 36 (c) 35 (d) 41
28. 28.If 20 March is a Friday, what day of the week is 3 April? (a) Saturday (b) Sunday (c) Thursday (d) Friday
29. 29.What is 2/9 of 99? (a) 77 (b) 33 (c) 22 (d) 11
30. 30.If 6x + 26 = 68, what is x? (a) 7 (b) 42 (c) 8 (d) 6
31. 31.Every pair follows the same rule: 3 : 20, 5 : 30, 6 : 35. What is 4 : ? (a) 26 (b) 25 (c) 21 (d) 24
32. 32.The simple interest on ₹1000 for 4 years is ₹280. What is the rate per year? (a) 28% (b) 7% (c) 8% (d) 6%
33. 33.What is the smallest number of sweets that can be shared equally among 10 children or among 12 children, with none left over? (a) 22 (b) 60 (c) 120 (d) 61
34. 34.A teacher has 48 pencils and 108 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 60 (b) 12 (c) 6 (d) 48
35. 35.Every pair follows the same rule: 3 : 21, 4 : 28, 6 : 42. What is 9 : ? (a) 62 (b) 64 (c) 27 (d) 63
36. 36.2/3 + 3/8 = ? (a) 13/12 (b) 25/24 (c) 5/11 (d) 1
37. 37.If 3x + 29 = 35, what is x? (a) 2 (b) 6 (c) 3 (d) 1
38. 38.What is the smallest number you must add to 138 to make it divisible by 8? (a) 6 (b) 7 (c) 5 (d) 2
39. 39.A bag marked ₹760 is sold at a 25% discount. What is its selling price? (a) ₹570 (b) ₹190 (c) ₹950 (d) ₹735
40. 40.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹15 (b) ₹12 (c) ₹6 (d) ₹18

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