Maths Olympiad Sample Paper (Practice)

Maths Olympiad topic 20: Maths Olympiad mock test · Set 19 · 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 71, 63, 77 and 49? (a) 66 (b) 67 (c) 65 (d) 64
2. 2.If 4x − 2 = 6, what is x? (a) 2 (b) 8 (c) 3 (d) 1
3. 3.A square has a perimeter of 24 cm. What is its area? (a) 49 sq cm (b) 12 sq cm (c) 24 sq cm (d) 36 sq cm
4. 4.A shopkeeper buys a toy for ₹740 and sells it for ₹962. What is his profit percent? (a) 25% (b) 35% (c) 30% (d) 31%
5. 5.A rectangle has an area of 34 sq cm and a length of 17 cm. What is its width? (a) 17 cm (b) 2 cm (c) 4 cm (d) 3 cm
6. 6.What is the remainder when 393 is divided by 5? (a) 4 (b) 3 (c) 2 (d) 1
7. 7.Today is Tuesday. What day of the week will it be after 97 days? (a) Wednesday (b) Sunday (c) Monday (d) Tuesday
8. 8.If 3x + 15 = 33, what is x? (a) 18 (b) 6 (c) 7 (d) 16
9. 9.Which fraction is greater: 2/3 or 1/4? (a) 1/4 (b) They are equal (c) 2/3
10. 10.Which fraction is greater: 3/4 or 1/6? (a) 1/6 (b) 3/4 (c) They are equal
11. 11.What is the simple interest on ₹7500 at 4% per year for 2 years? (a) ₹8100 (b) ₹600 (c) ₹300 (d) ₹900
12. 12.A teacher has 33 pencils and 44 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 1 (b) 11 (c) 33 (d) 132
13. 13.A shopkeeper buys a toy for ₹300 and sells it for ₹255. What is his loss percent? (a) 45% (b) 20% (c) 15% (d) 10%
14. 14.A bag marked ₹500 is sold at a 15% discount. What is its selling price? (a) ₹75 (b) ₹575 (c) ₹425 (d) ₹485
15. 15.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 7 days (d) 6 days
16. 16.What is the simple interest on ₹8500 at 2% per year for 2 years? (a) ₹510 (b) ₹8840 (c) ₹340 (d) ₹170
17. 17.Two ribbons are 20 cm and 70 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) 50 cm (c) 20 cm (d) 10 cm
18. 18.What is the remainder when 824 is divided by 11? (a) 1 (b) 8 (c) 10 (d) 9
19. 19.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 1 day (d) 2 days
20. 20.What is 1/4 of 12? (a) 4 (b) 6 (c) 3 (d) 9
21. 21.A rectangle is 7 cm long and 4 cm wide. What is its area? (a) 22 sq cm (b) 35 sq cm (c) 28 sq cm (d) 11 sq cm
22. 22.What is the units digit of 2^28? (a) 6 (b) 4 (c) 8 (d) 2
23. 23.A shopkeeper buys a toy for ₹1000 and sells it for ₹700. What is his loss percent? (a) 35% (b) 30% (c) 25% (d) 31%
24. 24.₹153 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹68 (b) ₹17 (c) ₹102 (d) ₹85
25. 25.A rectangle is 6 cm long and 5 cm wide. What is its perimeter? (a) 17 cm (b) 30 cm (c) 22 cm (d) 11 cm
26. 26.What is the average of 60, 83, 77 and 64? (a) 73 (b) 70 (c) 71 (d) 72
27. 27.Two ribbons are 50 cm and 70 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 20 cm (b) 5 cm (c) 50 cm (d) 10 cm
28. 28.Two ribbons are 10 cm and 12 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) 10 cm (c) 1 cm (d) 2 cm
29. 29.What is 4/7 of 70? (a) 30 (b) 50 (c) 40 (d) 10
30. 30.What is the smallest number you must add to 146 to make it divisible by 12? (a) 2 (b) 11 (c) 9 (d) 10
31. 31.Which fraction is greater: 3/7 or 5/8? (a) 3/7 (b) They are equal (c) 5/8
32. 32.8.38 + 8.5 = ? (a) 16.78 (b) 9.23 (c) 16.98 (d) 16.88
33. 33.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹42 (b) ₹210 (c) ₹252 (d) ₹231
34. 34.What is the smallest number you must add to 221 to make it divisible by 11? (a) 8 (b) 9 (c) 1 (d) 10
35. 35.If 3x + 23 = 50, what is x? (a) 27 (b) 8 (c) 10 (d) 9
36. 36.A square has a perimeter of 60 cm. What is its area? (a) 256 sq cm (b) 225 sq cm (c) 60 sq cm (d) 30 sq cm
37. 37.What is the simple interest on ₹3000 at 4% per year for 3 years? (a) ₹120 (b) ₹3360 (c) ₹480 (d) ₹360
38. 38.If x/4 + 4 = 7, what is x? (a) 3 (b) 24 (c) 44 (d) 12
39. 39.What is the remainder when 109 is divided by 3? (a) 1 (b) 0 (c) 2
40. 40.What is the units digit of 3^27? (a) 1 (b) 9 (c) 7 (d) 3

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