Maths Olympiad Sample Paper (Practice)

Maths Olympiad topic 20: Maths Olympiad mock test · Set 687 · 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 teacher has 48 pencils and 60 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 6 (b) 48 (c) 240 (d) 12
2. 2.₹5000 is invested at 7% per year simple interest. What is the amount after 3 years? (a) ₹5350 (b) ₹1050 (c) ₹6050 (d) ₹6400
3. 3.Two bells ring every 9 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 189 min (b) 63 min (c) 30 min (d) 3 min
4. 4.In how many years will ₹8000 earn ₹1280 simple interest at 8% per year? (a) 1 year (b) 3 years (c) 4 years (d) 2 years
5. 5.In how many years will ₹4000 earn ₹360 simple interest at 3% per year? (a) 3 years (b) 2 years (c) 4 years (d) 6 years
6. 6.What is 30% of 900? (a) 2700 (b) 270 (c) 630 (d) 540
7. 7.Every pair follows the same rule: 3 : 20, 5 : 22, 8 : 25. What is 2 : ? (a) 18 (b) 21 (c) 20 (d) 19
8. 8.What is the simple interest on ₹3000 at 2% per year for 2 years? (a) ₹3120 (b) ₹60 (c) ₹120 (d) ₹180
9. 9.If x/2 + 3 = 11, what is x? (a) 28 (b) 19 (c) 8 (d) 16
10. 10.What is the average of 73, 68, 78, 80, 90 and 73? (a) 79 (b) 77 (c) 78 (d) 76
11. 11.₹2500 is invested at 3% per year simple interest. What is the amount after 3 years? (a) ₹2575 (b) ₹2800 (c) ₹2725 (d) ₹225
12. 12.If 7x − 5 = 51, what is x? (a) 7 (b) 8 (c) 9 (d) 56
13. 13.A teacher has 12 pencils and 18 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 12 (b) 36 (c) 3 (d) 6
14. 14.A bag marked ₹200 is sold at a 10% discount. What is its selling price? (a) ₹20 (b) ₹190 (c) ₹180 (d) ₹220
15. 15.₹260 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹160 (b) ₹100 (c) ₹20 (d) ₹130
16. 16.Which of these numbers is divisible by 6? (a) 5386 (b) 5372 (c) 5378 (d) 5376
17. 17.A rectangle is 15 cm long and 4 cm wide. What is its perimeter? (a) 34 cm (b) 38 cm (c) 19 cm (d) 60 cm
18. 18.What is the smallest number you must add to 410 to make it divisible by 11? (a) 3 (b) 9 (c) 7 (d) 8
19. 19.If 7x + 16 = 6x + 24, what is x? (a) 9 (b) 8 (c) 10 (d) 40
20. 20.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹275 (c) ₹300 (d) ₹250
21. 21.The average of 7 numbers is 44. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 44 (b) 90 (c) 32 (d) 33
22. 22.The average of 5 numbers is 37. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 37 (b) 5 (c) 73 (d) 41
23. 23.What is the value of the digit 8 in 38.164? (a) 80 (b) 8 (c) 0.08 (d) 0.8
24. 24.If 5x − 5 = 15, what is x? (a) 5 (b) 2 (c) 20 (d) 4
25. 25.Every pair follows the same rule: 2 : 6, 3 : 9, 9 : 27. What is 4 : ? (a) 12 (b) 13 (c) 11 (d) 8
26. 26.1/4 + 2/4 = ? (a) 3/8 (b) 3/4 (c) 1 (d) 1/2
27. 27.A rectangle is 10 cm long and 2 cm wide. What is its area? (a) 12 sq cm (b) 20 sq cm (c) 30 sq cm (d) 24 sq cm
28. 28.What is the smallest number you must add to 309 to make it divisible by 4? (a) 1 (b) 2 (c) 3
29. 29.If 25 August is a Friday, what day of the week is 7 September? (a) Saturday (b) Friday (c) Wednesday (d) Thursday
30. 30.Every pair follows the same rule: 2 : 3, 4 : 15, 8 : 63. What is 5 : ? (a) 27 (b) 24 (c) 6 (d) 25
31. 31.What is the average of 17, 16, 16, 33, 15 and 65? (a) 26 (b) 29 (c) 28 (d) 27
32. 32.What is the units digit of 4^51? (a) 3 (b) 5 (c) 6 (d) 4
33. 33.What is 6/7 of 77? (a) 77 (b) 67 (c) 11 (d) 66
34. 34.A batter has an average of 57 runs in 8 matches. How many runs are needed in the next match to raise the average to 61? (a) 65 (b) 61 (c) 93 (d) 36
35. 35.Which fraction is greater: 9/11 or 5/9? (a) They are equal (b) 9/11 (c) 5/9
36. 36.₹280 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹80 (b) ₹40 (c) ₹200 (d) ₹140
37. 37.Every pair follows the same rule: 2 : 4, 3 : 9, 5 : 25. What is 4 : ? (a) 16 (b) 8 (c) 6 (d) 17
38. 38.What is the value of the digit 6 in 15.862? (a) 0.006 (b) 0.06 (c) 6 (d) 0.6
39. 39.Two bells ring every 8 minutes and every 14 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 22 min (b) 112 min (c) 56 min (d) 2 min
40. 40.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

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