Maths Olympiad Sample Paper (Practice)

Maths Olympiad topic 20: Maths Olympiad mock test · Set 260 · 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 110 sq cm and a length of 11 cm. What is its width? (a) 20 cm (b) 11 cm (c) 99 cm (d) 10 cm
2. 2.Two bells ring every 15 minutes and every 21 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 36 min (b) 315 min (c) 105 min (d) 3 min
3. 3.What is the smallest number you must add to 187 to make it divisible by 10? (a) 7 (b) 3 (c) 2 (d) 4
4. 4.The average of 8 numbers is 14. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 8 (b) 14 (c) 27 (d) 21
5. 5.A batter has an average of 31 runs in 5 matches. How many runs are needed in the next match to raise the average to 35? (a) 35 (b) 39 (c) 24 (d) 55
6. 6.If 2 notebooks cost ₹14, how much do 8 notebooks cost? (a) ₹63 (b) ₹20 (c) ₹112 (d) ₹56
7. 7.A batter has an average of 22 runs in 7 matches. How many runs are needed in the next match to raise the average to 27? (a) 62 (b) 40 (c) 32 (d) 27
8. 8.Which is the smallest: 0.53, 0.028, 0.493, 0.5? (a) 0.53 (b) 0.028 (c) 0.493 (d) 0.5
9. 9.Today is Monday. What day of the week will it be after 25 days? (a) Thursday (b) Saturday (c) Friday (d) Sunday
10. 10.1/2 + 8/9 = ? (a) 13/9 (b) 25/18 (c) 9/11 (d) 4/3
11. 11.If 1 May is a Tuesday, what day of the week is 14 May? (a) Sunday (b) Tuesday (c) Monday (d) Wednesday
12. 12.Which is the smallest: 0.23, 0.063, 0.166, 0.2? (a) 0.23 (b) 0.063 (c) 0.166 (d) 0.2
13. 13.₹490 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹441 (b) ₹490 (c) ₹245 (d) ₹49
14. 14.What is 40% of 520? (a) 312 (b) 2080 (c) 208 (d) 416
15. 15.Which fraction is greater: 1/3 or 3/4? (a) They are equal (b) 1/3 (c) 3/4
16. 16.A rectangle is 12 cm long and 9 cm wide. What is its area? (a) 21 sq cm (b) 108 sq cm (c) 120 sq cm (d) 42 sq cm
17. 17.Two bells ring every 20 minutes and every 24 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 120 min (b) 480 min (c) 4 min (d) 44 min
18. 18.₹2500 is invested at 4% per year simple interest. What is the amount after 5 years? (a) ₹2600 (b) ₹500 (c) ₹3000 (d) ₹3100
19. 19.If 10 January is a Saturday, what day of the week is 25 January? (a) Sunday (b) Tuesday (c) Saturday (d) Monday
20. 20.Which of these numbers is divisible by 3? (a) 810 (b) 814 (c) 811 (d) 808
21. 21.What is the average of 25, 44, 23 and 52? (a) 35 (b) 48 (c) 37 (d) 36
22. 22.Today is Friday. What day of the week will it be after 60 days? (a) Tuesday (b) Thursday (c) Wednesday (d) Monday
23. 23.Two bells ring every 12 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 54 min (b) 6 min (c) 504 min (d) 84 min
24. 24.What is the units digit of 2^16? (a) 2 (b) 6 (c) 4 (d) 8
25. 25.If 3 October is a Tuesday, what day of the week is 11 October? (a) Friday (b) Thursday (c) Wednesday (d) Tuesday
26. 26.Every pair follows the same rule: 2 : 14, 5 : 23, 9 : 35. What is 7 : ? (a) 49 (b) 29 (c) 30 (d) 19
27. 27.A teacher has 28 pencils and 36 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 8 (b) 4 (c) 2 (d) 28
28. 28.Two ribbons are 15 cm and 25 cm long. Both are cut into pieces of the same length with nothing left over. What is the longest each piece can be? (a) 1 cm (b) 10 cm (c) 15 cm (d) 5 cm
29. 29.Which of these numbers is divisible by 6? (a) 2138 (b) 2130 (c) 2125 (d) 2133
30. 30.If x/6 + 1 = 13, what is x? (a) 72 (b) 84 (c) 12 (d) 77
31. 31.What is the average of 20, 47, 27 and 46? (a) 36 (b) 37 (c) 35 (d) 34
32. 32.In how many years will ₹6500 earn ₹1950 simple interest at 10% per year? (a) 4 years (b) 6 years (c) 3 years (d) 2 years
33. 33.Every pair follows the same rule: 1 : 1, 2 : 8, 6 : 216. What is 3 : ? (a) 60 (b) 27 (c) 3 (d) 28
34. 34.If 3x + 13 = 2x + 16, what is x? (a) 5 (b) 3 (c) 29 (d) 4
35. 35.A batter has an average of 56 runs in 5 matches. How many runs are needed in the next match to raise the average to 62? (a) 62 (b) 36 (c) 68 (d) 92
36. 36.A rectangle is 17 cm long and 4 cm wide. What is its area? (a) 85 sq cm (b) 42 sq cm (c) 21 sq cm (d) 68 sq cm
37. 37.In how many years will ₹9000 earn ₹1890 simple interest at 7% per year? (a) 3 years (b) 4 years (c) 2 years (d) 6 years
38. 38.If 13 April is a Saturday, what day of the week is 6 May? (a) Sunday (b) Wednesday (c) Tuesday (d) Monday
39. 39.5/8 + 1/6 = ? (a) 3/7 (b) 19/24 (c) 3/4 (d) 5/6
40. 40.If 4x + 3 = 2x + 25, what is x? (a) 13 (b) 14 (c) 11 (d) 12

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