Maths Olympiad Sample Paper (Practice)

Maths Olympiad topic 20: Maths Olympiad mock test · Set 523 · 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 smallest number you must add to 322 to make it divisible by 11? (a) 8 (b) 3 (c) 9 (d) 7
2. 2.What is the remainder when 218 is divided by 5? (a) 4 (b) 1 (c) 3 (d) 2
3. 3.Two ribbons are 15 cm and 21 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) 15 cm (c) 3 cm (d) 6 cm
4. 4.₹7000 is invested at 11% per year simple interest. What is the amount after 5 years? (a) ₹3850 (b) ₹10850 (c) ₹7770 (d) ₹11620
5. 5.Which of these numbers is divisible by 8? (a) 5305 (b) 5304 (c) 5317 (d) 5300
6. 6.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 6 days (c) 14 days (d) 5 days
7. 7.What is the remainder when 389 is divided by 5? (a) 4 (b) 1 (c) 2 (d) 3
8. 8.6.68 + 3.2 = ? (a) 9.78 (b) 7 (c) 9.98 (d) 9.88
9. 9.Every pair follows the same rule: 4 : 13, 7 : 25, 9 : 33. What is 5 : ? (a) 18 (b) 14 (c) 17 (d) 16
10. 10.A shopkeeper buys a toy for ₹860 and sells it for ₹516. What is his loss percent? (a) 45% (b) 35% (c) 41% (d) 40%
11. 11.If 8x + 18 = 82, what is x? (a) 7 (b) 9 (c) 8 (d) 64
12. 12.Every pair follows the same rule: 2 : 6, 4 : 10, 8 : 18. What is 7 : ? (a) 11 (b) 17 (c) 21 (d) 16
13. 13.Every pair follows the same rule: 2 : 4, 6 : 36, 9 : 81. What is 3 : ? (a) 9 (b) 5 (c) 10 (d) 6
14. 14.What is 5/6 of 18? (a) 3 (b) 18 (c) 15 (d) 16
15. 15.If 1 October is a Thursday, what day of the week is 17 October? (a) Monday (b) Sunday (c) Saturday (d) Friday
16. 16.What is the smallest number you must add to 59 to make it divisible by 3? (a) 2 (b) 1
17. 17.8 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 57 days (b) 8 days (c) 20 days (d) 56 days
18. 18.What is the smallest number you must add to 365 to make it divisible by 11? (a) 10 (b) 8 (c) 2 (d) 9
19. 19.What is the units digit of 3^41? (a) 3 (b) 1 (c) 9 (d) 7
20. 20.If 7x − 12 = 51, what is x? (a) 9 (b) 63 (c) 8 (d) 10
21. 21.What is the units digit of 7^37? (a) 9 (b) 7 (c) 3 (d) 1
22. 22.If 4 mangoes cost ₹28, how much do 10 mangoes cost? (a) ₹280 (b) ₹77 (c) ₹70 (d) ₹34
23. 23.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 25 (b) 36 (c) 67 (d) 56
24. 24.A rectangle is 20 cm long and 12 cm wide. What is its area? (a) 64 sq cm (b) 32 sq cm (c) 240 sq cm (d) 260 sq cm
25. 25.What is the smallest number of sweets that can be shared equally among 12 children or among 42 children, with none left over? (a) 504 (b) 168 (c) 84 (d) 54
26. 26.What is 1/2 of 6? (a) 3 (b) 6 (c) 2 (d) 4
27. 27.Two bells ring every 18 minutes and every 42 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 6 min (b) 60 min (c) 756 min (d) 126 min
28. 28.Two bells ring every 20 minutes and every 28 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 140 min (b) 4 min (c) 48 min (d) 560 min
29. 29.Two bells ring every 10 minutes and every 15 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 25 min (b) 150 min (c) 5 min (d) 30 min
30. 30.A shopkeeper buys a toy for ₹400 and sells it for ₹320. What is his loss percent? (a) 15% (b) 20% (c) 25% (d) 80%
31. 31.If 22 April is a Friday, what day of the week is 6 May? (a) Thursday (b) Friday (c) Saturday (d) Sunday
32. 32.1/3 + 4/7 = ? (a) 19/21 (b) 1/2 (c) 6/7 (d) 20/21
33. 33.What is the remainder when 230 is divided by 12? (a) 1 (b) 10 (c) 2 (d) 3
34. 34.What is the simple interest on ₹8000 at 2% per year for 2 years? (a) ₹160 (b) ₹480 (c) ₹8320 (d) ₹320
35. 35.What is the remainder when 512 is divided by 11? (a) 6 (b) 8 (c) 7 (d) 5
36. 36.Which of these numbers is divisible by 4? (a) 784 (b) 789 (c) 787 (d) 782
37. 37.If 5x + 2 = x + 38, what is x? (a) 10 (b) 6 (c) 11 (d) 9
38. 38.A square has a perimeter of 28 cm. What is its area? (a) 49 sq cm (b) 14 sq cm (c) 28 sq cm (d) 64 sq cm
39. 39.Every pair follows the same rule: 2 : 14, 4 : 16, 6 : 18. What is 8 : ? (a) 19 (b) 20 (c) 21 (d) 56
40. 40.Which is the smallest: 0.362, 0.038, 0.42, 0.4? (a) 0.362 (b) 0.038 (c) 0.42 (d) 0.4

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