Maths Olympiad Sample Paper (Practice)

Maths Olympiad topic 20: Maths Olympiad mock test · Set 515 · 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 11, 14, 18 and 45? (a) 24 (b) 21 (c) 23 (d) 22
2. 2.Every pair follows the same rule: 3 : 27, 5 : 125, 6 : 216. What is 4 : ? (a) 64 (b) 34 (c) 36 (d) 28
3. 3.What is 20% of 400? (a) 80 (b) 800 (c) 160 (d) 320
4. 4.If 4x + 17 = 3x + 26, what is x? (a) 10 (b) 43 (c) 11 (d) 9
5. 5.₹205 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹205 (b) ₹165 (c) ₹41 (d) ₹164
6. 6.If 4x + 7 = 31, what is x? (a) 6 (b) 7 (c) 5 (d) 24
7. 7.A teacher has 35 pencils and 40 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 35 (b) 1 (c) 280 (d) 5
8. 8.The average of 8 numbers is 13. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 16 (b) 24 (c) 27 (d) 13
9. 9.Which fraction is greater: 2/9 or 2/3? (a) 2/3 (b) They are equal (c) 2/9
10. 10.A batter has an average of 27 runs in 3 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 20 (c) 37 (d) 47
11. 11.If 8 notebooks cost ₹56, how much do 5 notebooks cost? (a) ₹53 (b) ₹35 (c) ₹280 (d) ₹42
12. 12.A batter has an average of 26 runs in 4 matches. How many runs are needed in the next match to raise the average to 31? (a) 31 (b) 36 (c) 51 (d) 25
13. 13.A batter has an average of 60 runs in 3 matches. How many runs are needed in the next match to raise the average to 68? (a) 68 (b) 32 (c) 92 (d) 76
14. 14.What is the average of 43, 40, 27 and 38? (a) 38 (b) 36 (c) 37 (d) 39
15. 15.1/2 + 3/4 = ? (a) 3/2 (b) 2/3 (c) 5/4 (d) 1
16. 16.Every pair follows the same rule: 4 : 64, 5 : 125, 6 : 216. What is 2 : ? (a) 9 (b) 8 (c) 32 (d) 62
17. 17.A bag marked ₹900 is sold at a 15% discount. What is its selling price? (a) ₹765 (b) ₹1035 (c) ₹885 (d) ₹135
18. 18.A rectangle has an area of 60 sq cm and a length of 15 cm. What is its width? (a) 4 cm (b) 8 cm (c) 5 cm (d) 45 cm
19. 19.₹6000 is invested at 10% per year simple interest. What is the amount after 2 years? (a) ₹6600 (b) ₹7800 (c) ₹1200 (d) ₹7200
20. 20.A shopkeeper buys a toy for ₹680 and sells it for ₹952. What is his profit percent? (a) 40% (b) 45% (c) 35% (d) 41%
21. 21.If 1 January is a Wednesday, what day of the week is 14 January? (a) Monday (b) Wednesday (c) Thursday (d) Tuesday
22. 22.If 15 April is a Wednesday, what day of the week is 2 May? (a) Saturday (b) Sunday (c) Monday (d) Friday
23. 23.A bag marked ₹820 is sold at a 15% discount. What is its selling price? (a) ₹805 (b) ₹943 (c) ₹697 (d) ₹123
24. 24.A square has a perimeter of 24 cm. What is its area? (a) 12 sq cm (b) 49 sq cm (c) 36 sq cm (d) 24 sq cm
25. 25.A rectangle has an area of 102 sq cm and a length of 17 cm. What is its width? (a) 7 cm (b) 12 cm (c) 85 cm (d) 6 cm
26. 26.The simple interest on ₹6500 for 2 years is ₹1170. What is the rate per year? (a) 18% (b) 10% (c) 9% (d) 8%
27. 27.A bag marked ₹1720 is sold at a 50% discount. What is its selling price? (a) ₹2580 (b) ₹1670 (c) ₹860 (d) ₹861
28. 28.Every pair follows the same rule: 3 : 8, 6 : 35, 8 : 63. What is 7 : ? (a) 47 (b) 48 (c) 49 (d) 12
29. 29.A teacher has 30 pencils and 48 erasers. She makes identical gift packs using all of them. What is the greatest number of packs she can make? (a) 30 (b) 6 (c) 3 (d) 18
30. 30.Two bells ring every 15 minutes and every 25 minutes. They ring together at 9:00. After how many minutes will they next ring together? (a) 40 min (b) 375 min (c) 5 min (d) 75 min
31. 31.Which is the smallest: 0.7, 0.656, 0.011, 0.71? (a) 0.7 (b) 0.656 (c) 0.011 (d) 0.71
32. 32.In how many years will ₹3000 earn ₹600 simple interest at 5% per year? (a) 5 years (b) 8 years (c) 4 years (d) 3 years
33. 33.A square has a perimeter of 60 cm. What is its area? (a) 256 sq cm (b) 30 sq cm (c) 225 sq cm (d) 60 sq cm
34. 34.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 9 days (d) 4 days
35. 35.What is 1/6 of 12? (a) 4 (b) 3 (c) 2 (d) 10
36. 36.If 2x − 6 = 16, what is x? (a) 12 (b) 5 (c) 11 (d) 22
37. 37.Every pair follows the same rule: 4 : 23, 5 : 24, 7 : 26. What is 8 : ? (a) 26 (b) 28 (c) 29 (d) 27
38. 38.Every pair follows the same rule: 3 : 6, 4 : 8, 6 : 12. What is 2 : ? (a) 3 (b) 5 (c) 4 (d) 6
39. 39.A rectangle has an area of 128 sq cm and a length of 16 cm. What is its width? (a) 112 cm (b) 9 cm (c) 16 cm (d) 8 cm
40. 40.If 12 July is a Sunday, what day of the week is 11 August? (a) Tuesday (b) Monday (c) Wednesday (d) Thursday

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