Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 865 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.In a class of 32 children, 15 like tea, 27 like coffee and 11 like both. How many like at least one of the two? (a) 20 (b) 31 (c) 32 (d) 42
2. 2.In a class of 46 children, 23 like dance, 16 like music and 3 like both. How many like neither? (a) 10 (b) 13 (c) 7 (d) 3
3. 3.In a class of 36 children, 20 like maths, 18 like science and 1 like neither. How many like both? (a) 35 (b) 2 (c) 3 (d) 1
4. 4.In a class of 34 children, 14 like maths, 20 like science and 2 like both. How many like at least one of the two? (a) 33 (b) 34 (c) 32 (d) 30
5. 5.In a class of 32 children, 21 like maths, 13 like science and 9 like both. How many like only maths? (a) 19 (b) 21 (c) 12 (d) 4
6. 6.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
7. 7.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 20 (b) 10 (c) 25 (d) 21
8. 8.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 39 (c) 12 (d) 36
9. 9.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 20 (c) 25 (d) 10
10. 10.What is the 30th term of the AP 14, 20, 26, 32, …? (a) 188 (b) 194 (c) 180 (d) 174
11. 11.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 21 (c) 14 (d) 42
12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 5 (b) 4 (c) 2 (d) 3
13. 13.The mean of 5 numbers is 39. When the number 63 is added to them, what is the new mean? (a) 44 (b) 43 (c) 51 (d) 39
14. 14.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
15. 15.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
16. 16.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 5 (b) 9 (c) 12 (d) 6
17. 17.The mean of 4 numbers is 10. When the number 15 is added to them, what is the new mean? (a) 11 (b) 12 (c) 10 (d) 13
18. 18.In a class of 33 children, 23 like cricket, 10 like football and 4 like both. How many like only cricket? (a) 19 (b) 4 (c) 23 (d) 6
19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 19 (d) 21
20. 20.What is the median of 3, 28, 24, 22, 40, 4 and 35? (a) 22 (b) 28 (c) 24 (d) 25
21. 21.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 3/4 (c) 1/3 (d) 1/4
22. 22.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 110° (b) 250° (c) 71° (d) 70°
23. 23.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
24. 24.How many factors does 17 have? (a) 3 (b) 1 (c) 2 (d) 4
25. 25.3 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 21 (c) 42 (d) 24
26. 26.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 55 (d) 66
27. 27.A cuboid is 4 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 48 sq cm (b) 176 sq cm (c) 44 sq cm (d) 88 sq cm
28. 28.What is the distance between the points (9, 8) and (15, 16)? (a) 100 (b) 14 (c) 11 (d) 10
29. 29.What is the mode of 11, 17, 6, 7, 11, 17 and 11? (a) 7 (b) 17 (c) 11 (d) 6
30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 18 (b) 19 (c) 7 (d) 17
31. 31.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
32. 32.There are 3 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 36 (c) 18 (d) 21
33. 33.A bag has 5 yellow balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 5 (c) 6 (d) 2
34. 34.How many prime numbers are there between 40 and 60? (a) 6 (b) 5 (c) 4 (d) 7
35. 35.What is the smallest prime factor of 91? (a) 1 (b) 2 (c) 13 (d) 7
36. 36.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 42 (c) 49 (d) 28
37. 37.In a class of 29 children, 20 like mangoes, 10 like bananas and 7 like both. How many like at least one of the two? (a) 30 (b) 29 (c) 16 (d) 23
38. 38.A drawer has lots of green, red, blue and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 2 (c) 4 (d) 5
39. 39.What is the 32nd term of the AP 7, 9, 11, 13, …? (a) 69 (b) 62 (c) 71 (d) 64
40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 3 (b) 4 (c) 5 (d) 6

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