Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 385 · 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 51 children, 27 like mangoes, 27 like bananas and 9 like both. How many like at least one of the two? (a) 45 (b) 36 (c) 54 (d) 51
2. 2.How many factors does 24 have? (a) 6 (b) 7 (c) 9 (d) 8
3. 3.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
4. 4.In a class of 36 children, 15 like cricket, 27 like football and 11 like both. How many like at least one of the two? (a) 42 (b) 31 (c) 36 (d) 20
5. 5.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 16 (c) 48 (d) 144
6. 6.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 240 (c) 20 (d) 25
7. 7.A drawer has lots of yellow, black, green, red and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 5 (c) 2 (d) 10
8. 8.What is the sum of all the whole numbers from 1 to 17? (a) 306 (b) 154 (c) 136 (d) 153
9. 9.A bag has 8 green balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 15 (c) 9 (d) 10
10. 10.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
11. 11.In a class of 37 children, 21 like cricket, 26 like football and 11 like both. How many like only cricket? (a) 10 (b) 21 (c) 15 (d) 11
12. 12.What is the 34th term of the AP 2, 5, 8, 11, …? (a) 102 (b) 99 (c) 104 (d) 101
13. 13.What is the mode of 17, 4, 9, 4, 9, 3 and 4? (a) 3 (b) 9 (c) 17 (d) 4
14. 14.A drawer has lots of yellow, white, red, green and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 5 (c) 2 (d) 6
15. 15.A bag has 5 red balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 6 (b) 7 (c) 14 (d) 2
16. 16.What is the mean of 2, 2, 6, 20 and 15? (a) 10 (b) 9 (c) 8 (d) 11
17. 17.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
18. 18.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 70° (b) 140° (c) 110° (d) 250°
19. 19.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 28 (c) 49 (d) 42
20. 20.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2 × 3 × 7²
21. 21.How many factors does 100 have? (a) 9 (b) 10 (c) 7 (d) 8
22. 22.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
23. 23.What is the 13th term of the AP 5, 11, 17, 23, …? (a) 72 (b) 78 (c) 77 (d) 83
24. 24.In a class of 31 children, 15 like mangoes, 16 like bananas and 6 like both. How many like only mangoes? (a) 15 (b) 10 (c) 6 (d) 9
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/36 (c) 5/11 (d) 1/6
26. 26.In a class of 39 children, 19 like dance, 23 like music and 9 like both. How many like neither? (a) 7 (b) 6 (c) 9 (d) 15
27. 27.4 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 7 (c) 16 (d) 12
28. 28.What is the mode of 20, 13, 4, 13, 13, 4 and 15? (a) 13 (b) 20 (c) 4 (d) 15
29. 29.What is the sum of the first 12 terms of the AP 3, 6, 9, …? (a) 234 (b) 252 (c) 468 (d) 36
30. 30.If a + b = 9 and ab = 20, what is (a − b)²? (a) 81 (b) 61 (c) 41 (d) 1
31. 31.How many prime numbers are there between 70 and 100? (a) 6 (b) 7 (c) 5 (d) 8
32. 32.What is the mode of 2, 14, 4, 19, 14, 4 and 14? (a) 19 (b) 14 (c) 2 (d) 4
33. 33.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 45° (c) 55° (d) 90°
34. 34.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 100° (b) 150° (c) 80° (d) 130°
35. 35.Two angles of a triangle are 60° and 80°. What is the third angle? (a) 140° (b) 120° (c) 100° (d) 40°
36. 36.If a + b = 7 and ab = 12, what is a² + b²? (a) 49 (b) 25 (c) 37 (d) 73
37. 37.What is the distance between the points (3, 15) and (9, 7)? (a) 14 (b) 10 (c) 11 (d) 100
38. 38.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 50° (b) 130° (c) 65° (d) 40°
39. 39.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 24 (c) 37 (d) 25
40. 40.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 29 (c) 21 (d) 22

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