Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 352 · 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 41 children, 22 like cricket, 15 like football and 5 like both. How many like neither? (a) 9 (b) 5 (c) 4 (d) 14
2. 2.In a class of 25 children, 20 like dance, 7 like music and 3 like both. How many like neither? (a) 4 (b) 3 (c) 1 (d) 2
3. 3.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 5/8 (d) 3/8
4. 4.What is the distance between the points (1, 6) and (13, 1)? (a) 17 (b) 14 (c) 169 (d) 13
5. 5.In a class of 24 children, 15 like tea, 14 like coffee and 5 like neither. How many like both? (a) 11 (b) 5 (c) 19 (d) 10
6. 6.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 5/6 (b) 1/6 (c) 1/5 (d) 1/3
7. 7.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 5 times (d) 8 times
8. 8.In how many different ways can the letters of the word STAR be arranged? (a) 48 (b) 16 (c) 24 (d) 12
9. 9.What is the mode of 20, 1, 20, 17, 17, 20 and 7? (a) 17 (b) 7 (c) 1 (d) 20
10. 10.A bag has 5 blue, 4 red and 8 green balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 4/17 (c) 4/13 (d) 13/17
11. 11.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
12. 12.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
13. 13.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 10 (b) 20 (c) 25 (d) 15
14. 14.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 90 (c) 45 (d) 55
15. 15.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 171 (c) 60 (d) 57
16. 16.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 32 (c) 16 (d) 20
17. 17.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 68 (c) 60 (d) 50
18. 18.How many prime numbers are there between 10 and 40? (a) 10 (b) 7 (c) 9 (d) 8
19. 19.What is the 25th term of the AP 7, 14, 21, 28, …? (a) 176 (b) 175 (c) 168 (d) 182
20. 20.In a class of 32 children, 21 like mangoes, 12 like bananas and 9 like both. How many like only mangoes? (a) 12 (b) 20 (c) 3 (d) 21
21. 21.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 169 (c) 78 (d) 156
22. 22.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 25 (d) 20
23. 23.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
24. 24.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 57 (b) 66 (c) 48 (d) 58
25. 25.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 15 (c) 14 (d) 8
26. 26.What is the midpoint of the line joining (4, 12) and (8, 8)? (a) (2, 2) (b) (12, 20) (c) (6, 10) (d) (10, 6)
27. 27.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 110 (d) 121
28. 28.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 20 (c) 30 (d) 15
29. 29.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 69 (c) 72 (d) 23
30. 30.A canteen sells 7 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 14 (c) 9 (d) 21
31. 31.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 66 (b) 132 (c) 144 (d) 24
32. 32.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 70° (c) 45° (d) 110°
33. 33.What is the median of 24, 9, 12, 15, 19, 13 and 21? (a) 13 (b) 15 (c) 19 (d) 16
34. 34.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 2/3 (d) 1/3
35. 35.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 90 (c) 20 (d) 100
36. 36.What is the median of 36, 4, 8, 7 and 34? (a) 8 (b) 9 (c) 7 (d) 34
37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 240 (d) 120
38. 38.A drawer has lots of black, blue, white and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 5 (c) 8 (d) 2
39. 39.A bag has 6 blue balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 11 (c) 7 (d) 8
40. 40.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 25° (b) 155° (c) 110° (d) 95°

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