Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 21 · 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 49 children, 26 like dance, 25 like music and 7 like both. How many like neither? (a) 12 (b) 5 (c) 6 (d) 7
2. 2.A drawer has lots of green, blue, yellow and red 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) 2 (d) 8
3. 3.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
4. 4.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 2/3 (c) 5/6 (d) 1/4
5. 5.What is the median of 21, 1, 6, 14, 7, 28 and 2? (a) 14 (b) 6 (c) 8 (d) 7
6. 6.Which term of the AP 20, 23, 26, 29, … is 137? (a) 42nd (b) 40th (c) 39th (d) 41st
7. 7.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 325 (c) 288 (d) 315
8. 8.A bag has 7 blue, 4 red and 5 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 9/16 (c) 7/16 (d) 5/8
9. 9.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) 21 (c) 29 (d) 22
10. 10.How many prime numbers are there between 80 and 90? (a) 4 (b) 2 (c) 1 (d) 3
11. 11.What is the distance between the points (3, 9) and (15, 14)? (a) 14 (b) 17 (c) 169 (d) 13
12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 9 (b) 18 (c) 19 (d) 20
13. 13.In a class of 18 children, 10 like tea, 8 like coffee and 2 like neither. How many like both? (a) 16 (b) 3 (c) 1 (d) 2
14. 14.A bag has 3 black balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 5 (c) 4 (d) 9
15. 15.What is the median of 11, 40, 26, 19 and 37? (a) 26 (b) 19 (c) 37 (d) 27
16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 7 (b) 6 (c) 5 (d) 8
17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 19 (d) 20
18. 18.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
19. 19.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 9 (c) 5 (d) 6
20. 20.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/18 (c) 1/11 (d) 1/12
21. 21.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/8 (c) 1/8 (d) 7/8
22. 22.In a class of 29 children, 24 like cricket, 10 like football and 6 like both. How many like at least one of the two? (a) 28 (b) 29 (c) 22 (d) 34
23. 23.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
24. 24.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
25. 25.How many factors does 90 have? (a) 13 (b) 10 (c) 12 (d) 11
26. 26.In which quadrant does the point (−1, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
27. 27.What is the 23rd term of the AP 16, 23, 30, 37, …? (a) 154 (b) 161 (c) 170 (d) 177
28. 28.In a class of 11 children, 5 like tea, 7 like coffee and 1 like neither. How many like both? (a) 1 (b) 3 (c) 10 (d) 2
29. 29.What is the median of 11, 30, 38, 36, 34, 2 and 27? (a) 34 (b) 30 (c) 27 (d) 36
30. 30.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/6 (c) 1/11 (d) 5/11
31. 31.What is the 36th term of the AP 9, 15, 21, 27, …? (a) 219 (b) 216 (c) 210 (d) 225
32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 15 (b) 14 (c) 5 (d) 16
33. 33.In a class of 34 children, 23 like dance, 18 like music and 10 like both. How many like only dance? (a) 13 (b) 16 (c) 8 (d) 23
34. 34.What is the 21st term of the AP 17, 21, 25, 29, …? (a) 97 (b) 84 (c) 80 (d) 101
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 1/18 (c) 2/11 (d) 1/12
36. 36.In a class of 34 children, 18 like cricket, 17 like football and 8 like both. How many like at least one of the two? (a) 34 (b) 27 (c) 35 (d) 19
37. 37.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 72 (c) 24 (d) 8
38. 38.What is the 25th term of the AP 19, 26, 33, 40, …? (a) 187 (b) 168 (c) 194 (d) 175
39. 39.What is the sum of the roots of x² − 10x + 24 = 0? (a) 11 (b) 9 (c) 10 (d) 24
40. 40.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 145° (b) 75° (c) 140° (d) 35°

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad