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IMO Mock Test – Class 9
IMO Mock Tests for Class 9 is designed for International Math Olympiad Preparation.
The IMO Class 9 online mock test paper is free for all students.
This paper has 50 questions.
Time allowed is 60 minutes.
There are 3 sections: 20 questions in section I, 20 in section II and 10 in section III.
The IMO Mock tests for Class 9 given here will help the student get an accurate idea of the types of questions asked in the International Math Olympiad and also help prepare timing and accuracy.
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Question 1 of 50
1. Question
Category: Logical ReasoningStudy the following information and answer the question given below it.A blacksmith has five iron articles A, B, C, D and E, each having a different weight.
(i) A weighs twice as much as B.
(ii) B weighs four and a half times as much as C.
(iii) C weighs half as much as D.
(iv) D weighs half as much as E.
(v) E weighs less than A but more than C.
Which of the following is the lightest? 
Question 2 of 50
2. Question
Category: Logical ReasoningChoose the odd numeral pair/group.

Question 3 of 50
3. Question
Category: Logical ReasoningSelect a figure from amongst the options which will continue the same series as established by the five Problem Figures.

Question 4 of 50
4. Question
Category: Logical ReasoningOut of four figures marked (A), (B), (C) and (D) three are similar in a certain manner. However one figure is not like the other three. Choose the figure which is different from the rest.

Question 5 of 50
5. Question
Category: Logical ReasoningIn the matrix there are eight designs and one space is left blank as shown by a question mark.Which answer figures will replace the question mark?

Question 6 of 50
6. Question
Category: Logical ReasoningThe bank balance of Puran is more than that of Sushma but less than the bank balance of Singh.If the bank balance of Puran, Sushma and Singh be x, y and z respectively then which of the following is correct?

Question 7 of 50
7. Question
Category: Logical ReasoningFind the number of triangles in the given figure.

Question 8 of 50
8. Question
Category: Logical ReasoningWhich number will replace the question mark?

Question 9 of 50
9. Question
Category: Logical ReasoningThere are three pillars X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance A climbs on X 5 cm but slips down 1 cm. B climbs on Y 6 cm but slips down 3 cm. C climbs on Z 7 cm but slips down 2 cm. If each requires 50 chances to reach the top of the pillar, what is the height of the shortest pillar?

Question 10 of 50
10. Question
Category: Logical ReasoningGroup the given figures into three classes using each figure only once.

Question 11 of 50
11. Question
Category: Logical ReasoningIf 324 × 150 = 54, 251 × 402 = 48 and 523 × 345 = 120, then 651 × 345 = ?

Question 12 of 50
12. Question
Category: Logical ReasoningFind the figure which contains the Fig. (X) as its embedded part.

Question 13 of 50
13. Question
Category: Logical ReasoningIn the number 5904627813 first and sixth digits are interchanged; and similarly the positions of second and seventh digits and so on are interchanged. Which of the following will be the 4th digit from the right after the new arrangement?

Question 14 of 50
14. Question
Category: Logical ReasoningIn the given matrix the values of A, B and C respectively are ____.

Question 15 of 50
15. Question
Category: Logical ReasoningTwo cars start from opposite places on a main road, 150 km apart. First car runs for 25 km and takes a right turn and then runs 15 km. It then turns left and runs for another 25 km and then
takes the direction to reach the main road. In the mean time, due to a minor break down the other car has run only 35 km along the main road. What would be the distance between the two cars at
this point? 
Question 16 of 50
16. Question
Category: Logical ReasoningNeelam, who is Rohit’s daughter, says to Indu, “Your mother Reeta is the younger sister of my father, who is the third child of Sohanji.” How is Sohanji related to Indu?

Question 17 of 50
17. Question
Category: Logical ReasoningIf Moon is called Star, Star is Sun, Sun is Earth, Earth is Jupiter, Jupiter is Mars and Mars is Mercury, where does man live?

Question 18 of 50
18. Question
Category: Logical ReasoningIn the given figure, square represents doctors, triangle represents ladies and circle represents surgeons. Which letter represents the ladies who are both doctors and surgeons?

Question 19 of 50
19. Question
Category: Logical ReasoningIn the given question, which number will replace the question mark?

Question 20 of 50
20. Question
Category: Logical ReasoningIf the positions of the third and tenth letters of the word DOCUMENTATION are interchanged, and likewise the positions of the fourth and seventh letters, the second and sixth letters, are also interchanged, then which of the following will be eleventh letter from the right end?

Question 21 of 50
21. Question
Category: Mathematical ReasoningIf x < –1, then which of the following expressions holds?

Question 22 of 50
22. Question
Category: Mathematical ReasoningIf the perimeter of a rectangular garden plot is 80 metres, which of the following could be the length of one of its sides?
I. 30 metres II. 40 metres III. 50 metres 
Question 23 of 50
23. Question
Category: Mathematical ReasoningIn the adjoining figure, circles with centres at L, M and N each have a radius of 2 units and are placed as shown here. If PQRS is the smallest rectangle that will enclose the 3 circles, what is
the area of PQRS?

Question 24 of 50
24. Question
Category: Mathematical ReasoningIf 3x + 2y = 17 and x and y are positive integers, then y could be which of the following?

Question 25 of 50
25. Question
Category: Mathematical ReasoningIn the given figure l1  l2. Which of the following must be true?

Question 26 of 50
26. Question
Category: Mathematical ReasoningIn the adjoining figure, point P the intersection of lines l1 and l2 has coordinates (a, b) as shown here. Which of the following could be the ordered pair (a, b)?

Question 27 of 50
27. Question
Category: Mathematical ReasoningIn the given figure, three equilateral triangles have a common vertex then x + y + z =

Question 28 of 50
28. Question
Category: Mathematical ReasoningIf a right triangle has sides of length 1 and 2, which of the following could be the length of the remaining side?
I. 1 II. √2 III. 3 
Question 29 of 50
29. Question
Category: Mathematical ReasoningThe expression (a + b + c)^{2} + (a + b – c)^{2} + (a – b + c)^{2} + (b + c – a)^{2} equals ____.

Question 30 of 50
30. Question
Category: Mathematical ReasoningA die is rolled 10,500 times. The frequency of each outcome is shown in the table. What is the empirical probability of the outcomes of multiples of 3?

Question 31 of 50
31. Question
Category: Mathematical ReasoningIn Δ’s ABC and PQR, AB = PQ, BC = QR are extended to X and Y respectively and ∠ABX = ∠PQY.
Under which congruency criterion, the triangles are congruent? 
Question 32 of 50
32. Question
Category: Mathematical ReasoningFind the value of (117649/1771561)^{1/6}

Question 33 of 50
33. Question
Category: Mathematical ReasoningABCD is a trapezium, in which AB  DC, AD ^ AB and E & F are points on AD & BC respectively.BD is joined. If ∠EFC = 110°, ∠ABD = 60°, ∠BDC = x° and ∠DCF = y°, then values of x and y are
____. 
Question 34 of 50
34. Question
Category: Mathematical ReasoningFill in the blank :
If a straight line meets two other straight lines so as to make the sum of the two interior angles on one side of the transversal less than two right angles, then the other straight lines extended infinitely, will meet ____ the transversal. 
Question 35 of 50
35. Question
Category: Mathematical ReasoningWhich of the following options in Column I with reasons in Column II is correct with respect to the following question :
How many linear equations in x and y can be satisfied by x = 1 and y = 3?Column I Column II (A) Only one as only x = 1, y = 3 is given. (B) Exactly two one for x = 1, second for y = 3. (C) Infinitely many one for x = 1, second for y = 3 and third for x + y = 3. (D) Exactly three as point (1, 3) lies on graph and through one point infinite lines can pass, so we get infinite graphs or infinite equations. 
Question 36 of 50
36. Question
Category: Mathematical ReasoningIf the product of two surds is a rational number, then each one of them is called the _____ of the other _____.

Question 37 of 50
37. Question
Category: Mathematical ReasoningIf one leg of an isosceles rightangled triangle is increased by 6 cm and the other leg is increased by 4 cm, then change in area of the triangles is 24 sq cm. Find the length of the leg of the original triangle.

Question 38 of 50
38. Question
Category: Mathematical ReasoningRemainder when a2 + b2 + 2(ab + bc + ca) is divided by (a + b + 2c) is _______.

Question 39 of 50
39. Question
Category: Mathematical ReasoningThe value of ______.

Question 40 of 50
40. Question
Category: Mathematical Reasoningll the three quadrilaterals ADEC, ABIH and BCGF are squares and ∠ABC = 90°. If the area of ADEC = x^{2} and area of AHIB = y^{2}(x^{2} > y^{2}), then find the area of BCGF?

Question 41 of 50
41. Question
Category: Everyday MathematicsA class starts at 10 a.m. and lasts till 1.27 p.m. Four periods are held during this interval. After every period, 5 minutes are given free to the students. The exact duration of each period is ____.

Question 42 of 50
42. Question
Category: Everyday MathematicsIn Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimations,what is the average of different probable weights of Arun?

Question 43 of 50
43. Question
Category: Everyday MathematicsA man walked diagonally across a square plot. Approximately, what was the percent saved by not walking along the edges?

Question 44 of 50
44. Question
Category: Everyday MathematicsA man purchases two clocks A and B at a total cost of ` 650. He sells A at 20% profit and B at a loss of 25% and gets the same selling price for both the clocks. What are the purchasing prices of A and B respectively?

Question 45 of 50
45. Question
Category: Everyday MathematicsEight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire rental of the car, then the share of each of the remaining persons is increased by ____ of the original share.

Question 46 of 50
46. Question
Category: Everyday MathematicsA student was asked to divide a number by 6 and add 12 to the quotient. He, however, first added 12 to the number and then divided it by 6, getting 112 as the answer. The correct answer should have been ____.

Question 47 of 50
47. Question
Category: Everyday MathematicsReema bought x pens at ₹ 2.60 each and y greeting cards at 80 paise each. If the pens cost ₹ 12 more than the cards, the equation involving x and y is _____.

Question 48 of 50
48. Question
Category: Everyday MathematicsTo make a marriage tent, poles are planted along the perimeter of a square field at a distance of 5 metres from each other and the total number of poles used is 20. What is the area (in sq. metres) of the square field?

Question 49 of 50
49. Question
Category: Everyday MathematicsHussain’s weight is 5/4 times the weight of Rahim. Their total weight is 90 kg. What is Hussain’s weight?

Question 50 of 50
50. Question
Category: Everyday MathematicsIn a class, the number of boys is more than the number of girls by 12% of the total strength. The ratio of boys to girls is _____.