IMO Previous Year Paper Solution class 7

SOF International Mathematics Olympiad 2020 Paper class 7

Logical Reasoning

1. In the given figure, the triangle represents  leaders, rectangle represents honest people  and circle represents biased people. Which  of the following represents honest leaders  who are not biased?  

                                                 

A. 4 

B. 5  

C. 6  

D. 7 

Ans : 1. (B): 5 is common in rectangle and triangle  only. So, 5 represents honest leaders who are not  biased. 

2. If each vowel is removed from the given  below arrangement, then which of the  following is 6th to the left of 8th element  from the right end?  

M P x q - e L i J #d e F @ z t M 8 A 1 p r t * 7 q d  

A. @ 

B. d  

C. F 

D. #  

Ans : 2. (C): After removing all the vowels, the new  arrangement becomes  

M P x q - L J #d F @ z t M 8 1 p r t * 7 q d  

8th element from right end is 1 and 6th to the left  of 1 is F. 

3. If in a certain code language, FEMALE is  coded as HODPHI, then how will FACING  be coded in that language?  

A. IPDLHQ                                          B. JPLFEJ  

C. JQLEEI                                           D. JQLFDI  

Ans : 3. (D): We have,  

FEMALE reverse  ELAMEF  

Now,  E   L   A   M  E   F 

         +3 +3 +3 +3 +3 +3  

          H   O  D   P   H   I  

Similarly, FACING reverse GNICAF   

Now, G   N    I   C   A   F     

         +3 +3 +3 +3 +3 +3     

          J    Q   L   F   D    I 

4. A sheet of paper is folded in a particular  manner and a punch is made as shown.  Select a figure from the options that would  most closely resembles the unfolded form  of the given sheet. 

                                               

 Ans : 4. (B) 

5. Find the minimum number of straight lines  required to form the given figure.  

                                                  

A. 16                                  B. 14  

C. 15                                  D. 18 

Ans ; 5. (A): Straight lines required are: AB, BC, CD,  DE, EG, GH, HA, DJ, JK, KC, AN, LM, MF, NF, HP,  NP i.e. 16 in number. 

                                                      

6. Select the correct water image of the given figure.

                                                        

  

Ans : 6. (A):         

7. Which of the following will be the second  highest number, if middle digit and last digit  of each of the given numbers are decreased  and increased by 1 respectively?  

                                846, 942, 695, 786, 895 

A. 942 

B. 846  

C. 895 

D. 786  

 Ans : 7. (C): After decreasing and increasing the middle  digit and last digit by 1, 

                    we get  837, 933, 686, 777, 886  

                    So, second highest number is 886, which comes  from 895.

8. Which of the following options will complete  the pattern in the given figure?    

                                                           

 Ans : 8. (B)                  

9. Which of the following elements satisfies  the given Venn diagram? 

                                                  

A. Fathers, Males, Girls 

B. Teachers, School, Students  

C. Indians, Surgeons, Doctors  

D. Pigeons, Birds, Sparrows  

Ans. 9. (C)             

10. Which of the following options does not satisfy the same conditions of placement of dots as in the given figure?  

                                                               

Ans .10. (B): 

11. If it is possible to make a meaningful English  word using the first, fourth, sixth, eighth  and tenth letter of the word AGGRESSIVE,  then the second letter of that word is the  answer. If no such meaningful word is  formed, then give ‘X’ as answer. If more  than one such word is formed, then give  ‘M’ as answer.  

A. M 

B. A  

C. E 

D. X  

Ans .11. (A): The first, fourth, sixth, eighth and tenth letters  of the word AGGRESSIVE are: A, R, S, I and E.  So, words formed are:  ARISE, RAISE, etc.  

12. There is a certain relationship between  figures (i) and (ii). Establish the same  relationship between figures (iii) and (iv)  by selecting a suitable figure from the  options that will replace (?) in fig. (iv).  ?

                                              

Ans:12. (A)

13. Select a figure from the options which will  complete the given figure matrix.?      

                                                          

Ans :13. (A): In each row, third figure is obtained by  joining first two figures. 

14. M, N, O, P, Q, R, S and T are sitting in a  row facing North.  

(i) S is at 3rd position from the left end.  

(ii) P is the neighbour of Q and M. M is  at one of the ends.  

(iii) The person who is 4th to the left of N  is at the other end.  

(iv) T is not a neighbour of N who is to  the immediate right of O.  If R is at the first position, then who two  are in the middle?  

A.   N, S 

B.   P, Q  

C.  O, N 

D.  O, Q  

Ans .14. (C): The sitting arrangement is as follows:  R T S O N Q P M 

                                                      O and N are in the middle.

15. How many pairs of letters are there in the  word CONSONANT each of which have  same number of letters between them as  in the English alphabets?  

A. Two 

B. One  

C. Three  

D. More than three 

Ans. 15. (C):             

                   

Mathematical Reasoning

16. How many more squares must be shaded  so that the given figure has 2/5 as unshaded  fraction?  

A. 8                                                                         B. 6  

C. 5                                                                         D. 7  

Ans 16. (B): Total number of squares = 30  

                    Number of unshaded squares needed =  2 / 5  × 30 = 12  

                    Number of already unshaded squares = 18  

                    So, 18 – 12 = 6 squares must be shaded.  

17. Which of the following number line represents  0 –2 – 4?  

Ans 17. (C)  

18. Which rational number has to be multiplied  with 64 to get the result − 49 3 / 5  ?  

A.  −35 / 43                                                              B.  −31 / 40   

C.  −33 / 40                                                              D.  −37 / 43  

Ans 18. (B): Let the required rational number be X.  

So, x * 64 = -49 3/5

= x = -248/5 * 1/64 = -31/40

Direction (19-20): The given double bar graph  shows the various activities taken up by the boys  and girls in a particular group. Study the graph  carefully and answer the following questions.  

19. What is the difference between the average  number of boys and average number of  girls taken all the activities together?  

A. 10                                                                         B. 5  

C. 3                                                                           D. 16  

Ans 19. (C): Average number of boys  =  15 + 20 +15 + 35 + 30 / 5  =  115 / 5 = 23  

                    Average number of girls =  15 + 25 + 30 + 20 + 40 / 5  =  130 / 5 = 26 

                    So, required difference = 26 – 23 = 3 

20. Find the ratio of the number of boys taken  Music and Art together to the number of  girls taken Yoga and Karate together.  

A. 7: 9                                                                       B. 7: 11  

C. 9: 7                                                                       D. 8: 15  

Ans 20. (C): Number of boys taken Music and Art  together = 15 + 30 = 45  

                    Number of girls taken Yoga and Karate together  = 15 + 20 = 35  

                    So, required ratio =  45 / 35 = 9 / 7   i.e. 9: 7 

21. The value of  

A.  1 / 4                                                                    B.  1 / 16  

C.  1 / 64                                                                  D. 1 / 72  

Ans 21. (C): 

                                         

22. Prism is a polyhedron whose base and  top are  ____.  

A. Congruent                                                           B. Similar  

C. Proportional                                                        D. Different  

Ans 22. (A) 

23. In the figure (not drawn to scale),  ABC is an equilateral triangle and  ABD is an isosceles triangle with  DA = DB, find the value of x.  

                                                           

A. 14°                                                                      B. 16°  

C. 12°                                                                      D. 32°  

Ans  23. (A): In ΔABD,  

                     AD = BD (Given)   

                    ∠ABD = ∠DAB ( angle opposite to equal  sides are equal)  

                   Now, ∠ABD + ∠ADB + ∠DAB = 180°  (Angle sum property of a triangle)  

                    ⇒ 2∠ABD + 88° = 180°  ⇒ 2∠ABD = 180° – 88° = 92° 

                    ⇒ ∠ABD = 92° / 2 = 46°  

                      As, DABC is an equilateral triangle, 

                  so  ∠CBA = 60° 

                    ⇒ x + ∠DBA = 60°  

                    ⇒ x + 46° = 60°  

                    ⇒ x = 60° – 46° = 14°

24. Solve:   

A. xpq                                                                      B. 1 / xpq  

C. 1                                                                          D. xp-q  

Ans :

25. If 7 is multiplied with 8 more than a number,  it becomes the same as 3 is added to 15  times the same number. This fact can be  represented as  ______.  

A. 7(8 + x) = 3x – 15                                              B. 7x + 8 = 15x + 3  

C. 7(8 + x) = 15x + 3                                              D. 7(8 – x) = 3x + 15  

Ans 25. (C): Let the number be x.  

                     According to question, 7(8 + x) = 15x + 3

26. Which of the following statements is  correct?  

A. If lengths of any two sides of a triangle  are 8 cm and 11 cm, then the length  of its third side lies between 3 cm and  19 cm.  

B. It is possible to construct a unique  triangle, if all its three angles are  given. 

C. An angle of 30°, can’t be constructed  using compass and ruler.  

D. A triangle can be constructed by taking  two of its angles as 90° and 90°.  

Ans 26. (A) 

27. Subtract 18.569 from the sum of 208.056  and 48.685.   

A. 215.640                                                              B. 238.172  

C. 198.642                                                              D. 254.840  

Ans 27. (B): Sum = 208.056 + 48.685  = 256.741  

                     Required difference = 256.741 – 18.569  = 238.172  

28. What should be subtracted from 7a3 + 6a2 – 2 – 5a to get 4a3 – 7a + 5a2+ 8 ?  

A. 3a3 + a2 + 2a – 10  

 B. 4a3 - a2 - 2a + 8  

C. -2a3 - a2 + 3a – 4 

 D. 3a3 - 2a2 + a – 5  

  

Ans 28. (A): Let the required expression be X.  

                   So, (7a3 + 6a2 – 2 – 5a) – X = 4a3 – 7a + 5a2+ 8

                          X = (7a3 + 6a2 – 2 – 5a) – (4a3 – 7a + 5a2+ 8)  

                               = 7a3 + 6a2 – 2 – 5a – 4a3 + 7a – 5a2 – 8  

                               = 3a3 + a2 + 2a – 10  

29. Find the area of the given figure (not drawn  to scale).  

            

                                                             

A. 152 cm2                                                           B. 114 cm2  

C. 108 cm2                                                           D. 102 cm2  

Ans 29. (C):  

              

Area of rectangle ABCN = 12 × 3 = 36 cm2  

As, MC = NC – NM = 12 – 3 = 9 cm  

So, area of rectangle MLDC = 9 × 4 = 36 cm2  

Area of rectangle KJIH = 5 × 3 = 15 cm2  

As, GF = 14 – 3 – 4 = 7 cm  

So, area of rectangle GFED = 7 × 3 = 21 cm2 

Area of figure = (36 + 36 + 15 + 21) cm2  = 108 cm2  

30. Which of the following options is incorrect?  

A. x = 5 is the solution of 3x + 7 = 22. 

B. The equation 3x + 5 = 13 represents  “5 more than 3 times a number x  gives 13”.  

C. The solution of the equation 5x – 8  = 2 is x = 2.  

D. The solution of the equation 10 – 3x  = 1 is x = 4.  

Ans  30. (D): 

A. At x = 5  3x + 7 = 3(5) + 7 = 22  

    So, x = 5 is the solution of 3x + 7 = 22  

B. Correct 

C. 5x – 8 = 2 ⇒ 5x = 10 ⇒ x = 2  

    So, x = 2 is the solution of 5x – 8 = 2  

D. 10 – 3x = 1 ⇒ –3x = – 9  ⇒ x = 3 ≠ 4  

     So, x = 4 is not the solution of 10 – 3x = 1. 

31. Two numbers are in the ratio 7: 11. If 9  is added to each of the numbers, then  ratio becomes 11: 16. The numbers are  _______.  

A. 28 and 44                                                            B. 22 and 32  

C. 44 and 64                                                            D. 35 and 55  

Ans 31. (D): Let the numbers be 7x and 11x. 

                    According to question, 7x +9 / 11x + 9 = 11 / 16 

                                                         ⇒ 16(7x + 9) = 11(11x + 9)

                                                         ⇒ 112x + 144 = 121x + 99  

                                                         ⇒ 121x – 112x = 144 – 99 

                                                         ⇒ 9x = 45 ⇒ x = 5

                 So, the numbers are 7 × 5 = 35 and 11 × 5 = 55.   

32. In the given figure (not drawn to scale), ABC  is a straight line, ∠DBE is a right angle and  ∠a = ∠b = ∠c = ∠d. Find ∠a. 

                                            

A. 22.5°                                                                   B. 30°  

C. 45°                                                                      D. 60°  

Ans 32. (A): Since, ABC is a straight line.  

                 So, ∠a + ∠b + ∠c + ∠DBE + ∠d = 180°  

                ⇒ 4∠a + 90° = 180° [ ∠a = ∠b = ∠c = ∠d]  

                ⇒ 4∠a = 180° – 90° = 90°  ⇒ ∠a = 90  4  °  = 22.5° 

33. Which of the following figures do not have  any line of symmetry?  

                             

                       

 

34. A bag contains 30 blue ribbons, 15 red  ribbons and 5 black ribbons. If a ribbon is  drawn at random from the bag, then find  the probability of getting a red ribbon.  

A. 3/10                                                                       B. 5/12  

C. 15/25                                                                     D. 2/11  

Ans 34. (A): Total number of ribbons in the bag  = 30 + 15 + 5 = 50  

                     Probability of getting a red ribbon  =  Number of red ribbons in the bag /Total number of                                                                                                                                             ribbons in the bag 

 

                                                                              = 15 / 50

                                                                              =  3 / 10

35. Which of the following is greater than  16.3%?  

A. 163 out of 1000                                                     B. 113 out of 250  

C. 8 out of 50                                                             D. 39 out of 750 

Ans;35. (B): 16.3% = 163 / 10% * 1 /100  =163 / 1000  = 0.163  

                    A. 163 out of 1000 = 163 / 1000  = 0.163 

                    B. 113 out of 250 =  113 / 250  = 0.452  

                    C. 8 out of 50 =  8 / 50  = 0.16  

                    D. 39 out of 750 = 39 / 750  = 0.052