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CLASS 12
Contents ªª 4th IMO 2010 ªª 5th IMO 2011 ªª 6th IMO 2012 - SET A ªª 6th IMO 2012 - SET B ªª 7th IMO 2013 - SET A ªª 7th IMO 2013 - SET B ªª 8th IMO 2014 - SET A ªª 8th IMO 2014 - SET B
MTG Work-Books / olympiad books CLASS 1
International Mathematics Olympiad
National Science Olympiad
International English Olympiad
MTG CSS Series
CLASS 2
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
International English Olympiad
MTG CSS Series
International English Olympiad
MTG CSS Series
CLASS 3
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
MTG Work-Books / olympiad books CLASS 4
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
International English Olympiad
MTG CSS Series
International English Olympiad
MTG CSS Series
International English Olympiad
MTG CSS Series
CLASS 5
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
CLASS 6
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
MTG Work-Books / olympiad books CLASS 7
National Science Olympiad
International Mathematics Olympiad
National Cyber Olympiad
Science IQ Challenge
Math IQ Challenge
International English Olympiad
MTG CSS Series
Master Mental Ability in 30 Days
CLASS 8
International Mathematics Olympiad
National Science Olympiad
National Cyber Olympiad
International English Olympiad
MTG CSS Series
Math IQ Challenge
Science IQ Challenge
Psychology of Success
The Secrets of SUCCESS
Master Mental Ability in 30 Days
MTG Work-Books / olympiad books CLASS 9
International Mathematics Olympiad
Math IQ Challenge
National Science Olympiad
Science IQ Challenge
National Cyber Olympiad
Psychology of Success
The Secrets of SUCCESS
International English Olympiad
Master Mental Ability in 30 Days
CLASS 10
International Mathematics Olympiad
Math IQ Challenge
National Science Olympiad
Science IQ Challenge
National Cyber Olympiad
Psychology of Success
The Secrets of SUCCESS
International English Olympiad
Master Mental Ability in 30 Days
MTG Work-Books / olympiad books CLASS 11
International Mathematics Olympiad
Math IQ Challenge
Science IQ Challenge
National Science Olympiad
Psychology of Success
National Cyber Olympiad
The Secrets of SUCCESS
Master Mental Ability in 30 Days
CLASS 12
International Mathematics Olympiad
Math IQ Challenge
Science IQ Challenge
National Science Olympiad
Psychology of Success
National Cyber Olympiad
The Secrets of SUCCESS
Master Mental Ability in 30 Days
Class
1 to 10
JEE (Main & Advanced) | AIPMT | BOARDS | OLYMPIAD | NTSE
FOUNDATION COURSE For Classes 7, 8, 9 & 10 Class 7
Class 8
Class 9
Class 10
Class 8 4th
Year 2010
Copyright©2015. Science Olympiad Foundation (SOF)
4th IMO - 2010
SECTION I : LOGICAL REASONING 1.
The square tiles given here are arranged to show a pattern. Which expression can be used to determine the number of square tiles in Stage n? (A) 4n + 3
2.
Stage 1 Stage 2
2
(B) 5n + 2
(C) n + 6
Stage 3
Stage 4
3
(D) n + 6
Which of the following figures comes next in the given pattern ? ? ____
(A) 3.
(D)
(B) ROTAGAIL
(C) ROTAGILE
(D) OTAGILAR
If 'bat' is 'racket', 'racket' is 'football', 'football' is 'shuttle', 'shuttle' is 'ludo' and 'ludo' is 'carrom', what is cricket played with ? (A) Racket
5.
(C)
In a certain code INACTIVE is written as VITCANIE. How is ALIGATOR written in that code ? (A) ROTAGILA
4.
(B)
(B) Football
(C) Bat
(D) Shuttle
Shivani saw the restaurant sign shown below. Manager's Special Choose 1 main dish, 1 side dish, and 1 bread for ` 880. Main Dish Side Dish Bread Meat loaf Corn Dinner roll Biscuit Chickenfried steak Beans Mashed potatoes Macaroni & Cheese
How many different combinations are possible if Shivani buys the Manager's special ? (A) 8 6.
(C) 24
(D) 11
In the series 6 4 1 2 2 8 7 4 2 1 5 3 8 6 2 1 7 1 4 1 3 2 8, how many pairs of successive numbers have a difference of 2 each ? (A) Four
7.
(B) 16
(B) Five
(C) Six
(D) Seven
This Venn diagram is used to classify counting numbers according to a set of rules. Which one of the following numbers belongs in the region of the 32 diagram marked by the question mark ? 4 28
(A) 45
6
16 12
8
(B) 50
20
(C) 60
5
3 9
? 25
15 35 10
(D) 65 8.
If you cut out and fold the pattern shown on the right to make a cube, which letter will be on the face of the cube opposite the face labelled 3 ? (A) 2
4 th IMO | LevelI | Class 8
(B) 1
(C) 5 2
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 6
5 1 2 3 4 6
4th IMO - 2010
9.
The given chart shows how much the Party house charges for pizza parties for different number of people. If n stands for the number of people and C stands for the cost in `, which equation represents the information in the chart? (A) C = 5n + 100 (C) C = 5n + 40
(B) C = n + 45 (D) C = 2n + 35
Number of People
Cost
5
` 125
8
` 140
12
` 160
20
` 200
10. Which is the top view of the prism?
(A)
(B)
(C)
(D)
11. The given question consists of four figures 1, 2, 3 and 4 called the Problem Set. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the options that would replace the question mark (?) in fig. (4). Problem Set
? 1
(A)
2
3
(B)
4
(C)
(D)
12. Which number would replace the question mark in the series ? 7, 12, 19, ?, 39 (A) 39
(B) 28
(C) 26
(D) 24
13. Anusha remembers that her brother Kabir's birthday falls after 20 th May but before 28 th May, while Pia remembers that Kabir's birthday falls before 22 nd May but after 12 th May. On what date Kabir's birthday falls ? (A) 20 th May
(B) 21 st May
(C) 22 nd May
(D) 12 th May
14. The mirrorimage of the figure(X), when mirror is placed along PQ from amongst the four alternatives is___ P
Q
´ Fig. (X)
(A)
´
(B)
(C)
´
(D)
´
15. How many triangles are there in the given figure ? (A) 8
(B) 10
(C) 11
(D) 12 3
Copyright©2015. Science Olympiad Foundation (SOF)
4 th IMO | LevelI | Class 8
4th IMO - 2010
16. A is father of C and D is son of B. E is brother of A. If C is sister of D, how is B related to E ? (A) Daughter
(B) Brother
(C) Husband
(D) Sisterinlaw
17. If '–' means '´', '´' means '+', '+' means '¸' and '¸' means '–', then 40 ´ 12 + 3 – 6 ¸ 60 = ? (A) 7.95
(B) 16
(C) 44
(D) 4
18. Which letter will be the fifth from the right if the first and second, the third and fourth and so on are interchanged among each other in the word " COMPANIONATE"? (A) A
(B) I
(C) N
(D) O
19. Which one of the following sets is best represented in the adjoining diagram? (A) Animals, Insects, Cockroaches
(B) Country, States, Districts
(C) Animals, Males, Females
(D) States, Districts, Union territories
20. Find the missing character from among the given options. (A) 22
(B) 30
5 12
(C) 32
(D) 42
4
6
6
21 7 5
4
?
8
10
SECTION II : MATHEMATICAL REASONING 21. Supriya is standing in the Sun close to a lamp post. Supriya is 5 feet lamp post
tall and her shadow is 2 feet long. The shadow of the lamp post is 8 feet long. How tall is the lamp post ? (A) 20 ft
?
(B) 18 ft 5 ft
(C) 16 ft
8 ft
(D) 14 ft
2 ft
22. What is the value of 3(x 2 – 4x) when x = 5? (A) 5 23. The value of
(B) 15
(C) 30
(D) 55
(C) 107
(D) 109
1 1 1 + + is ____ -2 /3 -3 / 4 (216) (256) (32) -1/5
(A) 102
(B) 105
24. What is the value of x in the given equation? (3 x + 1) (2 x - 3) ( x + 3) (3 x - 1) + = + 16 7 8 14 (A) 2
(B) 4
(C) 3
(D) 5
25. Last year Mr. Nitin earned ` 5,800 from the corn he grew on his farm. This year he expects a 7% increase in the income from corn. How much does he expect to earn from corn this year? (A) ` 406
(B) ` 6,206
(C) ` 8,600
(D) ` 9,600
26. The radius of the large circle is equal to the diameter of the small circle. If the area of the small circle is 13 m 2 , what is the area of the shaded region? (A) 55 m 2 4 th IMO | LevelI | Class 8
(B) 48 m 2
(C) 39 m 2
4
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 26 m 2
4th IMO - 2010
27. If DRTW @ DABC , what is the measure of ÐT in the given figure ? (A) 12°
B
T
(B) 72° (C) 80°
A
72°
18°
C
R
W
(D) 90° 120 m 2 n -3
28. Write (A)
60 m 5 n -2
in simplest form using only positive exponents. Assume that m ¹ 0 and n ¹ 0.
2n 3
m
(B)
2
(C)
3
m n
2m 3 n
(D)
1 2m 3 n
29. A 2 cm long grasshopper can jump 160 cm. If a 6 metre tall animal had the same height and jump ratio, how far could he jump? (A) 48 m
(B) 480 m
(C) 180 m
(D) 8000 m
30. John made the given grid to show the location of some things in his garden. Which ordered pair best represents the point on the grid labelled "Tree" ? (A) (2, 6) (B) (3, 1) (C) (1, 3) (D) None of these 31. Students at a local college were asked how many hours they slept last night. The adjoining chart shows the data. A bar graph of this data will be made on a grid that is 20 units. What scale would be most appropriate for the axis labelled "Number of Students" ? (A) 1 unit = 1 student
(B) 1 unit = 2 students
y 9 8 7 Swing set 6 5 4 Tree Birdbath 3 2 Flowers 1 0 1 2 3 4 5 6 7 8 9
Hours of Sleep 6 7 8 9 More than 10
x
Number of Students 14 26 28 15 6
(C) 1 unit = 10 students (D) 1 unit = 28 students
32. ABCD is a parallelogram. The angle bisectors of ÐA and ÐD meet at O. The measure of ÐAOD is ____. (A) 45°
(B) 90°
(C) Depends on the angles A and D
(D) Not able to determine from given data
33. Which of the following numbers does NOT have a multiplicative inverse? (A) -
1 3
(B) 0
(C) 1
(D) 3
34. The radius of the cylinder whose lateral surface area is 704 cm 2 and height 8 cm, is ____. (A) 6 cm
(B) 4 cm
(C) 8 cm
(D) 14 cm
35. Which expression is equivalent to 5[4 + 3(x – 6)] ? (A) 15x – 10
(B) 15x – 70
(C) 15x – 14 5
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 15x – 110 4 th IMO | LevelI | Class 8
4th IMO - 2010
36. Between which two consecutive whole numbers 1, 000 lies ? (A) 29 and 30
(B) 30 and 31
(C) 31 and 32
(D) 32 and 33
37. Which two quadrilaterals have exactly one line of symmetry ? (A) (1) and (5)
(B) (2) and (3)
(C) (1) and (4)
(D) (2) and (5)
(1)
(2)
38. Which of the following expressions represents the distance around the triangle ? (A) 5x + 39
(B) 4x – 37
(C) 4x + 39
(D) 6x + 47
(3)
(4)
40 – x
(5)
2x + 3 3x – 4
39. What are the lengths of the sides of a triangle that has a perimeter of 24 centimetres ? (A) 6 cm, 6 cm, 12 cm
(B) 7 cm, 7 cm, 10 cm
(C) 3 cm, 8 cm, 13 cm
(D) 4 cm, 5 cm, 15 cm
40. Manish saw the given figure while he was reading a book on astronomy. How is the distance from Venus to the Sun written in scientific notation ?
Sun
(A) 67.23 × 10 6 miles 67,230,000 miles
(B) 0.6723 × 10 8 miles (C) 6.723 × 10 4 miles Venus
(D) 6.723 × 10 7 miles
SECTION III : EVERYDAY MATHEMATICS 41. The Wright brothers had their first successful flight near Kitty Hawk, North Carolina. Mr. Satish finds it easy to remember the year in which the flight occurred because the number 3, 621, 502 , the square root of his telephone number is nearest to a whole number. In which year did the flight occur? (A) 1902
(B) 1903
(C) 1904
42. Dhruv plans on leaving his home in Delhi at 8:00 A.M. He will drive at an average speed of 40 km per hour and plans to arrive at his destination just before 11:00 A.M. If he makes no stops along the way, which of the four places is his destination? (A) w
(B) x
(C) y
(D) z
(D) 1905 Delhi
43. Jasmine is a much better tennis player than Reshma. They decide to have a contest. Every time Jasmine wins a game, she will earn 3 points and every time Reshma wins a game, she will earn 5 points. If they play 48 games and the final score is tied, how many games did Jasmine win ? (A) 50
(B) 40
(C) 30
(D) 18
44. Sushmita used 200 square tiles to tile her kitchen floor. Of these, 66 tiles were green. What percent of the tiles were green ? (A) 134% 4 th IMO | LevelI | Class 8
(B) 66%
(C) 33% 6
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 3.03%
4th IMO - 2010
45. Nalini and three of her friends worked together to make a quilt. The given table lists the fractional part of the quilt that each of the girls made. Which list shows the girls in order from the one who sewed the most to the one who sewed the least ? (A) Reena, Nalini, Shalini, Kamini (B) Shalini, Nalini, Kamini, Reena (C) Reena, Kamini, Nalini, Shalini (D) Kamini, Shalini, Nalini, Reena
Girl
Parts Sewn 3 Nalini 8 1 Kamini 5 2 Shalini 5 1 Reena 40
46. Two flower beds in a park are similar rectangles of same width. The longest side of the large flower bed is 24 cm long, and the longest side of the small flower bed is 8 cm. If L is the area of the large flower bed and S is the area of the small flower bed, which equation is true? (A) S = L – 16
(C) S =
(B) S = L + 16
1 L 9
(D) S =
1 L 3
47. A machine takes 12 minutes to fill 200 bottles of soda. At this rate, how many minutes will it take the machine to fill 500 bottles of soda? (A) 25 minutes
(B) 28 minutes
(C) 30 minutes
(D) 40 minutes
1 48. Jiah is building birdhouses. It takes her 3 hours to build 4 birdhouses. Which of the following is 2 an equivalent rate ?
(A) 14 hours to build 18 birdhouses
(B) 28 hours to build 35 birdhouses
(C) 7 hours to build 8 birdhouses
(D) 21 hours to build 28 birdhouses
49. Madhuri is on the fourth floor of a building. Her car is in the parking garage three levels below the ground floor. She gets in the elevator and travels from the fourth floor above ground level to the third floor below ground level. How many floors did she travel ? (A) 3
(B) 1
(C) 4
(D) 7
50. Mrs. Ravina needs to take a taxi to the doctor's clinic. The taxi ride costs ` 13.00 for the first km and ` 6 for each km thereafter. How much does Mrs. Ravina pay for a 2.3 km taxi ride? (A) ` 25
(B) ` 28
(C) ` 32
(D) ` 30
SPACE FOR ROUGH WORK
7
Copyright©2015. Science Olympiad Foundation (SOF)
4 th IMO | LevelI | Class 8
Class 8 5th
Year 2011
Copyright©2015. Science Olympiad Foundation (SOF)
2
5th IMO - 2011
Section I : Logical Reasoning 1. Choose a number from the options that will continue the same pattern and replace the question mark in the given series.
(A) 201
6, 13, 25, 51, 101, ___ ? (C) 203
2.
In a row of boys facing North, A is sixteenth from the left end and C is sixteenth from the right
(B) 202
(D) 205
end. B, who is fourth to the right of A, is fifth to the left of C in the row. How many boys are there
in the row ? (A) 39
(B) 40
(C) 41
(D) 42 P
3. Choose the correct mirror-image of Fig. (X) from amongst the options if the mirror is placed along PQ.
(A)
(B)
(C)
(D)
Fig. (X) Q
4. The given equation becomes correct due to the interchange of two signs. One of the four options under it specifies the interchange of signs in the equation which when made will make the equation correct. Find the correct option.
(A) ÷ and ×
(B) + and ×
5 + 6 ÷ 3 – 12 × 2 = 17 (C) + and ÷
(D) + and –
5. Choose one word which can be formed from the letters of the given word.
RECOMMENDATION (B) MEDIATE (C) REMINDER
(A) MEDICINE
6.
Figures (i), (ii), (iii) and (iv) constitute the Problem Set. There is a definite relationship between
(D) COMMUNICATE
figures (i) and (ii). Establish a similar relationship between figures (iii) and (iv) by selecting a suitable figure from the options that would replace the question mark (?) in fig. (iv).
(A)
(B)
(C)
(D)
Problem Set
? (i)
(ii)
SPACE FOR ROUGH WORK
Copyright©2015. Science Olympiad Foundation (SOF)
(iii)
(iv)
3
5th IMO - 2011
7. Choose the Venn diagram which best illustrates the three given classes "Dogs, Animals, Pets".
(A)
(B)
(C)
(D)
8. A matrix of certain characters is given. These characters follow a certain
2 3 4
trend, row-wise or column-wise. Find out this trend and choose the missing character from the given options.
(A) 2765
(B) 3125
(C) 8796
9.
Count the number of triangles in the given figure. (A) 20 (B) 22 (C) 23 (D) None of these
2 2 2
256 ? 46656
(D) 30008
10. Select a figure from amongst the options which would complete the pattern of Fig. (X). (A)
(C)
(B)
(D)
11. Choose that set of numbers from the options that is similar to the given set.
(A) (56, 52, 44)
(81, 77, 69) (B) (46, 61, 53) (C) (75, 71, 60)
(D) (92, 88, 79)
12. A man is facing north-west. He turns 90° in the clockwise direction and then 135° in the anti
clockwise direction. Which direction is he facing now? (A) East (B) West (C) North
(D) South
13. Select from amongst the options as to how the pattern would appear when the transparent sheet is folded along the dotted line.
(A)
(B)
(C)
(D)
SPACE FOR ROUGH WORK
Copyright©2015. Science Olympiad Foundation (SOF)
4
5th IMO - 2011
14. Choose the odd numeral pair/group. (A) 5 : 50 (B) 8 : 128
(C) 11 : 242
(D) 15 : 370
15. If ZIP = 30 and ZAP = 38, then how will you code VIP? (A) 174 (B) 43 (C) 34
(D) 113
16. How many 5's are there in the following number sequence which are immediately preceded by 7 and immediately followed by 6?
7 5 5 9 4 5 7 6 4 5 9 8 7 5 6 7 6 4 3 2 5 6 7 8 (A) One
(B) Two
(C) Three
(D) Four
17. There are seven figures, the first and last of which are un-numbered and the remaining are numbered as 1, 2, 3, 4 and 5. These seven figures form a series. However, one of the five numbered figures does not fit into the series. Find that figure from the options given below.
1
(A) 5
(B) 2
2
3
4
5
(C) 3
(D) 4
18. Select a figure from amongst the options which will continue the same series as established by
C
(D)
C
19. Group the given figures into three classes using each figure only once.
(A) 1, 3, 6; 2, 4, 9; 5, 7, 8
(B) 1, 5, 7; 2, 8, 9; 3, 4, 6
(C) 1, 3, 9; 2, 5, 6; 4, 7, 8
(D) 1, 3, 9; 2, 4, 7; 5, 6, 8 SPACE FOR ROUGH WORK
Copyright©2015. Science Olympiad Foundation (SOF)
S
S
C
C
Problem Figures
C
TS
(C)
C
TS
C
(B)
C
TS
T
(A)
TS
TS
the five Problem Figures.
?
5
5th IMO - 2011
20. Arrange the given words in a meaningful sequence and then choose the most appropriate sequence from amongst the options provided below.
1.
Police
(A) 1, 2, 3, 4, 5
2. Punishment
3. Crime
(B) 3, 1, 5, 4, 2
4. Justice
(C) 3, 1, 4, 5, 2
5. Judgement (D) 5, 4, 3, 2, 1
Section II : Mathematical reasoning 21. The sum of two numbers is 12 and their product is 35. What is the sum of the reciprocals of these
numbers? 12 (A) 35
1 (B) 35
(C)
7 32
35 8
(D)
22. The ages of Mira, Tina and Sania are in the ratio 6 : 4 : 7 respectively. If the sum of their ages is 34 years, what is Sania's age?
(A) 12 years
(B) 10 years
(C) 18 years
(D) 14 years
23. Mehul plants 15376 apple trees in his garden and arranges them so that there are as many rows as there are apple trees in each row. The number of rows is _____.
(A) 124
(B) 126
(C) 134
(D) 144
Direction (Q. 24-25): Study the following table carefully to answer the following questions. Marks Obtained by Five Students in Three Subjects out of 100 Student
Subjects Math
Science
English
Mohit
94
83
74
Sameer
72
88
68
Rachna
86
75
66
Purab
90
61
82
Mansi
68
67
71
24. What are the average marks obtained by all the students in Math? (A) 137 (B) 82 (C) 75
(D) 98
25. What is the respective ratio of marks obtained by Mansi in Science and English together to the marks obtained by Rachna in the same subjects?
(A) 17 : 18
(B) 11 : 13
(C) 46 : 47 SPACE FOR ROUGH WORK
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 21 : 23
6
5th IMO - 2011
26. Find the value of
(A) 0.02
3
0.000064 . (B) 0.2
(C) 2
(D) None of these
27. Which of the following numbers is exactly divisible by 99?
(A) 114345
(B) 135792
(C) 3572404
(D) 913464
28. The difference between the place value and the face value of 6 in the numeral 856973 is _____.
(A) 973
(B) 6973
(C) 5994
(D) None of these
(C) 13.9
(D) 20
8 .6 × 5 .3 + 8 .6 × 4 .7 is _____. 29. The value of 4.3 × 9.7 − 4.3 × 8.7
(A) 3.3
(B) 6.847
30. Shreya bought an article and sold it for 125% per cent of its cost price. What was the cost price of the article, if Shreya sold it for ` 30,750?
(A) ` 24,600
(B) ` 25,640
(C) ` 24,250
(D) ` 23,200
31. What would be the cost of laying carpet on a floor which has length and breadth in the respective ratio of 32 : 21 and perimeter 212 feet, if the cost per square foot of laying carpet is ` 2.5 ?
(A) ` 6,720
(B) ` 5,420
(C) ` 7,390
(D) None of these
(C) 5
(D) 7
32. If 2n – 1 + 2n + 1 = 320, then n is equal to _____.
(A) 6
(B) 8
33. A sum of money invested at compound interest amounts to ` 800 in 3 years and to ` 840 in 4 years. The rate of interest per annum is _____.
1 (A) 2 2 %
(B) 4%
(C) 5%
2 (D) 6 3 %
34. In a simultaneous throw of two dice, what is the probability of getting a total of 7 ?
(A)
1 6
(B)
1 4
(C)
2 3
(D)
3 4
35. If 35% of a number is 12 less than 50% of that number, then the number is _____.
(A) 40
(B) 50
(C) 60 SPACE FOR ROUGH WORK
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 80
7
5th IMO - 2011
36. Smallest angle of a triangle is equal to two-third the smallest angle of a quadrilateral. The ratio of the angles of the quadrilateral is 3 : 4 : 5 : 6. Largest angle of the triangle is twice its smallest angle. What is the sum of second largest angle of the triangle and largest angle of the quadrilateral?
(A) 160°
(B) 180°
(C) 190°
(D) 170°
37. Soha purchased an item for ` 9,600 and sold it for loss of 5 per cent. From that money she purchased another item and sold it for gain of 5 per cent. What is her overall gain/loss?
(A) Loss of ` 36
x 38. If x
(A)
3/2
(B) Profit of ` 24
(C) Loss of ` 24
(D) None of these
16 (C) 25
8 (D) 27
= ( x 3 / 2 ) x , then the value of x is _____.
3 2
(B)
9 4
39. What number will come in place of question mark?
( 8 × 8 )1/ 2 + (9)1/ 2 = (?)3 + 8 − 340 (A) 7
(B) 19
(C) 18
(D) 9
40. Which of the following statements is INCORRECT? (A) All rhombuses are parallelograms. (B) All squares are not parallelograms. (C) All rectangles are not squares. (D) All squares are trapeziums.
Section III : Everyday Mathematics 41. The total area of a circle and a rectangle is equal to 1166 sq. cm. The diameter of the circle is 28 cm. What is the sum of the circumference of the circle and the perimeter of the rectangle if the length of the rectangle is 25 cm ? (A) 186 cm (B) 182 cm (C) 184 cm (D) 132 cm 3 th 42. of a number is 20 more than half of the same number. The required number is _____. 4 (A) 50 (B) 180 (C) 90 (D) 80 43. A merchant has 140 litres, 260 litres and 320 litres of three kinds of oil. He wants to sell the oil by filling the three kinds of oil separately in tins of equal volumes. The volume of such a tin is _____.
(A) 20 litres
(B) 13 litres
(C) 16 litres
SPACE FOR ROUGH WORK
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 70 litres
8
5th IMO - 2011
44. The ratio of ages of Kunal and Deepesh is 3 : 5. After 10 years this ratio becomes 5 : 7. What is the present age of Deepesh?
(A) 20 years
(B) 25 years
(C) 50 years
(D) 15 years
45. Out of a number of electronic items, Rohit purchases 60% coloured T.Vs. 5% of these are found
to be defective. The percentage of defective T.Vs in all is _____. (A) 3% (B) 6% (C) 12%
(D) Can't be determined
46. The difference between compound interest and simple interest for 3 years @ 20% p.a. is ` 152.
What is the principal lent in each case ? (A) ` 1200 (B) ` 1155
(C) ` 1187.50
(D) None of these
47. A can do a piece of work in 10 days, B can do it in 15 days. If they both work together they can
finish the work in _____. (A) 9 days (B) 8 days
(C) 10 days
(D) 6 days
48. A path of uniform width runs all around the inside of a rectangular field 116 metres by 68 metres
and occupies 720 square metres. Find the width of the path. (A) 1 metre (B) 1.5 metres (C) 2 metres
(D) 4 metres
49. Mohan gets 3 marks for each correct answer and loses 2 marks for each wrong answer. He attempts
30 problems and obtains 40 marks. The number of problems solved correctly is _____. (A) 10 (B) 15 (C) 20 (D) 25
50. Harry goes to a shop to buy a watch costing ` 1404 including sales tax of 8%. He asks the shopkeeper to reduce the price of the watch so that he can save an amount equal to the sales
tax. The reduction in the price of the watch is _____. (A) ` 108 (B) ` 104 (C) ` 112.32 SPACE FOR ROUGH WORK
Copyright©2015. Science Olympiad Foundation (SOF)
(D) None of these
Class 8 6th
SET A Year 2012
Copyright©2015. Science Olympiad Foundation (SOF)
2
6th IMO - SET A Section I : Logical Reasoning
1.
Latika delivers bottled water to stores in Delhi. She delivers to MTG's Bookstore every 6th day and to Sammy's Bookstore every 9th day. On Thursday the 4th, she will deliver water to both of these stores. How many days after that will she deliver to both stores on
the same day again? (A) 17
(B) 18
(C) 19
(D) 16
2.
Find out the correct letter pair from the options, to denote the same relationship among the group of letters as established between the sets given below.
(A) AC : RU
RT : WZ :: _______ : _______ (B) AB : PW (C) PR : LM
(D) TU : WX
3. If 'FRIIHH' stands for 'COFFEE', how will you write 'NOODLES'? (A) RSSHPIW (B) PQQFNGU (C) QRRGOHV (D) RSSHPIV 4. Terrorists who are not hard-core criminals are represented by ______. (A) 2
(B) 3
(C) 4
(D) 1
5. A tourist drives 10 km towards east and turns to the right hand and drives 3 km. Then he drives towards west (turning to his right) 3 km. He then turns to his left and drives 2 km. Finally he turns to his right and travels 7 km. How far is he from his starting point and in which direction would
he be ? (A) 10 km, East
6.
The relationship in the first set (1 & 2) of Problem Figures is given. Based on the same relationship,
(B) 5 km, South
(C) 8 km, West
(D) 5 km, West
find the suitable figure from answer figures to fit in the blank space of second set (3 & 4).
(A)
7.
Find the odd one amongst the set of figures of a series.
(A) Q
(B)
(B) R
(C)
(C) T
Copyright©2015. Science Olympiad Foundation (SOF)
(D)
(D) U
3
6th IMO - SET A 8.
Find a figure from the options in which Fig. (X) is embedded as its part. (A)
(B)
(C)
(D)
9.
Select the figure from the options which completes the Fig.(X)
(A)
(B)
(C)
(D)
10. Select the figure from the options which should complete the series formed by Problem Figures 1, 2, 3 and 4.
(A)
(B)
(C)
(D)
11. The Sharmas have three children Sunita, Sanjay and Sheela. Sunita is married to Sonil Mahajan and they have a son Shoban. Sheela marries Sanjay Bhandari and Vinit and Lily are their children. Sanjay
(Sunita's brother) is younger to Sunita but elder to Sheela. What is the surname of Shoban ? (A) Bhandari (B) Sharma (C) Mahajan (D) None of these
12. Study the following letter-number arrangement and answer the question given below. B 8 4 C R M 9 P D K W F A 2 E J 7 X U Q H L T Y 6 G S If every alternate letter/number is dropped in the above arrangement beginning with dropping '4' as first number to be dropped, which of the following will be third to the right of the fifth letter/
number from left end? (A) W (B) 2
(C) 7
(D) A
13. Find the missing number in Fig.(X).
(A) 56
(B) 58
(C) 60
(D) 62
14. If '>' denotes '+', '', and '='
denotes ' 8
−3 (D) 8.0 × 10 > 6 %
24. Which of the following describes a square root of 41 ? (A) Between 5 and 6 (B) Between 6 and 7 (C) Between 20 and 21 (D) Between 40 and 42 25. If 3x –1 + 3x +1 = 90, then x is equal to ______. (A) 1 (B) 3
(C) 2
(D) 0
26. How many cars were sold in the first quarter of the year ?
(A) 60
(B) 90
(C) 50
(D) 100
27. A merchant marks his goods at ` 300 and allows a discount of 25 %. If he still gains 12.5 %, then the cost price of article is _____. (A) ` 220 (B) ` 200 (C) ` 240 (D) ` 260 28. Consider the following statements. If a money is loaned at simple interest then the :
2 %. 3 (ii) money gets doubled in 5 years if the rate of interest is 20 %.
(iii) money becomes four times in 10 years if it gets doubled in 5 years.
(i) money gets doubled in 5 years if the rate of interest is 16
Of these statements : (A) (i) and (ii) are correct (C) (ii) alone is correct
(B) (iii) alone is correct (D) None of these
29. Evaluate (326541829)2 – 326541833 × 326541825.
(A) 4
(B) 326541819
(C) 32651838
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 16
6
6th IMO - SET A
30. The figure shows a triangle on a coordinate plane. Which of the following shows the triangle translated 3 units to the right and 1 unit down ?
(A)
(B)
(C)
(D)
31. Find the measure of largest angle of a quadrilateral if the measures of its interior angles are in
the ratio of 3 : 4 : 5 : 6. (A) 60° (B) 120°
5 x − 1 x − 1 1 32. Solve for x : x − 2 x − = + 3 3 2 3 (B) –31 (A) 2
(C) 90°
(D) Can't be determined
(C) – 20
(D) −
1 2
33. How many numbers are there between 200 and 800 which are divisible by both 5 and 7 ?
(A) 35
(B) 16
(C) 17
(D) Can't be determined
34. Find the area of the given figure.
(A) 128 m2
(B) 228 m2
(C) 328 m2
(D) 628 m2
35. In the given diagram, equilateral triangle EDC surmounts square ABCD. Find ∠BED represented by x, where EBC = a°.
(A) 45°
(B) 60°
(C) 30°
(D) None of these
Copyright©2015. Science Olympiad Foundation (SOF)
7
6th IMO - SET A
Direction (36 & 37) : The Pie graph depicts the budget of a family 'X '. The total monthly income of the family is ` 3080.
36. How many degrees should be there in the central angle of the sector for miscellaneous expenses?
(A) 60 degrees
(B) 55 degrees
(C) 46 degrees
(D) 36 degrees
37. How much total expenses are incurred on food, clothing and conveyance every month ?
(A) ` 1794
(B) ` 1684
(C) ` 1664
(D) ` 1694
38. The largest four-digit number which is a perfect cube, is ______. (A) 8000 (B) 9261 (C) 9999
(D) None of these
39. If x : y = 5 : 2, then (8x + 9y) : (8x + 2y) is ______. (A) 22 : 29 (B) 26 : 61 (C) 29 : 22
(D) 61 : 26
40. Closure property for rational numbers is satisfied in case of _______. (A) Addition (B) Subtraction (C) Multiplication
(D) All of these
Section III : Everyday Mathematics 41. For a journey the cost of a child ticket is 1/3rd of the cost of an adult ticket. If the cost of the tickets for 4 adults and 5 children is ` 85, the cost of a child ticket is ______.
(A) ` 5
(B) ` 6
(C) ` 10
(D) ` 15
42. The ratio of present ages of Rahul and Deepesh is 3 : 5. 10 years later this ratio becomes 5 : 7.
What is the present age of Deepesh ? (A) 20 years (B) 50 years
(C) 25 years
(D) 40 years
43. A person wants to reduce the trade tax so he calculates his profit on the sale price instead of on the cost price. In this way by selling an article for ` 280 he calculates his profit as 14 is the actual profit percentage?
(A) 20 %
(B) 16.66 %
(C) 25 %
2 %. What 7
(D) None of these
44. A rectangular tank 25 cm long and 20 cm wide contains water to a depth of 5 cm. A metal cube of side 10 cm is placed in the tank so that one face of the cube rests on the bottom of the tank.
Find how many litres of water must be poured into the tank so as to just cover the cube ? (A) 1 L (B) 1.5 L (C) 2 L (D) 2.5 L
45. In the morning batch at 'a school' we have observed that when five students took seat on each bench, 4 students remained unseated. But when eleven students took seat per bench, 4 benches
remained vacant. The number of students in the morning batch were? (A) 55 (B) 48 (C) 26
(D) 44
46. On the April 1, 2012 Megha's salary increased from ` 10,000 to ` 16,000. Simultaneously the rate of income tax decreased by 37.5%. So the amount of income tax paid by Megha remains constant,
what is the amount of income tax paid by her ? (A) ` 3000 (B) ` 6000
(C) ` 1600
Copyright©2015. Science Olympiad Foundation (SOF)
(D) Can't be determined
8
6th IMO - SET A
47. Mr. Gupta drives at a speed of 60 km/hr for 6 hours from Chandigarh to Delhi. Mr. Verma drives his car at an average speed of 45 km/hr for the same journey. How much time does Mr. Verma
take to complete the journey? (A) 7 hrs (B) 8 hrs
(C) 9 hrs
(D) 11 hrs
48. The volume of a cylinder is 48.125 cm 3, which is formed by rolling a rectangular paper sheet along the length of the paper. If a cuboidal box (without any lid i.e., open at the top) is made from the same sheet of paper by cutting out the square of side 0.5 cm from each of the four corners of
the paper sheet, then what is the volume of this box ? (B) 38 cm3 (C) 19 cm3 (A) 20 cm3
49. Mrs. Priya earns 18000 per month. She spends
things. The amount she saves is _____. (A) ` 7120 (B) ` 5250
(D) 28 cm3
1 7 on household items and on rest of the 8 12 (C) ` 5520
(D) ` 6562.5
50. Nita walks from her house 160 metres north and from there 630 metres west to visit her friend. While coming back, she walked diagonally from her friend's house, back to her home. What distance
did she walk while returning ? (A) 730 m (B) 800 m
(C) 1250 m SPACE FOR ROUGH WORK
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(D) 650 m
Class 8 6th
SET B Year 2012
Copyright©2015. Science Olympiad Foundation (SOF)
2
6th IMO - SET B Section I : Logical Reasoning
1.
Which one of the following Venn diagrams correctly illustrates the relationship among the classes : Diseases, Leprosy, Scurvy?
(A)
(B)
(C)
(D)
2. If '×' means '+', '÷' means '–', '–' means '×' and '+' means '÷', then 14 × 3 ÷ 11 – 3 + 121 = ____.
3 (A) 14 9
(B) 2
(C) 16
8 11
(D) 5
3. In a certain code, '256' means 'you are good'; '637' means 'we are bad' and '358' means 'good and
bad'. Which of the following numbers represents 'you' in that code ? (A) 2 (B) 5 (C) 8 (D) 3
4.
Select a figure from amongst the options which will continue the same series as established by the four Problem Figures.
Problem Figures ? P
R
S
(C)
(B)
(A)
Q
(D)
5.
Count the number of triangles in the given figure. (A) 12 (B) 14 (C) 16 (D) None of these
6.
Which of the following option figures will complete the figure (X)?
? Fig.(X)
(A)
(B)
(C)
(D)
7. Choose the options which most closely resembles the mirror-image of the given combination if the mirror is placed vertically to the right. QUANTITIES N S (B) SETITNAUQ (C) QUA TITI E
QUANTITIES
(A)
8.
Select the related number from the given options. 5 : 100, 4 : 64 :: 4 : 80, 3 : ? (A) 26 (B) 48 (C) 60 Copyright©2015. Science Olympiad Foundation (SOF)
(D)
(D) 54
3
6th IMO - SET B
9. If the following words are arranged in the alphabetical order, which word will appear at the end?
(A) Olympic
(B) Olympia
(C) Oval
(D) Ovulet
10. From his house, Vishal went 15 km to the North. Then he turned West and covered 10 km. Then, he turned South and covered 5 km. Finally, turning to East, he covered 10 km. How far and in which direction is he from his house ?
(A) 10 km East
(B) 10 km West
(C) 10 km North
(D) 10 km South
11. In a march past, seven persons are standing in a row. R is standing left to Q but right to P. O is standing right to N and left to P. Similarly, S is standing right to Q and left to T. Find out the person standing in the middle.
(A) P
(B) Q
(C) R
(D) O
12. Select a figure from the given options in which Figure (X) is embedded as its part.
(A)
(B)
(C)
(D)
13. Two different positions of a dice has been shown below. If 4 dots are at the top what number will be just below it?
(A) 1
(B) 3
(C) 4
(D) 5
14. Ajit is fatter than Ranjit who is thinner than Bhushan. Mohan is thinner than Ajit but fatter than Bhushan. Two other men are fatter than Ajit. Who is the thinnest?
(A) Ajit
(B) Ranjit
(C) Bhushan
(D) Mohan
15. Five students participated in an examination and each scored different marks. Nidhi scored higher than Mamta. Kavita scored lower than Prashant but higher than Nidhi. Anil's score was between Mamta and Nidhi. Which of the following pairs represents the highest and the lowest scorers respectively?
(A) Nidhi, Kavita
(B) Kavita, Mamta
(C) Anil, Kavita
(D) Prashant, Mamta
16. Mohit is the brother of Beena. Beena is the wife of Raj. Raj is the brother of Megha. What is the relation of Megha to Mohit?
(A) Sister
(B) Sister-in-law
(C) Mother-in-law
(D) No specific relation
17. How many consonants are there in the below sequence which are immediately preceded by a symbol and immediately followed by a digit? E G 4 B H 7 5 @ K 8 D N £ Q Z $ W 3 C 1 9 * L B 2 S 6
(A) One
(B) Two
(C) Three
Copyright©2015. Science Olympiad Foundation (SOF)
(D) None
4
6th IMO - SET B
18. A pile of cubes of equal size is arranged as shown in the figure. Now the block is dipped into a bucket full of red paint so that only the surfaces of the block get coloured. How many cubes are without any colour?
(A) 20
(B) 14
(C) 30
(D) 18
19. If it is possible to make a meaningful word with the second, third, fifth and eighth letters of the word PARAGRAPH which of the following will be second letter of that word? If more than one such
word can be made, give X as the answer. If no such word can be made, give M as the answer. (A) X (B) M (C) G (D) P
20. The triangle, rectangle and circle shown here respectively represent the urban, hard working and educated people. Which one of the areas marked I-VII is represented by the urban hard working people who are not educated?
I III
II
V
VI
(A) II
(B) I
IV VII (C) IV
(D) III
Section II : Mathematical reasoning 21. What is the value of the given expression ? ( 16 )2 + 64 3
(A) 4
(B) 8
512 − 3 64 (C) 16
(D) 6
22. Which of the following pictures appears to have rotational symmetry ?
(A)
(B)
(C)
(D) None of these
23. Aisha needs to buy 300 sheets of construction paper. The office supply store sells construction paper in the following packages. Which of the following is the least expensive way
Paper Purchase Package Number of Sheets Price
for Aisha to buy 300 sheets of construction paper ? (A) 6 packages of paper W (B) 4 packages of paper X (C) 3 packages of paper Y (D) 2 packages of paper Z
Copyright©2015. Science Olympiad Foundation (SOF)
W
50
` 4.50
X
75
` 5.10
Y
100
`10.75
Z
150
` 12.25
5
6th IMO - SET B 24. Which of the following statements is incorrect for rational numbers ?
(A) The rational number 0 is the additive identity for rational numbers.
(B) The rational number 1 is the multiplicative identity for rational numbers.
(C) Subtraction is associative for rational numbers.
(D) There are infinite rational numbers between any two given rational numbers.
25. Solve for x :
(A)
1 2
3x + 4 x +1 = 6x + 7 2x + 3 (B) −
5 4
(C) 1
(D) 3
Direction (26 & 27) : A bar diagram depicting the changes in the students strength of a college in four faculties from 1990-91 to 1992-93 is shown.
26. How many times was the total strength of the strength of Commerce students in 1991-92 ? (A) 3 times (B) 4 times (C) 5 times (D) 6 times 27. How much percent was the increase in Science students in 1992-93 over 1990-91 ? 2 (D) 75% (A) 50% (B) 150% (C) 66 % 3 28. Find the area of the field ABCDEFGA in which AL = 30 m, AM = 70 m, AN = 90 m, AO = 110 m, AE = 135 m, AB = 36 m , LG = 40 m, NF = 42 m, MC = 54 m, and OD = 46 m.
(A) 9010 m2
(B) 8000 m2
(C) 8670 m2
(D) 9730 m2
29. The population of a country is 3.2 × 106. There are 8 × 105 children. Find the number of adults.
(A) 3 × 103
(B) 8 × 103
(C) 2.4 × 106
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 2.4 × 105
6
6th IMO - SET B
30. In the kite ABCD, AD = CD = 8 cm, ∠ADC = 60°, ∠DCB = 130° and AB = CB. Find ∠ABC.
(A) 50°
(B) 40°
(C) 60°
(D) 25°
31. A rectangular picture is 16 cm long and 10 cm side. It has a 2 cm border around it as shown in the figure. Calculate the area of the border, giving your answer in square millimetres.
(A) 1200 mm2
(B) 120 mm2
(C) 12000 mm2
32. The number of edges of the given figure is ______.
(A) 18
(B) 12
(C) 14
(D) 16
(D) 120000 mm2
33. In a parallelogram,
Statement 1 : Diagonals bisect each other.
Statement 2 : Diagonals divide the parallelogram into two triangles.
(A) Only statement 1 is true. (C) Both statement 1 and 2 are true.
(B) Only statement 2 is true. (D) Both statement 1 and 2 are false.
34. A bag contains 4 red, 3 pink and 8 white balls. One ball is drawn at random. Find the probability that the ball drawn is not red.
(A)
1 5
(B)
8 11
1 1 4 35. If x + = 5 , find the value of x + 4 . x x (A) 8 (B) 3
(C)
11 15
(C) 5
(D)
3 11
(D) 7
1 36. A sum of ` 2540 is lent out into two parts, one at 12 % and another one at 12 % . If the total 2 annual income is ` 311.60, the money lent at 12 % is _____.
(A) ` 1180
(B) ` 1360
(C) ` 1240
(D) ` 1340
37. The length of longest pole that can be placed on the floor of a room is 10 m and the length of the longest pole that can be placed in the room is 10 2 m. The height of the room is _____.
(A) 6 m
(B) 7.5 m
(C) 8 m
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 10 m
7
6th IMO - SET B th
1 38. A tree increases annually by of its height. By how much will it increase after 2 years, if it 8 stands today 64 cm high? (A) 72 cm (B) 74 cm (C) 75 cm (D) 81 cm 39. What is the smallest number by which 3600 be divided to make it a perfect cube? (A) 9 (B) 50 (C) 300 (D) 450 40. If x : y = 2 : 3 and 2 : x = 1 : 2, then the value of y is ______. 1 (A) 4 (B) 6 (C) 3
(D)
3 2
Section III : Everyday Mathematics 41. A boat goes downstream and covers the distance between two ports in 4 hours, while it covers the same distance upstream in 5 hours. If the speed of the stream is 2 km/hr, find the speed of boat in still water.
(A) 16 km/hr
(B) 18 km/hr
(C) 20 km/hr
(D) 15 km/hr
42. Garima wants to plant 50625 roses and arranges them in such a way that there are as many rows
as there are roses in a row. The number of roses in a row are _____. (A) 365 (B) 165 (C) 625
(D) 225
43. Latika owns a mobile worth ` 10000. She sells it to Priya at a profit of 10% based on the worth of the mobile. Priya sells the mobile back to Latika at a loss of 10%. In this transaction Latika gets ______.
(A) No profit no loss
(B) Profit of ` 1000
(C) Profit of ` 1100
(D) Loss of ` 1100
44. A trader lists his articles 20% above C.P. and allows a discount of 10% on cash payment. His gain
percent is ______. (A) 10%
(B) 8%
(C) 6%
(D) 5%
45. The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 m3.
The breadth of the wall is ______. (A) 30 cm (B) 40 cm
(C) 22.5 cm
(D) 25 cm
46. A swimming pool is 25 m long, 15 m broad and 5 m deep. Find the cost of cementing its floor
and the walls at the rate of ` 10 per sq. metre. (A) ` 3840 (B) ` 7750
(C) ` 6960
(D) None of these
47. The value of a machine depreciates every year at the rate of 10% on its value at the beginning of
that year. If the present value of the machine is ` 729, its worth 3 years ago was _____. (B) ` 800 (C) ` 1000 (D) ` 750.87 (A) ` 947.10
48. The population of the world in 2000 was 6.5 × 10 9. It is estimated that by 2070 the population of
the world will be 1.03 × 1010. Find the estimated increase in the population from 2000 to 2070. (B) 3.8 × 109 (C) 10.3 × 109 (D) 3.8 × 108 (A) 4.8 × 108
49. Pratik had ` 425.82 in his account. How much does he have in his account after he makes a deposit
of ` 120.75 and a withdrawal of ` 185.90? (A) ` 126.82 (B) ` 538.82
(C) ` 630.76
Copyright©2015. Science Olympiad Foundation (SOF)
(D) ` 360.67
8
6th IMO - SET B
50. Three different containers contain different qualities of mixtures of milk and water, whose measurements are 403 kg, 434 kg and 465 kg. What biggest measure must be there to measure
all the different quantities exactly? (A) 1 kg (B) 7 kg
(C) 31 kg SPACE FOR ROUGH WORK
Copyright©2015. Science Olympiad Foundation (SOF)
(D) 41 kg
Class 8 7th
SET A Year 2013
Copyright©2015. Science Olympiad Foundation (SOF)
2
7th IMO - Set A
logical reasoning 1.
Select a figure from the options which will continue the series established by the four problem figures.
1. 3. 5. A. B. C. D.
A.
5.
If in a certain code ‘56431’ is written as ‘RSHTU’ and ‘98270’ as ‘MLKPA’, then how will ‘9517’ be written in the same code?
B.
C.
A. B. C. D.
6.
Raman walks 50 m North. Then he turns right and walks 30 m. Then he turns right and walks 35 m. Then he turns left and walks 15 m. Then he again turns right and walks 15 m. In which direction and how many metres away is he from his original position?
A. B. C. D.
7.
Out of the 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.
A. B. C. D.
8.
How many dots lie opposite to the face having three dots, when the given figure is folded to form a cube?
A. B. C. D.
D.
2.
Pointing to a man in a photograph, a woman says, "He is the only son of the only daughter-in-law of my only son's father." How is the man related to the woman?
A. B. C. D.
Son Father Son-in-law Grandson
3.
Which of the following options will complete the pattern in figure (X)?
Figure (X)
A.
B.
C.
D.
4.
Arrange the given words in a meaningful sequence and then choose the most appropriate sequence.
Cutting Vegetable Cooking 1, 2, 4, 5, 3 3, 2, 5, 1, 4 4, 3, 1, 5, 2 5, 3, 2, 1, 4
2. 4.
Dish Market
MURP MRUP MRPU MRPT
45 30 30 45
metres West metres East metres West metres East
a b c d
2 4 5 6
Copyright©2015. Science Olympiad Foundation (SOF)
3
7th IMO - Set A 9.
Select a figure from the options, which satisfies the same conditions of placement of the dot as in figure (X).
Figure (X)
A.
B.
C.
12. Study the following arrangement carefully and answer the question given below: R DAK 5 B I 2 M J E N 9 7 U Z V 1 W 3 H 4 FY8 P6 T G How many such consonants are there in the above arrangement each of which is immediately preceded by a vowel and immediately followed by a number?
A. B. C. D.
None One Two Three
13. There is a square transparent sheet with a given pattern is given. Figure out from the options as to how the pattern would appear when the transparent sheet is folded along the dotted line.
A.
B.
C.
D.
D.
10. Given question consists of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Fig. (Z) shows the manner in which the folded paper has been cut. Choose a figure from the options which would most closely resemble the unfolded form of piece of paper.
14. Which of the following Venn diagrams best illustrates the relationship among the three classes : "Truck, Ship, Goods"?
A.
B.
C.
D.
11. If '×' means 'is father of ', '+' means 'is sister of ', '–' means 'is brother of ', and '÷' means 'is mother of ', then which of the following statements means 'S is grand-daughter of P'?
A. B. C. D.
P×T+R÷S P÷Q–R÷S–T P×R–T×S P÷Q–R×S+T
A.
B.
C.
D.
15. In a certain code language 'in pe ba' means 'he is late', 'le ba se' means 'she is early' and 'pa ta in' means 'he leaves soon'. Which word in that language means late ?
A. B. C. D.
pe in ba Data is inadequate
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4
7th IMO - Set A
16. Select the pair that has a relationship similar to given pair.
A.
B.
C.
D.
A.
B.
C.
D.
100 361 389 400
19. Select a figure from the options which is the mirrorimage of the Problem Figure.
17. Select a figure from the options in which figure (X) is embedded as one of its part.
A. B. C. D.
A.
B.
C.
D.
20. Minimum number of straight lines required to form the given figure is __________.
18. Which number will replace the question mark in number pattern?
A. B. C. D.
22 20 18 24
Mathematical reasoning 21. The given figure shows a cuboid with a total surface area 202 cm2 . Find the volume of cuboid.
D.
200 cm3
n +1 + 7 ⋅ 3n−1 22. The simplified value of 2 ⋅ 3 is 1−n
A. B. C.
72 cm3 36 cm3 180 cm3
A. B. C. D.
1 3 –1 0
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1 3n + 2 − 2 3
5
7th IMO - Set A 23. The pie chart shows a percentage breakdown of 1000 votes in student elections. How many votes did Sushanth receive?
A. B. C. D.
450 396 390 410
29. In the given figure, ABCD is a rhombus and ∠BCD = 80°. Find x and y respectively.
A. B. C. D.
550 350 330 450
24.
The A. B. C. D.
division of rational numbers is Commutative Associative Neither commutative nor associative Both A and B
25. If (a + b) : (b + c) : (c + a) = 6 : 7 : 8 and a + b + c = 14, then find the value of c.
A. B. C. D.
6 8 14 7
1 26. If 4x + 4x + 4x + 4x + 4x + 4x + 4x + 4x = 512 , then −3 ? what is the value of x A. 0.50 B. 0.75 C. –0.75 D. –4.25 27. Consider the given diagram. (figure not drawn to scale)
If the area of ABCD is equal to the area of DEHG, then the ratio of area of shaded to unshaded part is ______ .
A. B. C. D.
72 : 113 1:5 26 : 113 36 : 113
A. B. C. D.
40°, 70°, 80°, 50°,
20° 50° 30° 40° 2
1 1 3 2 × 1 + 1 ÷ 3 3 is _________. 4 3 8
30. The value of
A.
B.
C.
D.
1 3 1 4 6 1 1 3 1 5 2 3
31. Find the square root of 6
A. B. C. D.
2.410 2.529 2.113 2.482
115 . 289
32. Three numbers are in the ratio 3 : 2 : 1. The sum of their cubes is 246924. Find the largest number.
A. B. C. D.
51 38 61 57
33. The area of a rectangle is given by 6x2y + 4y 2 x and the width of the rectangle is given by 2xy. Find the perimeter of rectangle.
A. B. C. D.
6x 3x 8x 6x
+ + + +
8y 4y 6y 4y
+ + + +
2xy 2xy 4xy 4xy
34. Difference between smallest 4-digit perfect square and greatest 4-digit perfect square is
28. Find the number of coins, 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder with a height of 10 cm and a diameter of 4.5 cm.
A. B. C. D.
8777 1012 9801 7777
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6
7th IMO - Set A
35. Which solid would be formed by the given net?
A. B. C. D.
Triangular Pyramid Square Pyramid Hexagonal Pyramid Rectangular Pyramid
everyday Mathematics 36. A dairyman pays ` 6.40 per litre of milk. He adds water and sells the mixture at ` 8 per litre, thereby making 37.5% profit. The proportion of water to milk received by the customers is
A. B. C. D.
1 1 1 1
: : : :
10 12 15 20
A. B. C. D.
30 60 72 90
birds birds birds birds
A. B. C. D.
A. B. C. D.
15 16 18 25
` ` ` `
12,000 13,000 11,000 14,000
40. A man walking at the speed of 4 km/hr crosses a square field diagonally in 3 minutes. The area of the field is
A. B. C. D.
57 67 77 87
A. B. C. D.
5 years 10 years 20 years 37 years th
39. Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond five years. If he pays a total interest of ` 11,400 at the end of nine years, how much money did he borrow?
A. B. C. D.
9 43. Monika purchased a pressure cooker at of 10 its selling price and sold it at 8% more than its S.P.
38. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is
42. Hitesh is 40 years old and Rohit is 60 years old. How many years ago was the ratio of their ages 3 : 5?
37. A fires 5 shots to B’s 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed
the number of members in the group is
Find her gain percent.
A. B. C. D.
20% 10% 30% 40%
44. Sanket earns twice as much in the month of March as in each of the other months of the year. What part of his entire annual earnings was earned in March?
A.
1 7
B.
1 6
C.
2 11
D.
2 13
45. A pineapple costs ` 7 each. A watermelon costs ` 5 each. X spends ` 38 on these fruits. The number of pineapples purchased is
18000 m2 19000 m2 20000 m2 25000 m2
41. A group of students decided to collect as many paise from each member of the group as is the number of members. If the total collection amounts to ` 59.29,
A. B. C. D.
2 3 4 Data is inadequate
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7
7th IMO - Set A
ACHIEVERS SECTION 46. Select the incorrect match with respect to the representation of numbers on the number line.
A.
Natural Numbers
The line extends indefinitely only to the right side of 1.
B.
Whole Numbers
The line extends indefinitely to the right, but from 0. There are no numbers to the left of 0.
C.
D.
Integers
Rational Numbers
The line extends indefinitely on both sides and you can see numbers between –1, 0; 0, 1, etc.
A. B. C. D.
I
Only Only Both Both
II
I right II right I and II are right I and II are wrong.
48. A school has 8 tables of dimensions 1 m by 1 m, 26 tables of dimensions x m by 1 m and 15 tables of dimensions x m by x m. All the tables are of equal height. Based on this information answer the question given below: If the tables are placed together to form a large rectangular table, then the dimension of the table formed is __________.
A. B. C. D.
(3x (3x (5x (5x
+ – – –
4)(5x 4)(5x 4)(4x 4)(5x
+ 2) – 4) – 4) + 4)
49. Study the two statements given below carefully. Statement 1 : A pyramid is a polyhedron whose base and top are congruent polygons and whose other faces i.e., lateral faces are parallelograms in shape.
The line extends indefinitely on both sides and you can see numbers between –1, 0; 0, 1, etc.
47. Which of the following Venn diagrams is right?
Statement 2 : A prism is a polyhedron whose base is a polygon (of any number of sides) and whose lateral faces are triangles with a common vertex.
A. B. C. D.
Statement-1 is true and Statement-2 is false. Statement-1 is false and Statement-1 is true. Both the statements are true. Both the statements are false.
50. Match the solids in Column-I with their top view in Column-II.
(a)
(b)
(c)
(d)
A. B. C. D.
Column-I
Column-II
(p)
(q)
(r)
(s)
(a) (a) (a) (a)
→ → → →
(p); (q); (q); (q);
(b) (b) (b) (b)
SPACE FOR ROUGH WORK
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→ → → →
(q); (c) → (r); (d) → (s) (p); (c) → (r); (d) → (s) (r); (c) → (s); (d) → (p) (r); (c) → (p); (d) → (s)
Class 8 7th
SET B Year 2013
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2
7th IMO - Set B
logical reasoning 1.
There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the options that would replace the question mark (?) in figure 4. Problem figure
A.
B.
2.
4.
If each of the letters in the English alphabet is assigned odd numerical value beginning A = 1, B = 3 and so on, what will be the total value of the letters of the word INDIAN?
A. B. C. D.
5.
Find out how will the key figure (X) look like after 90° rotation clockwise?
A.
B.
C.
D.
6.
Select a suitable figure from the options which will replace the question mark so that a complete series is formed.
A.
B.
C.
D.
7.
If stands for ‘addition’, stands for ‘subtraction’, stands for ‘division’, stands for ‘multiplication’ and stands for ‘equal to’, then which of the following options is correct?
86 88 89 96
C.
D. A set of figures carrying certain numbers, is given. Assuming that the number in each set follows a similar pattern, find the missing number.
A. B. C. D.
3.
Study the diagram given here and answer the question that follows.
35 48 72 120
Workers who are members of Union.
Workers who are hardworking. Workers who are experienced
Number 4 represent :
A. B.
C.
D.
Members of the Union. Members of the Union as well as hardworking and experienced workers. Hardworking and experienced workers not members of the Union. Hardworking workers members of the Union who are not experienced.
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3
7th IMO - Set B
A. B. C. D.
7 3 5 2
43 6 1 4 62365 7324 5626
8.
The digits of each of the following five numbers are written in reverse order and five new numbers are obtained : 513 726 492 865 149 Which of the following will be the third digit of the second highest new number?
A. B. C. D.
1 5 7 8
9.
A solid cube of each side 8 cms, has been painted red, blue and black on pairs of opposite faces. It is then cut into cubical blocks of each side 2 cms.
How many cubes have no face painted?
A. B. C. D.
0 4 8 12
10. Select a figure from amongst the options which when placed in the blank space of figure (X) would complete the pattern.
A.
B.
3. 4. The A. B. C. D.
S is the brother of T. T is the daughter of Q. grandmother of S is ____. P Q R T
12. In a dinner party both fish and meat were served. Some took only fish and some only meat. There were some vegetarians who did not accept either. The rest accepted both fish and meat. Which of the following logic diagrams correctly reflects this situation?
A.
B.
C.
D.
13. The given question consist of a set of three figures 1, 2 and 3 showing a sequence of folding of a piece of paper. Figure (3) shows the manner in which the folded paper has been cut. Choose a figure from the options which would most closely resemble the unfolded form of piece of paper.
C.
A.
B.
C.
D.
D.
11. Given that
1. 2.
P is the mother of Q. R is the son of P.
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4
7th IMO - Set B
14. Count the number of pentagons in the given figure.
A. B. C. D.
16 12 8 None of these
15. There is a definite relationship between figures 1 and 2. Establish a similar relationship between figures 3 and 4 by selecting a suitable figure from the options that would replace the question mark (?) in figure (4).
A.
B.
C.
D.
A. B. C. D.
25 125 156 625
641228742153862171413286 How many pairs of alternate numbers have a difference of 2? A. B. C. D.
From the original position given in the above figure, A and B move one arm length clockwise and then cross over to the corner diagonally opposite; C and D move one arm length anti-clockwise and cross over the corner diagonally opposite. The original configuration ADBC has now changed to
A. B. C. D.
CBDA BDAC DACB ACBD
17. Study the number series given below and answer the question that follows.
19. Select the one from the options which satisfies the same conditions of placement of the dots as in figure (X).
16. Find the missing number in the given number pattern.
18. The following question is based on the diagram given below showing four persons stationed at the four corners of a square region as shown.
One Two Three Four
A.
B.
C.
D.
20. Five girls are sitting in a row facing south. Priya is not adjacent to Shalini or Niti. Priti is not adjacent to Shalini and is at extreme right end. Priya is adjacent to Mahi. Mahi is at the middle in the row. Then, Priti is adjacent to whom out of the following?
A. B. C. D.
Priya Shalini Niti Mahi
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5
7th IMO - Set B
Mathematical reasoning 21. If 3x+y = 81 and 81x–y = 38, then find the values of x and y respectively.
A. B. C. D.
3, 1 1, 3 –1, 3 –1, –3
22. The given figure shows a set of concentric squares. If the diagonal of the innermost square is 2 units, and if the distance between the corresponding corners of any two successive squares is 1 unit, find the difference between the areas of the eighth and the seventh squares, counting from the innermost square.
A. B. C. D.
38 40 30 20
units units units units
Step-3 : D is at a distance of 6.5 cm on CY. With A as centre, draw an arc of length 6.5 cm. It cuts CY at D.
Step-4 : Complete the quadrilateral ABCD. ABCD is the required quadrilateral.
A. B. C. D.
27. Which of the following prime factorisation is used to find the cube root of 13824?
A. B. C. D.
5 5 5 5
: : : :
16 9 10 8
24. Simplify : æ a b c ö÷æç a 2 b 2 c 2 ab bc ca ö÷ çç + - ÷ç + + - + + ÷÷ çè 2 8 5 ÷øçè 4 64 25 16 40 10 ø
A.
a3 b3 c3 3abc + + 8 512 125 80
B.
a3 b3 c3 3abc + + + 8 512 125 80
C.
3abc a 3 b3 + c3 8 512 80
D.
a3 + b3 + c3 – 3abc
25. Factorize x p – 8y p – 4x q + 32y q . 3 2
A. B. C. D.
(p (p (p (p
A. B. C. D.
2×2×2×2×2×2×2×2×2×3×3×3 2×2×2×2×2×2×2×2×2×2×3×3×3 3×3×3×2×2×2×2×2×2×2×2 3×3×3×3×2×2×2×2×2×2×2×2
28. Using Euler’s formula, find the value of P, Q and R.
23. If x : y = 5 : 12, y : z = 8 : 3 and z : w = 9 : 16 then find x : w.
Step-1 Step-2 Step-3 Step-4
3 2
3 2
3 2
+ 2q)(p – 2q) (x2 – 2xy + 4y2) – 2q)(x2 + 2xy + 4y2)(x – 2y) + 2q)(p – 2q)(x – 2y)(x2 + 2xy + 4y2) + 2q)(x2 + 2xy + 4y2)
26. Identify the wrong step in the construction of quadrilateral ABCD, where AB = 4 cm, BC = 5 cm, CD = 6.5 cm, ∠B = 105° and ∠C = 80°. Step-1 : Start with taking BC = 5 cm. On B, draw an angle of 105° along BX and 80° along CY. Step-2 : Locate A 4 cm away on BX. We now have B, C and A. The fourth point D is on CY.
Faces
8
5
Q
Vertices
P
6
13
Edges
12
R
30
A. B. C. D.
P 6 6 7 9
Q 19 18 20 6
R 9 10 9 20
29. Which of the following does not vary directly?
A.
B. C. D.
30. The is A. B. C. D.
Speed of a vehicle and time taken to cover a fixed distance Number of days worked and amount of earning Number of books and their price Number of units of current used and amount of charge for consumption largest 5-digit number exactly divisible by 91 99921 99918 99981 99971
31. The simple interest on a certain sum of money for 2 years at 6% per annum is ` 300. The compound interest at the same rate and for the same time will be:
A. B. C. D.
` ` ` `
310 308 307 309
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6
7th IMO - Set B
32. In a class of 100 students, 30% of the students offered English, 20% offered Hindi. If a student is selected at random, what is the probability that he has offered English? 3 A. 2 B. 4 5 3 3 C. D. 10 5
4 34. If x +
A. B. C. D.
64 52 40 38
1 x
4
= 194, find the value of x3 +
1 x3
.
35. Which of the following is the net of the given cube (not drawn to scale)?
33. Look at the given data. 21, 10, 30, 22, 33, 5, 37, 12, 12, 25, 42, 15, 39, 26, 32, 18, 27, 28, 19, 29, 35, 31, 24, 36, 18, 20. The frequency distribution is given below : P Groups Tally marks Frequency 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Groups 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60
I IIII II IIII IIII IIII III I
1 7 9 8 1 0
Q Tally Marks
Frequency
I IIII II IIII IIII IIII II I I
1 7 9 7 1 1
Which of the following tables represent the data? A. Only P B. Only Q C. Neither P nor Q D. None of these
A.
B.
C.
D.
everyday Mathematics 36. The total of the ages of Jiya, Kunal and Sagar is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Sagar? A. 24 years B. 32 years C. 34 years D. 38 years 37. Two tailors X and Y are paid a total of ` 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? A. ` 200 B. ` 250 C. ` 300 D. None of these
38. Rohan and Shivam are working on an assignment. Rohan takes 6 hours to type 32 pages on computer, while Shivam takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
A. B. C. D.
7 8 8 8
hours 30 minutes hours hours 15 minutes hours 25 minutes
39. A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds.
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7
7th IMO - Set B
A. B. C. D.
16 : 5 16 : 15 6:5 15 : 1
40. Sam invested ` 15,000 at the rate of 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be
A. B. C. D.
` ` ` `
16,500 16,525.50 16,537.50 18,150
41. A housing society has been allotted a square piece of land measuring 2550.25 sq. m. What is the side of the plot?
A. B. C. D.
50.25 m 50.5 m 50.65 m 50.05 m
42. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
A. 20 hours B. 18 hours
C. D.
25 hours 19 hours
43. Arun and Sajal are friends. Each has some money. If Arun gives ` 30 to Sajal, then Sajal will have twice the money left with Arun. But, if Sajal gives ` 10 to Arun, then Arun will have thrice as much as is left with Sajal. How much money does each have?
A. B. C. D.
` ` ` `
50, 42, 50, 34,
` ` ` `
190 24 90 62
44. One-third of Mohit’s marks in Mathematics exceeds a half of his marks in English by 30. If he got 240 marks in the two subjects together, how many marks did he get in English?
A. B. C. D.
42 50 60 180
45. A man walked diagonally across a square region. Approximately, what was the percent saved by not walking along the edges?
A. B. C. D.
20 24 30 33
% % % %
ACHIEVERS SECTION 46. Which of the following is correct with respect to the given solids?
I
47. Study the two statements carefully and choose the correct answer. 2
II
æ 25 ö÷0 æ 64 ö÷- 3 1 ÷÷ Statement 1 : Solution of çç ÷ ¸ + çç 1/ 4 çç 3 çè125 ÷ø (256 625) è 64 ÷ø 3 is 2 Statement 2 : Law of Indices is
Top view A. (I)
B. (I)
Front view (I)
(II)
Side view
æ a ö÷m a m -n 1n n çç ÷ = and a 0 = 1. = , = , a a a èç b ÷ø an bm 1
(II)
(I)
A. B. C. D.
Both the Statements are true. Statement-1 is false and Statement-2 is true. Both the Statements are false. Statement-1 is true and Statement-2 is false.
48. Which of the following statements is correct?
C. (II)
(I)
(II)
D. (I)
(II)
(II)
A. B. C.
D.
Subtraction is commutative for integers. Division is associative for rational numbers. Multiplication is not associative for whole numbers. Addition is closed for natural numbers.
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8
7th IMO - Set B
49. In the given diagram, ABC, BDE and CDF are straight lines. (figure not drawn to scale)
C. D.
140°, 120° 120°, 120°
50. Garima is driving a car constantly at a speed of the 20 km/hour. Answer the following questions on basis of time-distance graph for this situation. (P) Coordinates on graph for the time taken by Garima to drive 80 km. (Q) The distance covered by Garima in 4½ hours.
Find ∠CDE and ∠ABD respectively
A. B.
60°, 30° 90°, 120°
A. B. C. D.
P (4, 80) (80, 4) (20, 4) (4, 20)
SPACE FOR ROUGH WORK
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Q 90 km 80 km 85 km 95 km
Class 8 8th
Set A Year 2014
Copyright©2015. Science Olympiad Foundation (SOF)
8th IMO - Set A
1
Logical Reasoning 1.
2.
3.
Answer the question referring to the symbol-letternumber sequence given below: P: 3 # R U 2 + >APYB 4 Q : S £ 5 N ⇔ F G 8 * D 7Y R : O * HT6 @ C 9 Z K ⊗ 1 What is the difference between the total letters and total symbols, which are used in the series of P, Q and R? A. Eight B. Nine C. Six D. Seven In a certain code language, the word HURDY-GURDY is written as GF-GE and HOB-NOB is written as BE-CA. How will the word HUGGER-MUGGER be written in that language? A. EI-AG B. EI-GA C. EF-GA D. FF-GA
A.
A. B.
C.
D.
6.
Shivam and Varun want to visit the museum after their exam. Shivam's exam finishes on 9th April and he is leaving for a holiday on 12th April. Varun's exam will be over by 10th April after which he is free. On which of the following dates can the two definitely meet? A. 10th April B. Either 10th or 11th April C. 11th April D. Either 11th or 12th April
7.
B.
8.
C.
4.
There is a certain relationship between fig. (i) and (iii). Establish the similar relationship between fig. (ii) and (iv) by selecting a suitable figure from the options which will replace the (?) in fig. (iv).
D.
? (i)
A.
C.
(ii)
(iii)
B.
D.
(iv)
Select the correct mirror image of the given below combination of letters, if the mirror is placed vertically to the left. LoGiCaLReAsOnInG
Find the missing figure which will replace the (?) in Problem Figures to complete the series. Problem Figures
?
5.
9.
GnInOsAeRLaCiGoL GnInOsAeRLaCiGoL GnInOsAeRLaCiGoL GnInOsAeRLaCiGoL
A, B, C, D, E, F, G and H are sitting around a circle facing the centre. D is second to the left of H, who is third to the left of A. B is fourth to the right of C, who is the immediate neighbour of H. G is not a neighbour of B or C. F is not a neighbour of B. How many of them are sitting between C and B? A. Two B. Four C. Two or Four D. Three Introducing a man, a woman says, "His wife is the only daughter of my father". How is the man related to the woman? A. Brother B. Father-in-law C. Maternal uncle D. Husband P, Q and R are three cities on a map. P is north of Q and ∠PQR is 45° in clockwise direction. In what direction is R from Q? A. North-East B. North-West C. South-East D. South-West
10. The given figure shows the net of a cube. Which two faces lie opposite to each other? A. P and Q B. P and U C. Q and T D. S and U
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P Q R U
S
T
2
8th IMO - Set A
11. The given figures show a series of patterns formed by using circles.
Pattern 1 Pattern 2 Pattern 3 Pattern 4 How many more circles are there in Pattern 10 than in Pattern 8? A. 4 B. 6 C. 8 D. 10
12. The characters in given figures follows a certain rule row-wise or column-wise. Identify the rule and find the missing number.
18
?
24
21 16 17
8 25 12
17 9 23
20
19
16
A. B. C. D.
2. 3. 4. 5.
No two students get the same marks. V always scores more than P. P always scores more than Q. Each time either R scores the highest and T gets the least, or alternatively S scores the highest and U or Q scores the least. If R gets most, V should be ranked not lower than . A. Second B. Third C. Fourth D. Fifth
14. If the first half of the English alphabet series are written in reverse order, then which letter should be 8th letter to the left of 14th letter from the right end? A. E B. G C. F D. I 15. Which of the following shapes is exactly embedded in Fig. (X)?
1 8 16 9
Fig. (X)
13. Read the following information and answer the following question: 1. Seven students P, Q, R, S, T, U and V take a series of tests.
A.
C.
B.
D.
MATHEMATICAL REASONING 2 5 10 5 16 55 3 × − 4 + − 3 × 2 − − 3 × − 32 16. Simplify: 3 9 1 × − × − 2 14 7
A.
C.
1082 81 7 −133 81
B. D.
1082 81 7 133 81 −
17. Mohit wins if he picks up a face card from the given cards. Find the probability of Mohit's winning.
3
7
7
5/7 1/7 2/7 6/7
5 3
A. B. C. D.
3
A
K 5
3
K
7
A
7
18. Find the square root of 21
A.
B.
C.
D.
33 58 39 4 58 29 4 57 27 4 52
2797 . 3364
4
19. Find the value of z. z + 6.1 =
A. B. C. D.
0.5( z − 0.4) 0.6( z − 2.71) − 0.35 0.42
–2.8 2.8 4.2 –3.41
Copyright©2015. Science Olympiad Foundation (SOF)
8th IMO - Set A
3
20. In the given figure, if PC and PD are the bisectors of ∠BCD and ∠ADC respectively, then find ∠ABC. D
25°
C
30° P
A
A. B. C. D.
100°
B
205° 180° 300° 150°
21. Which of the following is INCORRECT for an exterior angle of a regular polygon with n sides? A. All exterior angles of a polygon add upto 360°. B. Exterior angle = 180° – Interior angle 360° Exterior angle
C.
n=
D.
Each exterior angle =
22. The is A. B. C. D.
27. Study the pie-chart and answer the question based on it. VARIOUS EXPENDITURES (IN PERCENTAGE) INCURRED IN PUBLISHING A BOOK Royalty 15%
Printing Cost 20%
Transportation Cost 5%
(n − 2) × 180° n
A O M L K
N J
Paper Cost 20%
Promotion Cost 10%
order of rotational symmetry in the given figure . 4 2 1 Infinitely many
23. If the given figure is made up of 3 identical regular polygons, then find (i) ∠ABC (ii) ∠DIN (iii) ∠IOC (i) (ii) (iii) A. 120° 60° 120° B. 100° 60° 120° C. 120° 60° 60° D. 120° 80° 100°
26. The points P, Q, R and S lie on a straight line. The ratio of the length of PQ to the length of QR is 3 : 4 and the ratio of the length of PR to the length of RS is 2 : 1. Find the ratio of the length of QR to the length of PS. A. 7 : 19 B. 10 : 21 C. 21 : 8 D. 8 : 21
B D
C E F
I H
G
24. To reduce a rational number in its standard form, we divide its numerator and denominator by their . A. L.C.M B. H.C.F C. Product D. Multiple 25. If 21998 – 21997 – 21996 + 21995 = K⋅21995, then the value of K is . A. 1 B. 2 C. 3 D. 4
Binding 30%
Which of the following two expenditures together have a central angle of 108°? A. Binding and Transportation B. Printing and Paper C. Royalty and Promotion D. Promotion and Paper
28. Sonu's grandmother is 80 years old and Sonu is 20 years old. How many years ago was his grandmother 7 times as old as Sonu? A. 8 years B. 10 years C. 12 years D. 15 years 29. Calculate the perimeter and area of the given figure respectively, if radius of circle is 7 cm. 18 cm
16 cm
12 cm 20 cm
14 cm
A. B. C. D.
144 156 122 140
16 cm
cm, cm, cm, cm,
462 562 294 394
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cm2 cm2 cm2 cm2
4
8th IMO - Set A
30. A design has been drawn on a tile. ABCD and PQRS both are in the shape of a rhombus. Find the total area of semi-circles drawn on each side of rhombus ABCD. A P D
3 cm 3 cm
Q
S R
3 cm
5 cm
B
A. B. C. D.
A. B. C. D.
8y2 + 16y 9y2 + 72y 72y2 + 9y 18y2 + 4y
+ + + +
124 144 144 164
33. If the distance travelled by a car in one hour is 210 km, then the distance travelled by the same car with the same speed in 60 seconds is . A. 4500 m B. 3160 m C. 3500 m D. 4230 m 34. To construct a unique rectangle, the minimum number of measurements required is _____. A. 4 B. 3 C. 2 D. 1
C
142.843 cm2 128.973 cm2 39.286 cm2 157.14 cm2
31. Which of the following values are equal? (Q) 40 (P) 14 (R) 04 (S) 41 A. P and Q B. Q and R C. P and R D. P and S 32. If we divide 15(y + 3) (y 2 – 16) by 5(y 2 – y – 12) and multiply the result by 3(y + 4), we get .
35. Which of the following shows distributive property of multiplication over addition for rational numbers?
A.
3 1 5 3 1 3 5 − × + − = − × + − × − 4 3 7 4 3 4 7
B.
3 1 5 3 1 5 − × + − = − × − − 4 3 7 4 3 7
C.
3 1 5 1 3 5 − × + − = + − × − 4 3 7 3 4 7
D.
3 1 5 1 5 3 − × + − = + − − 4 3 7 3 7 4
EVERYDAY MATHeMATICS 36. Tanya and Priya left Town P and travelled in opposite directions to Town Q and Town R respectively at 7:30 a.m. Tanya was travelling at a speed of 68 km/hr while Priya was travelling at a speed of 52 km/hr. How far apart are they at 9:30 a.m.? A. 320 km B. 230 km C. 136 km D. 240 km 37. During a mass drill exercise, 6250 students of different schools are arranged in rows such that the number of students in each row is equal to the number of rows. In doing so, the instructor finds out that 9 children are left out. Find the number of children in each row. A. 46 B. 79 C. 85 D. 69
38. ` 350 is divided among P, Q and R in the ratio 2 : 5 : 3. Find the amount of money that the child with the largest share got. A. ` 175 B. ` 180 C. ` 145 D. ` 160 39. Garima has 150 picture cards. Tarun has 110 picture cards. How many cards must Garima give to Tarun so that Tarun will have 4 times as many cards as Garima? A. 100 B. 140 C. 82 D. 98 40. The digit in the tens place of a two digit number is 3 more than the digit in the units place. Let the digit at units place be b. Then the number is . A. 11b + 30 B. 10b + 30 C. 11b + 3 D. 10b + 3
Copyright©2015. Science Olympiad Foundation (SOF)
8th IMO - Set A
5
41. The cost of a chocolate is ` (x + 4) and Rohit bought (x + 4) chocolates. Find the total amount paid by him in terms of x. A. x2 + 8x + 16 B. 8x2 + 16x + 12 C. 6x2 + 2x + 14 D. 8x2 + x + 16
Find an equation for the number of ancestors in a generation n. A. 2n B. n + 2 C. 2n D. n/2 1 cup of sugar. Another 2 recipe for the same fruit salad requires 2 tablespoons
42. There are 86,400 seconds in a day. How many days long is a second? Express your answer in scientific notation upto 3 decimal places. A. 1.157 × 10–6 B. 1.234 × 10–5 –5 C. 1.157 × 10 D. 1.432 × 10–4
44. One fruit salad recipe requires
43. While studying her family's history, Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex.
A.
B.
C.
D.
1 cup, how 16 much more sugar does the first recipe require? of sugar. If 1 tablespoon is equivalent to
Shikha
4 5 6 5 3 8 5 8
cup cup cup cup
45. Ananya took part in a race. She ran 1.7 km, jogged 2 hours and walked the remaining 300 m of 3 the race. If the total distance of the race was 17 km, for 1
Parents Past (Generation 1)
Grandparents Past (Generation 2)
Great-grandparents Past (Generation 3)
find her jogging speed.
A.
8 km/hr
B.
12 km/hr
C.
7 km/hr
D.
9 km/hr
Achievers Section 46. Identify P, Q and R.
A. B. C. D.
P
Rectangular prism Rectangular pyramid Rectangular pyramid Square prism
Q
R
Square prism Square prism Square prism Rectangular prism
Triangular pyramid Triangular prism Cuboid Triangular pyramid
47. Match the following: Column-I Column-II (a) Line Graph (i) S h o w s c o n t i n u o u s changes in data over periods of time. (b) Circle Graph (ii) C ompare parts of a whole. (c) Histogram (iii) Shows the frequency of data divided into equal groups. A. (a) → (i), (b) → (iii), (c) → (ii) B. (a) → (iii), (b) → (ii), (c) → (i) C. (a) → (i), (b) → (ii), (c) → (iii) D. (a) → (ii), (b) → (i), (c) → (iii)
Copyright©2015. Science Olympiad Foundation (SOF)
6
8th IMO - Set A
48. In the given figure (not drawn to scale), BA = BR and PQ is parallel to RS. Find x, y and z. R P
A
50° 32°
y
E
29°
B
x
C
z
D
S
Q
A. B. C. D.
x 58° 58° 48° 69°
y 69° 40° 59° 40°
z 40° 30° 70° 58°
49. A dice is rolled once. What is the probability that the number will be
(a) A factor of 36 (b) Odd (c) Less than 1 (a) A. 5/6 B. 1/6 C. 2/3 D. 5/6
(b) 1/4 1/2 1/3 1/2
(c) 1/6 1/6 0 0
50. Fill in the blanks: • ____P__ is the multiplicative identity of rational numbers. • There are _______ Q rational numbers between two given rational numbers. • Rational numbers are not associative for _______. R P Q R A. 0 infinite division B. 1 infinite division C. 1 finite subtraction D. 0 infinite addition
SPACE FOR ROUGH WORK
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Class 8 8th
Set B Year 2014
Copyright©2015. Science Olympiad Foundation (SOF)
8th IMO - Set B
1
Logical Reasoning 1.
2. 3.
In a certain code, the word COMEATONCE is written as XLNVZGLMXV. In the same code, which of the following would code OK? A. KL B. LM C. KM D. LP Count the number of circles in the given figure. A. 16 B. 15 C. 17 D. 18
576
a
96
144
b
192 P
288 Q
168 R
4.
Seven executives P, Q, R, S, T, U and W reach office in a particular sequence. U reaches immediately before P but does not immediately follow S. R is the last one to reach office. T follows immediately after P and is subsequently followed by W. Who ranks fourth in the sequence of reaching office? A. W B. U C. T D. None of these
336, 676, 484, 576,
384
A. B. C. D.
5.
Which of the following Venn diagrams best represents the relationship amongst, "Fractions, Rational numbers and Whole numbers"?
A.
C.
7.
There is a certain relationship between the figures P and Q & R and S. Identify the relationship and find the missing figure.
There is a certain rule followed in figures P, Q and R. Identify the rule and find the missing numbers a & b respectively.
6.
84 196 86 194
Study the following arrangement carefully and answer the question given below. R B B DAP$ 3 T J Q 5 4 S * 1 L+ V 9 N M 5 ÷ K 7 O If each symbol is first converted into a numeral and then all the numerals are converted into english letters, how many converted english letters will be there in the above arrangement of elements? A. 15 B. 11 C. 12 D. 13
B.
D.
? Q
P
R
S
A.
B.
C.
D.
8.
Identify the missing figure in the given figure matrix.
?
A.
B.
C.
D.
Copyright©2015. Science Olympiad Foundation (SOF)
2
The three different positions of a dice are given below:
3
3 6
5
6 1
3
NeWsPaPeR123456 1
Which number is on the face opposite to 1? A. 6 B. 2 C. 3 D. 5
10. There is a set of three figures X, Y and Z, showing a sequence of folding of a piece of paper. Figure (Z) shows the manner in which the folded paper has been cut. Choose the figure which would most closely resemble the unfolded form of paper.
X
Y
Z
A.
B.
C.
D.
11. At the end of a business conference 15 people are present. All shake hands with each other once. How many handshakes will there be altogether? A. 120 B. 91 C. 110 D. 105
Mirror
A. B. C. D.
654321RePaPsWeN NeWsPaPeR123456 654321R P PsWeN e a e
2
12. Select the correct mirror image of given below combination.
654321R PaPsW N e
9.
8th IMO - Set B
13. It is 3 o'clock in a watch. If the minute hand points towards the North-East, then the hour hand will point towards the . A. South B. South-West C. North-West D. South-East 14. If the first five words in the sentence, "Meeta Meets Mysterious Meena Many Times" are rearranged in the alphabetical order, then which will be the middle word? A. Meeta B. Meena C. Meets D. Mysterious 15. Shobha is the niece of Ashish. Ashish's mother is Priya. Kamla is Priya's mother. Kamla's husband is Hari. Krishna is the mother-in-law of Hari. How is Shobha related to Hari? A. Daughter B. Great granddaughter C. Grand niece D. Great grandson's daughter
MATHEMATICAL REASONING 16. If (3.9268) 2 = 15.42, then find the value of
154200. A. 3926.8 B. 392.68 C. 39.268 D. 3.9268
18. Solve for x :
17. Which of the following do not vary directly? A. Speed of a vehicle and time taken to cover a fixed distance. B. Number of days worked and amount of earnings. C. Number of books and their price. D. Number of units of current used and the amount of charge for consumption.
A. C.
x + 9 x − 4 5 x − 32 2 x − 3 + = − 28 3 9 35
19 29
B. D.
19. The difference of the area of the circumscribed and the inscribed square of a circle is 35 sq. cm. Find the area of the circle. A. 55 sq. m B. 70 sq. m C. 55 sq. cm D. 70 sq. cm
Copyright©2015. Science Olympiad Foundation (SOF)
–19 –29
x
8th IMO - Set B
3
20. The value of
A.
B.
C.
D.
125 64 9 8 6 5 4 9 9 4
2/3
0 1/ 2
36 1 ÷ + (625 / 256) −1/ 4 3 64
=
21. By what least number 3600 be divided to make it a perfect cube? A. 9 B. 50 C. 300 D. 450
26
.9 cm
A. B. C. D.
38.5
35.2 cm
cm
41
22 cm
cm
36.3 cm
33 cm
11 cm
.4
19.8
44 cm
5.5 cm
cm
22. Sneha cut the following figure out of a rectangular cardboard of length 70 cm and breadth 50 cm. Find the area of the figure.
11 cm
2722.5 cm2 2122 cm2 2577 cm2 2257 cm2
23. In the given figure, the angle formed between the hour and minute hand is A. 80° B. 40° C. 60° D. 30°
25. The perimeter of a rhombus is 146 cm and one of its diagonal is 55 cm. Find the other diagonal and the area of the rhombus. A. 24 cm, 660 cm2 B. 24 cm, 330 cm2 C. 48 cm, 660 cm2 D. 48 cm, 1320 cm2 26. A rectangular block of wood has dimensions 24 cm by 9 cm by 7 cm. It is cut up into bricks. Each brick is a cube of side 3 cm. Find the largest number of bricks that can be cut from the block. A. 48 B. 56 C. 49 D. 52 27.
Simplify : (a + b)3 + (a – b)3 + 6a(a 2 – b 2) A. 8a2 B. 8a2b C. 8a3b D. 8a3
28. If A : Rational numbers are always closed under division and R : Division by zero is not defined, then . A. Both A and R are true B. Both A and R are false C. A is true and R is false D. A is false and R is true
37.1 cm 36.3 c m 16.5 cm 44 cm
29. Two dice are tossed. The probability that the total score is a prime number is .
10
11
12
1
2
9
3 8
4 7
6
5
24. The number of chocolates in the three packets P, Q and R are in the ratio of 2 : 3 : 4. The total number of chocolates in the three packets is 270. Packet R sells 20 chocolates to packet P and 10 chocolates to packet Q. After this sale, what is the ratio of chocolates in packets P : Q : R? A. 8 : 9 : 10 B. 9 : 10 : 8 C. 8 : 10 : 9 D. 10 : 9 : 8
A.
1 6
B.
5 12
C.
1 2
D.
7 9
30. Which of the following statements is incorrect? A. A number is divisible by 3, if the sum of digits divisible by 3. B. A number is divisible by 9, if the sum of its digits is divisible by 9. C. A number is divisible by 4, if the number formed by its last two digits is divisible by 4. D. A number is divisible by 6, if the number is divisible by either 2 or 3.
Copyright©2015. Science Olympiad Foundation (SOF)
4
8th IMO - Set B
31. How many kg of pure salt must be added to 30 kg of 2% solution of salt and water to increase it to a 10% solution? 2 2 B. 3 kg A. 2 kg 3 3 1 2 C. 4 kg D. 6 kg 2 5 32. Which of the following pie charts represent the data shown below? Number of students opting different subjects
A.
No. of students
English
45
Maths
60
Physics
20
Chemistry
30
Economics
10
Hindi
15
30°
34. The size of a red blood cell is 0.000007 m and the size of a plant cell is 0.00001275 m. Compare these two, which of the following is correct? 3 A. A red blood cell is approximately of the plant 4 cell in size.
30°
Subject
50°
110° 40° 50° 80°
B.
40° 20° 60°
1 1 1 1 33. Simplify: − a 2b 2 c + ab 2 c − abc 2 − cb 2 a 2 + 2 3 4 5 1 2 1 2 1 cb a − c ab + ca 2b 6 7 8 7 2 2 1 2 1 1 2 2 A. ab c + a bc − abc + abc 10 2 28 8 7 2 2 1 2 11 2 1 2 B. − a b c + ab c − abc + a bc 10 2 28 8 1 2 2 7 2 10 1 2 C. a b c + ab c − abc + abc 2 14 12 5 8 D. None of these
120°
B.
C.
D.
90°
1 A red blood cell is approximately of the plant 4 cell in size. A red blood cell is approximately half of the plant cell in size. A red blood cell is approximately equal to the plant cell in size.
35. A card is drawn from a packet of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is
C.
120°
90°
50° 60°
30°
D.
100°
90°
30° 60° 40° 20°
10°
A.
C.
1 10 1 100
B. D.
9 100 2 100
EVERYDAY MATHeMATICS 36. A 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 A. 42 minutes B. 48 minutes C. 51 minutes D. 53 minutes 37. A man plants 15376 apple trees in his garden and arranges them so that there are as many rows as there are apples trees in each row. The number of rows is A. 124 B. 126 C. 134 D. 144
38. The price of tea being increased by 20%, a man reduces his consumption by 20%. By how much percent will his expenses for tea be decreased? A. 2% B. 4% C. 6% D. 8% 39. If a company sells a car with a marked price of ` 2,72,000 and gives a discount of 4% on ` 2,00,000 and 2.5% on the remaining amount of ` 72,000, then the actual price charged by the company for the car is A. ` 2,50,000 B. ` 2,55,000 C. ` 2,60,100 D. ` 2,62,200
Copyright©2015. Science Olympiad Foundation (SOF)
8th IMO - Set B
5
40. Ratio of the earnings of A and B is 4 : 7. If the earnings of A increase by 50% and those of B decrease by 25%, the new ratio of their earnings becomes 8 : 7. What are A's earnings? A. ` 21,000 B. ` 26,000 C. ` 28,000 D. Data inadequate
43. Sam invested ` 15,000 at 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be A. ` 16,500 B. ` 16,525.50 C. ` 16,537.50 D. ` 18,150
41. A train 150 m long is running with a speed of 68 km/hr. In what time will it pass a man who is running at 8 km/hr in the same direction in which the train is going? A. 6 sec B. 10 sec C. 9 sec D. 12 sec
44. Within a rectangular garden 10 m wide and 20 m long, we wish to pave a walk around the borders of uniform width so as to leave an area of 96 m2 for flowers. How wide should the walk be? A. 1 m B. 2 m C. 2.1 m D. 2.5 m
42. A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day? 1 A. 6 1 B. 9 2 C. 5 2 D. 7
45. Tickets numbered 1 to 30 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 5? 1 A. 5 3 B. 5 2 C. 5 1 D. 4
Achievers Section 46. Find the sum of a, b, c, d, e, f, g and h. h g
a b
f
c
d
e
47. Select the incorrect match. A. Mean proportion If A : B = x : y, then B:A=y:x B. Equivalent ratio Each term in a ratio multiplied/divided by the same number. C. Ratio Used to compare two or more than two quantities. D. Proportion It is an equality relation between two ratios. 48. Find the numerical value of P : Q where m + n −l
A.
720°
B.
360°
Q = x1/( a −b)
C.
540°
where a, b, c being all different.
D.
180°
(
A. C.
)
xn × l x
n+l − m
xm P = n x
1/( a − c )
1 : 2 1 : 1
Copyright©2015. Science Olympiad Foundation (SOF)
(
× x1/(b − c )
xl × m x
)
1/(b − a )
B. D.
l +m−n
and
(
× x1/(c − a )
)
1/( c −b )
2:1 None of these
6
8th IMO - Set B
49. If DE is internal bisector of ∠D, then find x & y respectively. G F
x A 35° E y
B
A. B.
70°
30°, 150° 20°, 120°
C
25°
D
C. D.
25°, 155° 155°, 25°
50. Study the statements and choose the correct option. Statement-1 : The square root of certain decimals are obtained by first changing the decimals into fractions with perfect squares as their numerators and denominators. Statement-2 : (26.1)2 lies between 400 and 900. A. Statement-1 is true and statement-2 is false. B. Statement-1 is false and statement-2 is true. C. Both statements 1 and 2 are false. D. Both statements 1 and 2 are true. SPACE FOR ROUGH WORK
Copyright©2015. Science Olympiad Foundation (SOF)
ANSWER KEYS 4 th IMO (2010) 1. (B) 11. (B) 21. (A) 31. (B) 41. (B)
2. (D) 12. (B) 22. (B) 32. (B) 42. (B)
3. (D) 13. (B) 23. (A) 33. (B) 43. (C)
4. (A) 14. (B) 24. (D) 34. (D) 44. (C)
5. (B) 15. (B) 25. (B) 35. (B) 45. (B)
6. (A) 16. (D) 26. (C) 36. (C) 46. (D)
7. (C) 17. (D) 27. (D) 37. (D) 47. (C)
8. (B) 18. (B) 28. (B) 38. (C) 48. (C)
9. 19. 29. 39. 49.
(A) (D) (B) (B) (D)
10. 20. 30. 40. 50.
(B) (B) (C) (D) (A)
7. 17. 27. 37. 47.
(C) (A) (A) (C) (D)
8. 18. 28. 38. 48.
(B) (A) (C) (B) (C)
9. 19. 29. 39. 49.
(B) (C) (D) (A) (C)
10. 20. 30. 40. 50.
(D) (B) (A) (B) (B)
7. 17. 27. 37. 47.
(D) (B) (B) (D) (B)
8. 18. 28. 38. 48.
(A) (D) (C) (B) (A)
9. 19. 29. 39. 49.
(D) (C) (D) (C) (B)
10. 20. 30. 40. 50.
(D) (D) (B) (D) (D)
7. (D) 17. (B) 27. (A) 37. (D) 47. (C)
8. (B) 18. (D) 28. (D) 38. (D) 48. (B)
9. 19. 29. 39. 49.
(D) (B) (C) (D) (D)
10. 20. 30. 40. 50.
(C) (A) (B) (B) (C)
5 th IMO (2011) 1. 11. 21. 31. 41.
(C) (A) (A) (A) (B)
2. 12. 22. 32. 42.
(B) (B) (D) (D) (D)
3. 13. 23. 33. 43.
(D) (B) (A) (C) (A)
4. 14. 24. 34. 44.
(A) (D) (B) (A) (B)
5. 15. 25. 35. 45.
(B) (C) (C) (D) (A)
6. 16. 26. 36. 46.
(A) (A) (B) (B) (C)
6 th IMO (2012) SET A 1. 11. 21. 31. 41.
(A) (C) (A) (B) (A)
2. 12. 22. 32. 42.
(A) (B) (B) (A) (C)
3. 13. 23. 33. 43.
(C) (B) (B) (C) (B)
4. 14. 24. 34. 44.
(D) (C) (B) (B) (B)
5. 15. 25. 35. 45.
(B) (C) (B) (A) (D)
6. 16. 26. 36. 46.
(D) (B) (A) (D) (D)
SET B 1. (B) 11. (C) 21. (D) 31. (C) 41. (B)
2. (C) 12. (D) 22. (C) 32. (A) 42. (D)
3. (A) 13. (B) 23. (B) 33. (A) 43. (C)
4. (A) 14. (B) 24. (C) 34. (C) 44. (B)
5. (B) 15. (D) 25. (B) 35. (D) 45. (B)
6. (D) 16. (D) 26. (D) 36. (A) 46. (B)
7 th IMO (2013) 1. (B) 11. (D) 21. (C) 31. (B) 41. (C)
2. (D) 12. (C) 22. (A) 32. (D) 42. (B)
3. (D) 13. (D) 23. (B) 33. (D) 43. (A)
4. (C) 14. (C) 24. (C) 34. (A) 44. (D)
SET A 5. (B) 6. (D) 15. (A) 16. (D) 25. (A) 26. (A) 35. (B) 36. (A) 45. (C) 46. (C)
7. (D) 17. (D) 27. (B) 37. (A) 47. (C)
8. (D) 18. (B) 28. (A) 38. (B) 48. (A)
9. 19. 29. 39. 49.
(D) (A) (B) (A) (D)
10. 20. 30. 40. 50.
(D) (B) (A) (C) (C)
1. (C) 11. (A) 21. (A) 31. (D) 41. (B)
2. (B) 12. (A) 22. (C) 32. (D) 42. (A)
3. (D) 13. (B) 23. (D) 33. (A) 43. (D)
4. (D) 14. (B) 24. (A) 34. (B) 44. (C)
SET B 5. (B) 6. (C) 15. (D) 16. (D) 25. (C) 26. (C) 35. (A) 36. (D) 45. (C) 46. (B)
7. (D) 17. (B) 27. (A) 37. (B) 47. (B)
8. (C) 18. (A) 28. (A) 38. (C) 48. (D)
9. 19. 29. 39. 49.
(C) (B) (A) (B) (D)
10. 20. 30. 40. 50.
(A) (A) (B) (C) (A)
8 th IMO (2014) 1. (B) 11. (C) 21. (D) 31. (A) 41. (A)
2. (D) 12. (A) 22. (B) 32. (B) 42. (C)
3. (B) 13. (C) 23. (C) 33. (C) 43. (C)
4. (A) 14. (D) 24. (B) 34. (C) 44. (C)
SET A 5. (B) 6. (C) 15. (B) 16. (C) 25. (C) 26. (D) 35. (A) 36. (D) 45. (D) 46. (B)
7. (D) 17. (B) 27. (D) 37. (B) 47. (C)
8. (D) 18. (B) 28. (B) 38. (A) 48. (A)
9. 19. 29. 39. 49.
(A) (A) (A) (D) (D)
10. 20. 30. 40. 50.
(B) (D) (D) (A) (B)
1. (D) 11. (D) 21. (D) 31. (A) 41. (C)
2. (A) 12. (A) 22. (A) 32. (B) 42. (A)
3. (A) 13. (D) 23. (C) 33. (B) 43. (C)
4. (D) 14. (A) 24. (C) 34. (C) 44. (B)
SET B 5. (B) 6. (A) 15. (B) 16. (B) 25. (D) 26. (A) 35. (A) 36. (B) 45. (A) 46. (B)
7. (B) 17. (A) 27. (D) 37. (A) 47. (A)
8. (A) 18. (A) 28. (D) 38. (B) 48. (C)
9. 19. 29. 39. 49.
(B) (C) (B) (D) (D)
10. 20. 30. 40. 50.
(A) (D) (D) (D) (D)
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