International Maths Olympiad 2020 Paper For Class 6 with Answer
SOF IMO 2020 Paper For Class 6
Logical Reasoning
1. If ROSE is coded as 5436, CHAIR is coded as 78915, then what will be the code for SEARCH?
A. 369578 B. 369758 C. 369537 D. 697845
ANS :(A): We have, Letters R O S E C H A I Codes 5 4 3 6 7 8 9 1
So, code for SEARCH is 369578
2. A set of three figures X, Y and Z showing a sequence of folding of a piece of paper is given. Fig. (Z) shows the manner in which the folded paper has been cut. Select the figure from the options which shows the unfolded form of fig. (Z).
Ans : (C)
3. Select a figure from the options which will continue the same series as established by the Problem Figures.
Ans : (B): In every next figure, the corner elements moves clockwise to the next corner.
4. How many 3’s are there in the given series which are immediately preceded by 9 as well as immediately followed by 6?
9 6 3 5 4 9 3 3 6 9 3 6 3 9 9 3 3 6 9 3 6
A. None B. One C. Two D. More than two
Ans : (C): 9 6 3 5 4 9 3 3 6 9 3 6 3 9 9 3 3 6 9 3 6
5. There is a certain relationship between the left pair of the alphabets. Establish the same relationship in the right pair and find the missing term. AG: IO::?: MS
A. EJ B. DK C. DJ D. EK
Ans: (D): In the left pair, A +8 I G +8 O Similarly, E +8 M K +8 S6. How many triangles are there in the given figure?
A. 20 B. 22 C. 23 D. 25
Ans : (D)
7. How many meaningful English words can be formed with the letters C, E, I, V using each letter only once in each word?
A. None B. One C. Two D. More than two
Ans (B): The meaningful word formed is VICE.
8. Kanika correctly remembers that Pratik’s birthday is before Sunday but after Thursday. Vipul correctly remembers that Pratik’s birthday is after Friday but before Monday. On which of the following days does Pratik’s birthday definitely fall?
A. Friday B. Sunday C. Saturday D. Monday
Ans :(C): According to Kanika, Pratik’s birthday falls on either Friday or Saturday.
According to Vipul, Pratik’s birthday falls on either Saturday or Sunday.
So, Pratik’s birthday falls on Saturday.
9. Two positions of a dice are shown below. If 5 is on the top, then which number will be at the bottom?
A. 1 B 6 C. 4 D. 3
Ans : (A): The numbers on opposite faces are: (1, 5), (2, 4) and (3, 6)
10. Select a figure from the options which satisfies the same conditions of placement of dots as in the given figure.
Ans . (B):
11. Pointing to a photograph, P said to his friend Q, “She is the only daughter of the father of my mother”. How is P related to the person in the photograph?
A. Daughter B. Son C. Nephew D. Husband
Ans (B): Father of P’s mother is P’s maternal grandfather. Only daughter of P’s maternal grandfather is P’s mother. Also P is male. So, P is the son of the person in the photograph.
12. In a row of 50 students, if Raman is 22nd from the top, then what is his rank from the bottom?
A. 28th B. 29th C. 30th D. 31st
Ans (B): Rank of Raman from the top = 22nd So, rank of Raman from the bottom = 50 – 22 + 1 = 29th
13. Which of the following figures will complete the given figure matrix?
Ans(B): In each row, third figure is the uncommon part of first two figures.
14. Find the water image of the given figure.
Ans(C):
15. Which of the following Venn diagrams best represents the relationship amongst, “Women, Mothers and Widows”?
Mathematical Reasoning
16. The additive inverse of the sum of the integers –9853 and –3187 is _____.
A. 6666 B. 4031 C. 10340 D. 13040
Ans. (D): Sum = (–9853) + (–3187) = –13040 So, additive inverse of – 13040 is 13040.
17. 6 tenths more than the sum of 3.25 and 5.79 is ________.
A. 15.04 B. 9.1 C. 9.64 D. 15.14
Ans.(C): Sum = 3.25 + 5.79 = 9.04
So, 6 tenths more than 9.04 = 9.04 + 0.6 = 9.64
18. Study the following statements and select the correct option.
P: A variable can take different values.
Q: The value of a variable which satisfies the given equation is called its solution.
A. Both P and Q are true. B. Both P and Q are false.
C. P is true but Q is false. D. P is false but Q is true.
Ans .(A)
19. A number is divisible by 4, if ________.
A. the sum of the digits is divisible by 4
B. the sum of the last two digits is divisible by 4
C. the number formed by its last two digits is divisible by 4
D. the last digit is divisible by 4
Ans.(C)
20. Which of the following is a perfect number?
A. 6 B. 12 C. 24 D. 8
Ans(A):
A. Factors of 6 = 1, 2, 3 and 6 \ Sum of factors = 1 + 2 + 3 + 6 = 12 which is twice of 6. So, 6 is a perfect number.
B. Factors of 12 = 1, 2, 3, 4, 6 and 12 \ Sum of factors = 1 + 2 + 3 + 4 + 6 + 12 = 28 ≠ 24
C. Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24 \ Sum of factors = 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60 ≠ 48
D. Factors of 8 = 1, 2, 4 and 8 \ Sum of factors = 1 + 2 + 4 + 8 = 15 ≠ 16
21. Given figure is made up of six regular hexagons. If the perimeter of the given figure is 108 cm, then find the length of each side of the hexagon.
A. 3 cm B. 12 cm C. 8 cm D. 6 cm
Ans.(D): Perimeter of figure = 108 cm
⇒ 18 × Side of hexagon = 108 cm
⇒ Side of hexagon = 108 / 18 = 6 cm
22. Which of the following number lines correctly represents (–5) – (–3)?
22. (A)
23. Which of the following set of angles can form a triangle?
A. 30°, 80°, 75° B. 45°, 65°, 65°
C. 95°, 20°, 68° D. 90°, 45°, 45°
Ans.(D): A. Sum of angles = 30° + 80° + 75° = 185° ≠ 180°
B. Sum of angles = 45° + 65° + 65° = 175° ≠ 180°
C. Sum of angles = 95° + 20° + 68° = 183° ≠ 180°
D. Sum of angles = 90° + 45° + 45° = 180°
24. The product of a natural number and its successor is always ________.
A. an odd number B. an even number
C. a prime number D. divisible by 3
Ans.(B)
25. Simplify:
A. (x + y): x B. y: x C. (x – y): y D. (x – y): x
Ans.(D): Number of students in the class = x , Number of girls = y
So, number of boys = x – y
Required ratio = x -y / x i.e., (x – y): x
27. How many minimum number of squares that must be shaded to make the given figure symmetric?
A. 1 B. 2 C. 3 D. 4
Ans. (B):
28. Find the area of the unshaded region of the given figure (not drawn to scale).
A. 78 cm²
B. 43 cm²
29. The points that lie in the exterior of ∠YOZ are/is
A. Only E B. Only D C. E and F only D. E, F and D
Ans.(D)
30. ________ is the additive identity and ________ is the multiplicative identity respectively for whole numbers.
A. 1, 2 B. 1, 0 C. 0, 2 D. 0, 1
Ans (D)
31. Find the difference between the largest 7-digit number and the smallest 7-digit number formed by using the digits 4, 0, 3, 9 and 7 (using each digit at least once).
A. 6993951 B. 6949530 C. 6963951 D. 6996951
Ans.(D): Largest 7-digit number formed = 9997430
Smallest 7-digit number formed = 3000479
Required difference = 9997430 – 3000479 = 6996951
32. How many right angles will you make, if you face South and turn clockwise to East?
A. Two B. Three C. One D. Five
Ans.(B):
3 right angle are made, when we move from South to East in clockwise direction.
33. Find the fraction with denominator 120 whose decimal value is 0.65.
A. 62 /120 B. 78 /120 C. 35 /120 D. 90/120
Ans.(B): 0 65 = 65 / 100 * 120 / 120 = 78 /120
34. Which of the following ratios are not in proportion?
A. ₹ 20: ₹ 150 and ₹ 70: ₹ 525
B. 350 g: 700 g and 1500 g: 3 kg
C. 3 L: 12 L and 400 mL: 1050 mL
D. 35 cm: 15 m and 70 m: 3 km
Ans.(C): A. ₹ 20: ₹ 150 = 2: 15 ₹ 70: ₹ 525 = 2: 15 So, they are in proportion.
B. 350 g: 700 g = 1: 2 1500 g: 3 kg = 1500 g: 3000 g = 1: 2 So, they are in proportion.
C. 3L: 12L = 1: 4 400 mL: 1050 mL = 8: 21 So, they are not in proportion.
D. 35 cm: 15 m = 35 cm: 1500 cm = 7: 300 70 m: 3 km = 70 m: 3000 m = 7: 300
So, they are in proportion.
35. The expression obtained when p is multiplied by 5 and then subtracted from 8 is _________.
A. 8 – 5p B. 5p – 8 C. 8p – 5 D. 8 + 5p
Ans (A): p multiplied by 5 = 5p
5p subtracted from 8 = 8 – 5p
Everyday Mathematics
36. The length, breadth and height of a room are 8 m 25 cm, 6 m 75 cm and 4 m 50 cm respectively. Determine the longest tape which can measure the three dimensions of the room exactly.
A. 25 cm B. 15 cm C. 75 cm D. 1 m 15 cm
Ans. (C) : Length of room = 8 m 25 cm = 825 cm
Breadth of room = 6 m 75 cm = 675 cm
Height of a room = 4 m 50 cm = 450cm
Length of the longest tape required = L.C.M. of ( 825, 675, 450 ) = 75cm
37. An athlete takes 4 rounds of a rectangular park 140 m long and 60 m wide. Find the total distance covered by him.
A. 800 m B. 1600 m C. 1200 m D. 2400 m
Ans. (B): Distance covered in 1 round = 2( length + width) = 2 ( 140 + 60 ) = 400 m
Distance covered in 4 round = 4 * 400 = 1600 m
38. A car travels 180 km in 6 hours and a bus travels 315 km in 9 hours at uniform speeds. Find the ratio of distance travelled by car to bus in one hour.
A. 7: 6 B. 5: 8 C. 8: 5 D. 6: 7
Ans. (D): Distance travelled by car in 6 hours = 180 km
Distance travelled by car in 1 hours = 180 km /6 = 30 km
Distance travelled by bus in 9 hours = 315 km
Distance travelled by bus in 1 hours = 315 km /9 = 35 km
Required ratio : 30 / 35 = 6 /7 i.e. 6 : 7
39. Kartik reads 200 pages of a book out of 320 pages. Kanika reads 3 / 5 of the same book. Who read less pages and by how much?
A. Kartik, 8 pages B. Kartik, 12 pages
C. Kanika, 8 pages D. Kanika, 12 pages
Ans. (C) : Number of Pages read by Kartik = 200
Number of Pages read by Kanika = 3/5 of 320 = 3/5 * 320 = 192
so, Kanika read 200 -192 = 8 pages less than Kartik.
40. Tarun bought 2 shirts of ₹ 250 each, 2 scarfs of ₹ 175.50 each and 4 belts of ₹ 75.75 each. How much amount of money did he spend in all?
A. ₹ 1248.50 B. ₹ 1154 C.₹ 1140.25 D.₹ 1812.50
Ans. (B) : Total Amount of money spent by Tarun = ₹( 2 * 250 + 2 * 175.50 + 4 * 75.75)
= ₹( 500 + 351 + 303) = ₹ 1154
41. On one day, the temperature on a hill at 7 p.m. was 6°C but at mid-night, it fell down to –4°C. By how many degrees did the temperature fall?
A. 5°C B. 6°C C. 7°C D. 10°C
Ans. (D) : Temperature on a hill at 7 p.m. = 6°C
Temperature at mid-night = – 4°C
Temperature fall during 7 p. m. to midnight = 6°C - ( – 4°C) = 10°C
42. A wheel makes 115 revolutions in 1 / 2 hour. At this rate, how many revolutions will it make in 8 hours?
A. 920 B. 2070 C. 1840 D. 1640
Ans. (C) : Number of revolutions made in 1/2 hour = 115
Number of revolutions made in 1 hour = 115 ÷ 1/2 = 115 * 2 = 230
So, number of revolutions made in 8 hours = 230 * 8 = 1840
43. Nandini had some fruits. She packed them into 36 packets of 12 fruits each. She found that she had 6 fruits left. How many fruits she had at first?
A. 426 B. 432 C. 204 D. 438
Ans. (D) : Number of Fruits in 36 packets = 36 * 12 = 432
As , 6 fruits are left.
so, number of fruits Nandini had at first = 432 + 6 = 438
44. Vaani buys a dress costs ₹ 2874. Which of the following is the correct roman numeral (in ₹ ) for the cost of the dress?
A. MMDCCLXXIV B. MMDCCCLXXIV
C. MMDCCCLXIV D. MMDCCCLXXVI
Ans. (B) : Cost of Dress = ₹ 2874
Roman numeral form of above cost is : MMDCCCLXXIV
45. A shopkeeper has 423 kg of sugar. He sells 42 kg of sugar every day. Estimate how much sugar is left after 6 days sale to the nearest hundred.
A. 200 kg B. 170 kg C. 175 kg D. 1
Ans. (A) : Total weight of sugar = 423 kg
Weight of sugar sold in 1 day = 42 kg
Weight of sugar sold in 6 days = 42 * 6 = 252 kg
so, weight of sugar left = 423 kg - 252 kg = 171 kg
171 kg when rounded off to nearest hundred gives 200 kg
Achievers Section
46. Match the figures given in the Column 1 with their line(s) of symmetry given in Column 2.
Column 1 Column 2
(P) Equilateral triangle (1) 0
(Q) Square (2) 3
(R) Parallelogram (3) 2
(S) Rhombus (4) 4
A. (P) → (2); (Q) → (4); (R) → (1); (S) → (3)
B. (P) → (2); (Q) → (4); (R) → (3); (S) → (1)
C. (P) → (4); (Q) → (2); (R) → (1); (S) → (3)
D. (P) → (2); (Q) → (1); (R) → (4); (S) → (3)
Ans. (A) :
47. The given bar graph shows the number of cars sold by two showrooms in five months. Study the graph carefully and answer the following questions.
(a) How many less cars were sold by Showroom P than Showroom Q in January, March and April altogether?
(b) Find the ratio of total cars sold in February to the total number of cars sold in 5 months.
(a) (b)
A. 8000 12:49
B. 8000 17:50
C. 7500 17:50
D. 7500 12:49
Ans. (D) : (a) Number of cars sold by Showroom P in January, March and April together
= 6000 + 7500 + 4500 = 18000
Number of cars sold by Showroom Q in January, March and April together
= 4500 + 12000 + 9000 = 25500
Required difference = 25500 - 18000 = 7500
(b) Total cars sold in February = 10500 + 7500 = 18000
Total number of cars sold in 5 months = 6000 + 4500 + 10500 + 7500 + 7500 + 12000 + 4500 + 9000 + 6000 +6000 = 73500
Required ratio = 18000 / 73500 = 12 /49 i.e 12 ; 49
48. Fill in the blanks and select the correct option.
The join of two adjacent vertices is called an P.
A Q is one that does not cross itself.
Two or more distinct lines meeting at a point are called R lines.
P Q R
A. Diagonal Simple curve Concurrent
B. Edge Curve Parallel
C. Diagonal Curve Parallel
D. Edge Simple curve Concurrent
Ans. (D)
49. Select the incorrect option.
A. The smallest 4-digit number having three different digits is 1002.
B. Whole numbers are always commutative under addition and multiplication.
C. All whole numbers are natural numbers.
D. 22222222 is divisible by 11.
Ans. (C) : 0 is a whole number which is not a natural number. so, all whole numbers are not natural number.
50. Study the following statement and select the correct option.
Statement 1: The largest 5-digit number having three different digits is 99987.
Statement 2 : A whole number is added to 10 and the same number is subtracted from 10. Then the sum of the resulting number is 20.
A. Both Statement 1 and Statement 2 are true.
B. Both Statement 1 and Statement 2 are false.
C. Statement 1 is true but Statement 2 is false.
D. Statement 1 is false but Statement 2 is true.
Ans. (A) : Statement 1: The largest 5-digit number having three different digits is 99987.
Statement 2 : let the whole number be x.
According to question,
( x + 10 ) + ( 10 - x ) = x + 10 +10 - x = 20
so, both Statement 1 and Statement 2 are true.
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