Class-notes-6

THE MATH EXPERT

International Math Olympiad Sample Paper

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IMO 2019 - GRADE 6 SAMPLE PAPER LOGICAL REASONING 1.

Find the missing number below:

(A) 118 (B) 324 (C) 121 (D) 356 2.

Count the number of squares in the given figure.

(A) 12 (B) 14 (C) 10 (D) 9 3.

Arrange the following words as they would appear in a dictionary and then choose the third word of the arrangement. (A) (B) (C) (D)

Ascertain Ascensive Ascent Ascetic

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4.

Which number would be on the opposite face of the number 6 if the given net of the cube is folded?

(A) 4 (B) 5 (C) 3 (D) 2 5.

A is in the West of B, B is in the South of C and D is in the North of C. In which direction of A is D? (A) North East (B) North West (C) South East (D) North

6. If D= 6, CAT= 8, find the value of LION. (A) 50 (B) 15 (C) 12.5 (D) 54

7. Pointing to a photograph, a man said, “That man’s father is my father’s only son”. Whose photograph was it? (A) (B) (C) (D)

His own His son His brother His father

8. Which of the following set of operations when replaces the asterisk will satisfy the below equation64 * 32 * 16 * 8 * 4 = 18 (A) (B) (C) (D)

/–+× –+/× +/–× /+×–

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9. Which figure would come next in the given figure pattern below?

(A)

(B)

(C)

(D)

10. Which of the following words can’t be formed from the letters from the word ADMINISTRATION? (A) RAT (B) RATION (C) TRANSISTOR (D) TRAIN

11. Observe the figure below and find the sum of the numbers which are present in any two of the shapes (Circle, Triangle, Rectangle).

(A) (B) (C) (D)

32 18 30 16 www.cuemath.com

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12. Rajiv walked 10 m towards South then turned right and walked 25 m. Then he turned right and walked 30 m. Now he turned left and walked 10 m. Finally, he turned left and walked 20 m. How far and in which direction is he from the starting point? (A) (B) (C) (D)

50 m East 35 m West 40 m North 35 m East

13. If the vowels of the word ‘REGULATION’ are arranged in alphabetical order first and then the consonants are arranged alphabetically, which letter will be third to the right of the third letter from left? (A) G (B) I (C) U (D) L 14. In a certain code, KNOWLEDGE has been written as YQPMLGIFG. How will EDUCATION be coded? (A) EWGFAPQVK (B) EWFGAPQKV (C) EFWGAPKQV (D) EWGFAPVQK 15. Choose the odd one out of the given figures.

(A) I (B) II (C) III (D) IV

MATHEMATICAL REASONING 16. Which of the following is divisible by 6? (A) 36744 (B) 57688 (C) 24664 (D) 10930 17. Evaluate: –71 + (–9) - (81) + (–9) + 1 – (–29) (A) 144 (B) –140 (C) 200 (D) –200 www.cuemath.com

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18. Which number must be added to –2367 to get –11993? (A) (B) (C) (D)

19. If

9516 14360 –9626 –9516

3 3 th of a number is 63, find th of that number. 9 7

(A) 189 (B) 81 (C) 96 (D) 91 20. If the temperature of a city on Monday was –2°C. It increases by 3°C on Tuesday and decreases by 1°C on Wednesday. What was the temperature on Wednesday? (A) –4°C (B) –3°C (C) 0°C (D) 1°C 21. Which of the following has been paired incorrectly? (A) MDCC - 1700 (B) LXVIII - 68 (C) DLXI - 561 (D) XCIX – 119 22. Rama’s age is five more than three times as Rohit. If 5 years ago, Rohit’s age was 10 years, find the Rama's age. (A) (B) (C) (D)

45 years 50 years 55 years 60 years

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23. Match the following diagrams with their respective conditions-

(A) 1→a, 2→b, 3→ c, 4→d (B) 1→a, 2→c, 3→ b, 4→d (C) 1→a, 2→d, 3→ b, 4→c (D) 1→a, 2→b, 3→ d, 4→c 24. How many lines of symmetry does the following figure have?

(A) (B) (C) (D)

0 1 5 4

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25. How many parts of Fig.B must be shaded to represent the same fraction as represented by Fig.A?

(A) 10 (B) 15 (C) 12 (D) 18 26. Read the following statements and mark the correct option:

(a) Every isosceles triangle is an equilateral triangle (b) Every equilateral triangle is an isosceles triangle (c) Every rectangle is a square (d) Every square is a rectangle (A) (a) True (b) True (c) True (d) True (B) (a) True (b) False (c) True (d) False (C) (a) False (b) True (c) False (d) True (D) (a) False (b) False (c) False (d) False 27. Which sign will fill in the gap below to satisfy the following expression? 3 – (4 – 5) ____ (3 – 4) – 5 (A) < (B) > (C) = (D) ≤

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28. Find the perimeter of the given figure.

(A) 9 cm (B) 16 cm (C) 18 cm (D) 17 cm 29. An even number maybe a-

(a) Whole Number (b) Fraction (c) Decimal (A) (B) (C) (D)

30. If I = (A) (B) (C) (D)

Only a Both a & b Both a & c a, b & c

14 4 7 8  and II =  , choose the correct option. 9 3 3 6

I < II I > II I = II Cannot be compared

31. How can we represent 305006713 in words? (A) (B) (C) (D)

Three crore fifty lakh six thousand seven hundred and thirteen Thirty crore five lakh six thousand seven hundred and thirteen Thirty crore fifty lakh six thousand seven hundred and thirteen None of the above

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32. Observe the figure and answer the question that follows.

(A) 15 (B) 14 (C) 17 (D) 10.5 33. Identify the CORRECT statement: (A) (B) (C) (D)

All sides are equal in an isosceles triangle At least two angles are equal in a scalene triangle. At least one angle of a right-angle triangle must be less than 30. All angles are equal in an equilateral triangle.

(Direction 34–35) Observe the given bar graph carefully and answer the following questions.

34. What fraction of the total number of students are in Grade 8? 7 72 5 (B) 36 7 (C) 36 5 (D) 72

(A)

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35. What is the difference between the number of students of Grade 7 & Grade 9 taken together and the number of students of Grade 5 & Grade 6 taken together? (A) (B) (C) (D)

20 40 10 30

EVERYDAY MATHEMATICS 36. Manya spent ₹ 395.47 on books, ₹ 37.65 on medicines and ₹ 89.45 on food. If she had seven ₹ 100, how much she is left with now? (A) (B) (C) (D)

₹ 137.43 ₹ 167.43 ₹ 177.43 ₹ 187.43

37. Aman got ₹ 100 and he went and bought 6 identical candies. He is now left with ₹ x. Find the price of one candy in terms of x. (A) ₹ 100 – 6x (B) ₹ (C) ₹

100𝑥 6 100 – 𝑥

6 𝑥 (D) ₹ 100 6

38. The weight of three baskets is 1

2 16 2 kg, kg and 3 kg. What will be the total weight of the baskets? 3 5 3

1 kg 5 2 (B) 10 kg 5 3 (C) 10 kg 5 4 (D) 10 kg 5

(A) 10

39. A container contains 100 L of milk. If the milk is poured in glasses each one having 10 ml capacity, how many glasses are required to empty the container? (A) 100 (B) 1000 (C) 10000 (D) 100000

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2 m is going to be made into a square of side 0.7 m. How much extra length of wire required to 5 make the required square?

40. A wire of length 2

(A) (B) (C) (D)

0.4 m 0.7 m 0.5 m 0.6 m

1 hours, watched a cricket match on TV for 40 minutes. 2 How much time will he be left with to complete his school assignments?

41. Ayan had 3 hours free in the evening. He played for 1

(A) (B) (C) (D)

40 minutes 1 hour 50 minutes Half an hour

42. A sum of money was distributed among Ravi & Rakesh in the ratio 6:7. If the difference between their shares is ₹ 20, find the amount that Ravi got. (A) (B) (C) (D)

₹ 260 ₹ 120 ₹ 130 ₹ 143

1 1 1 part of her monthly salary on books, th part on rent and th part on food, if she is now left with ₹ 3 4 5 1300, find her monthly salary.

43. Priti spent

(A) (B) (C) (D)

₹ 5000 ₹ 6000 ₹ 10000 ₹ 8000

44. Five shops A, B, C, D, and E are situated on a straight line. If the distance between A & D is 25 km, between B & E is 21 km and between B & D is 16 km, find the distance between A & B? (A) 10 km (B) 5 km (C) 6 km (D) 9 km 45. A diver is located 30 m below sea level. If he goes up by 10 m, find his new position. (A) (B) (C) (D)

–40m –20m –10m 20m

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ACHIEVER’S SECTION 46. A square of side 4 m consists of smaller identical squares. Some of the smaller squares are painted. If the cost of painting is ₹ 10.8 per m2, what will be the cost of painting the remaining part?

(A) ₹ 112 (B) ₹ 120 (C) ₹ 105 (D) ₹ 108

47. The fraction

1 as a decimal is A 8

3 th of 117 is B 9

10 Crores is equal to C millions Find the value of the expression. A ✕ C + B (A) 57.125 (B) 56.65 (C) 51.5 (D) 65.25

48. A large Pizza is shared by three friends Amar, Akbar & Anthony. Amar ate

1 th part of the pizza, Akbar ate 0.3 of it 5

2 th of it. 9 Based on the above situation, which of the following statements is true?

and Anthony ate

Statement 1: Akbar ate less pizza than Anthony Statement 2:

5 th part of the pizza is still left. 18

(A) Statement 1 is true (B) Statement 2 is true (C) Both of the statements are true (D) None of the statements are true.

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Directions (Q49–50) Study the pie chart given below and answer the following questions. The pie chart given below represents the marks scored by Anish in different subjects in degrees:

49. If the total marks scored by Anish was 480, how much did he score in Mathematics? (A) 240 (B) 180 (C) 120 (D) 90 50. Find his total marks in English and Computer Science. (A) 120 (B) 160 (C) 180 (D) 200

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ANSWERS 1. (B)

2. (B)

3. (A)

4. (C)

5. (A)

6. (C)

7. (B)

8. (aA

9.(B)

10.(C)

11. (D)

12. (B)

13. (A)

14. (B)

15. (B)

16. (A)

17. (B)

18. (C)

19. (B)

20. (C)

21. (D)

22. (B)

23. (C)

24. (C)

25. (B)

26. (C)

27. (B)

28. (C)

29. (A)

30. (A)

31. (D)

32. (D)

33. (D)

34. (C)

35. (D)

36. (C)

37. (C)

38. (B)

39. (C)

40. (A)

41. (C)

42. (B)

43. (B)

44. (D)

45. (B)

46. (D)

47. (C)

48. (B)

49. (C)

50. (B)

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SOLUTIONS LOGICAL REASONING 1.

Observe each one-fourth of the square: 9+11=20

20^2 = 400

12+13=25 25^2 = 625 5+9=14

14^2 = 196

8+10=18

18^2 = 324

2.

The squares are- ABFE, BCGF, CDHG, EFJI, FGKJ, GHLK, IJNM, JKON, KLPO, ADPM, ACKI, BDLJ, EGOM, FHPN.

3.

The correct sequence of the words as they would appear in a dictionary would beAscensive, Ascent, Ascertain, Ascetic Ascertain is the third word of this sequence

4.

Answer: Option C

5.

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6.

Each group is represented by its position and then divided by the number of letters in the group. D

=

CAT = LION =

6 1

=6

3+1+20 3

=

24 3

12+9+15+14 4

=8 = 12.5

7.

Answer: Option B

8.

Only the first option will satisfy the given equation 64 ÷ 32 - 16 + 8 × 4 = 2 - 16 + 32 = 34 - 16 = 18

9.

Follow any one character here. First, each one of them changes its position by one place and then by two places. The changes have been depicted with respect to ‘+’.

The next image in the sequence will be-

10. The word ADMINISTRATION has only one S so the word TRANSISTOR cannot be formed. 11. The number common between Circle & Triangle - 2 The number common between Rectangle & Triangle - 9 The number common between Circle & Rectangle - 5 Sum = 2+ 9 + 5 = 16

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12.

13. If the letters of the word REGULATION are arranged with vowels first followed by the consonants, all in the alphabetical order, the word becomes AEIOUGLNRT 3rd letter AEIOU GLNRT

Left end

3rd to the right of the 3rd letter

14.

15. All other figures have closed – shapes at the end but fig II does not.

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MATHEMATICAL REASONING 16. A number divisible by 6 must be divisible by 2 and 3 both. All the options are even numbers, so are divisible by 2 but only option A has a number whose sum of the digits is divisible by 3 or the whole number is divisible by 3. 17. -71 + (-9) - (81) + (-9) + 1 - (-29) = - 71 - 9 - 81 - 9 + 1 + 29 = - 170 + 30 = -140

18. Let the number to be added be ‘x’ x + (-2367) = (-11993) x = (-11993) - (-2367) x = -11993 + 2367 = - 9626

19.

𝟑 𝟗

th of a number is 63. Let the number be ‘x’ Now,

3 9

x = 63 × 3 7

of x is 63 9

= 189 3

of 189 = 81

20. The temperature on Monday

= -2°C

The temperature on Tuesday after 3°C increase = -2 + 3 = 1°C Temperature on Wednesday after 1°C decrease = 1 - 1 = 0°C

21. XCIX = 100 - 10 + 10 - 1 = 99 22. Let Rohit’s present age be x years So, Rama’s age will be- 5 + 3x If 5 years ago Rohit’s age was 10 years, his present age will be 15 years x = 15 years Rama’s age = 5 + 3 × 15 = 50 years

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23. Figure 1 is a Triangular pyramid with 4 faces, 4 vertices, and 6 edges. Figure 2 is a Triangular prism with 5 faces, 6 vertices, and 9 edges. Figure 3 is a Square pyramid with 5 faces, 5 vertices, and 8 edges. Figure 4 is a Pentagonal pyramid with 6 faces, 6 vertices, and 10 edges.

24. The figure can be divided into 5 identical parts so it has 5 lines of symmetry.

25. The fraction of figure A which is shaded is

𝟔 𝟏𝟎

=

𝟑 𝟓

Figure B has been divided into 25 parts. So, to get an equivalent fraction 15 parts has to be shaded as

𝟏𝟓 𝟐𝟓

=

𝟑 𝟓

26. Answer: Option C 27. 3 - (4 - 5) ____ (3 - 4) - 5 The expression on the left will give: 3 - (4 - 5) = 3 - (-1) = 3 + 1 = 4 The expression on the right will give: (3 - 4) - 5 = (-1) - 5 = -6 Hence, 4 > -6

28. The perimeter of the given figure-

=2+2+3+2+4+5 = 18 cm www.cuemath.com

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29. A fraction or a decimal can never be an even number.

30.

I=

II = 7 6

14

7 3

9

÷

÷

8 6

can be written as

Similarly, 7 4

can be written as

4 3

=

= 28 24 42 24

14 9

7 3

✕

3

✕

6 8

4

=

=

7 6

7 4

as an equivalent fraction. as an equivalent fraction.

Comparing the two fractions we get I < II. 31. Answer: Option C 32.

33. Answer: Option D 34. The total number of students

= 90 + 110 + 130 + 140 + 100 + 150 = 720

The number of students in Grade 8 = 140 Fraction =

140 7 = 720 36

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35. The number of students of Grade 7 & Grade 9 taken together = 130 + 100 = 230 The number of students of Grade 5 & Grade 6 taken together = 90 + 110 = 200 The difference = 230 - 200 = 30

EVERYDAY MATHEMATICS 36. Manya had seven ₹ 100 notes = ₹ 700 Total expenditure by Manya

= ₹ 395.47 + ₹ 37.65 + ₹ 89.45 = ₹ 522.57

She saved = ₹ 700 - ₹ 522.57 = ₹ 177.43

37. Let the price of 1 candy be ‘c’ Price of 6 candies

= 6c

He is now left with, x = 100 - 6c Rearranging the terms, the price of 1 candy, c=₹

100 − 𝑥 6

2 16 2 2 38. The total weight of the three baskets = 1 + + 3 = 10 kg 3 3 5 5 39. Capacity of 1 glass = 10 ml = 0.01 L 0.01 L capacity glasses are used to empty 100 L 0.01 L equals capacity of 1 glass 1 L equals capacity of

1 0.01

100 L equals capacity of

40. Side of the square Perimeter of a square

glass

1 0.01

× 100 = 10000 glasses

= 0.7 m = 4 × 0.7

2 Available length of the wire = 2 m 5

= 2.8 m = 2.4 m

Extra length of wire required = 2.8 m - 2.4 m = 0.4 m

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41. Number of free hours Ayan had

= 3 hours = 180 minutes 1 = 1 hours + 40 minutes 2

Number of hours he spent

= 90 minutes + 40 minutes = 130 minutes Time left for him to work on his assignment = 180 - 130 = 50 minutes

42. The ratio of money distributed: Ravi: Rakesh

=6:7

Amount Ravi gets

= 6x

Amount Rakesh gets = 7x The difference of their amount is = ₹ 20 or, 7x - 6x = 20 or, x = 20 Amount Ravi gets = 6x = ₹ 120

1 1 20 + 15 + 12 47 + + = = 3 4 5 60 60 47 60 − 47 13 Part of her income which she has saved = 1 = = 60 60 60

43. The total expenditure of Priti in parts =

13 60

1

part of her income equals ₹ 1300

1 part (or her whole income) equals ₹ 1300 ×

60 13

= ₹ 6000

44. Answer: Option D 45. The relative position of the diver with respect to the sea level = 30 m below sea level = - 30 m He goes up by 10 m so his new position now becomes = -30 + 10 = -20 m

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ACHIEVERS SECTION 46. Area of the whole square

= 4 × 4 = 16 m2

Area of the shaded portion of the square = 6 m 2 Area of the unshaded portion

= 16 - 6 = 10 m2

Cost of painting 1 m2 Cost of painting 10 m2

= ₹ 10.80 = ₹ 10.80 × 10 = ₹ 108

47. A = 0.125 B=

3 9

× 117 = 39

C = 100 A × C + B = 0.125 × 100 + 39 = 12.5 + 39 = 51.5

48. Amar ate

1

2

=

5

Akbar ate 0.3 = Anthony ate

10 3 10

2 9

2 3 2 5 13 Part of the pizza left = 1 - ( + + )=1= 18 10 10 9 18 Akbar ate more pizza than Anthony as 3 3×9 27 Akbar ate = = = 10 10×9 90 Anthony ate =

2

2×10

20

= 9×10 = 90 9

Comparing the above fractions, clearly, Akbar > Anthony

49. The central angle corresponding to Maths is 90° Marks he got in Maths out of a total of 480

=

90° 360°

× 480 =160

50. The total corresponding angle to English and Computer Science = 120° Total marks he got in English and Computer Science out of a total of 480 =

120° 360°

× 480

= 160

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