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ebook

INTERNATIONAL MATHEMATICS OLYMPIAD

5

Years (2012-2016) Solved Papers

CLASS

4

INSTANT

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CLASS 4

Contents Â

6th IMO 2012 - SET A

Â

6th IMO 2012 - SET B

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CLASS 1

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CLASS 3


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CLASS 4


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CLASS 5


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CLASS 6






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CLASS 7






Reasoning



Math IQ Challenge

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Error-free

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For Classes 6, 7, 8, 9, 10, 11 & 12 C lass 6

Class 8

Class 7

Class 9

Class 10































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Class 6

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2

6th IMO - SET A

SECTION I : LOGICAL REASONING 1.

Which of the the give given n recta rectangle ngle ha has s the la large rgest st

P

perimeter? (A) P

Q

(B) Q

R S

(C) R (D) S 2.

0

2

Which one one of the follow following ing has has NO NO line of symme symmetry ? (A)

3.

1

(B)

(C)

(D)

Find Fin d the va values lues of P and Q res respe pectively ctively.. 8800

10200

13000

Q

1 800

3

4

5





























th

6.

3

-

Ri y a i s 17th from the front in a queue. She is 19th from the end. Then how many students are there in the queue? (A )

7.

(B )

(C

(D)

Removin moving g which which of the follow following ing squa square re will result result no change in the perimeter of the given gure?

8.

(A )

(B )

(C)

(D)

If there there are are 6 ce cells lls around around one ce cell, ll, 8 ce cells lls around around two cells in a row, then number of cells around a row of three 1

cells is _____.

9.

(A )

(B )

(C)

(D)

2

Roha Ro han n wants wants to move just one ma matchstick tchstick to make make the equa equation tion correct. correct. Which Which





























4

6th IMO - SET A

SECTION II : MATHEMATICAL REASONING 11.. Which of the following 11 following is equivalent to "ve lakhs one hundred hundred and nine"? 501009

50109

(A)

(B)

500109

(C)

510090

(D)

12. The given given bar graph graph shows shows the height height of ve chil dren. What What is the diff erence betwee between n the height of the tallest child and the shortest child ? (A) (A) 45 cm (B) (B) 30 cm (C) (C) 60 cm (D) (D) 105 cm 13.. The perimeter of the star equals t he perimeter of t he hexagon (all 13 (all s ides are equal). equal).































5

6th IMO - SET A 16.. Find the value 16 value of Y to make make the expression expression tr ue. 8000 = 50 (A) 2

(B) 10

17. Arr ange the boxes in order, beginnin g from the heaviest to lightest. (A) P, Q, R, S (B) (B) Q, R, S, P (C) (C) R, P, S, Q

×

80

×

Y

(C) 20

(D) 100





























6

6th IMO - SET A

21.. Roman numeral e 21 equi qui valent to 89 is ___ _____ ___. _. (A) (A) LXIL (B) IXC (C) (C) XIC

(D) (D) LXXXIX

22.. Wh 22 What at is the weight weight of each each box? (A) 40 g (B) 60 g (C) (C) 240 g (D) 90 g 23. In which of the following dotted lines shows a line of symmetry?





























7

6th IMO - SET A

27. The capacity of a small container is 380 mL and the capacity of a big container is 1250 mL. If Aakash uses 8 small containers and 1 big container of water to ll up an empty tank, then what is the capacity of the tank? (A) 3750 mL (B) (B) 4290 mL (C) (C) 3040 mL (D) (D) 4190 mL 28.. Priya is practicing fo r a race. 28 race. She uses the

2 km

given map to nd the possible routes. The route must start from her home and and end at the park. She wants to run exactly 7 km.

Club m m k k 2 2

1 k m 1 km

Home

3 k m

m k 2

2 km





























8

6th IMO - SET A

32.. There are 200 32 200 people in a hall. They are divi ded equally in to 7 gro ups o f adult s and 3 groups of children. If there are 2 adults in each group, then how many children are there in each group ? (A) 30 (B) 60

(C) 70

(D) 62

33. Three friends, friends, Payal, Latika and Megha are at the corners of of a rectangular rectangular eld. Att w h i c h p o i n t s h o u l d t h ey m eet s o t h at t h e d i s t an c es t h ey w al k t o t h at p o i n t i s A minimized?

Payal E

4 km



























































2

6th IMO - SET B

SECTION I : LOGICAL REASONING





























3

6th IMO - SET B 4.

Look the alpha lphabe bett serie series s below below : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z





























4 9.

6th IMO - SET B How Ho w many possible possible combination combinations s of one day day and one month are the there re with 5 da days ys and 5 months?





























5

6th IMO - SET B 1 5. I f

+

+

+

+

= 2 7 80 an d

+

+

= 1 96 0.





























6

6th IMO - SET B

19.. Study the given bar 19 bar graph carefully carefully and answer the question that follows.











































































































































































































































































































































































































































































































































































































































































8th I IM MO - SET B

5

22. Mr. Mr. Kapoor lled 3L 500mL petrol in his car on 1st December, 2L 750 mL on 5 th December and 4L 250 mL on 9th December. How much petrol did he ll in his car in the rst week of December? A.

6 L 250 mL

B. 10 L 500 mL

C. 1 L 500 mL

D. 105000 mL

23. Last year, year, Mini celebrated her twelfth birthday. birthday. This year, year, her brother is twice as old as Mini. How old will be her brother in three years time? A.

26 years

B. 27 years

C. 29 years

D. 32 years

24. Varun has some stickers. He can share them equally with 6 friends. He can also share them equally with 8 friends. What is the fewest possible number of stickers he can have? A.

12

B. 32

25. Rohan' Rohan's s schoo schooll is

2

1 2

C. 24

kilometres from his house. He cycles this distance daily. One day,

his cycle tyre got punctured after he had gone he had to walk? A.

1

3 4

km

D. 48

B.

2

1

C.

km

2

1

1 4

3

kilometres. What was the distance

3 4

km

D.

1

1

km

4

26. Saurabh bought 56 kg 500 g of rice from one shop and 48 kg 750 g of rice from another. How much rice did he buy? A.

105 kg 150 g

B. 105 kg 250 g

C. 250 kg k g 105 g

D. 1052500 g

27. In a farm, there there are 9 hens and some cows. If there there are 26 legs altogether, altogether, how many cows are there? A.

5

B. 6

C. 4

D. 2

28. If one notebook contains 260 pages, how many pages do 185 notebooks contain? A.

4450

B. 4810

C. 48100

D. 5100

29. 4600 people were to be transported in 100 buses. How many people could 1 bus carry, if each bus carry equal number of people? A.

46

B. 460

C. 4500 Space for Rough Work

D. 200



























8th IMO - SET B

6

30. Gautam wakes up at 6:15 a.m., takes 45 minutes to get dressed, 12 minutes to eat breakfast and 20 minutes to reach school. At what time does he reach the school? A.

7:30 a.m.

B. 7:32 a.m.

C. 7:28 a.m.

D. 7:35 a.m.

ACHIEVERS SECTION

31. The given bar graph shows the favourite ice-cream avours of a group of children. _____ of the children prefer strawberry avour.

A.

1/4

B. 1/5

C. 1/6

D. 4/15

32. Alia is thinking of a fraction. The numerator is 4 more than the denominator. denominator. The numerator and the denominator have only three common factors 1, 2 and 4. The denominator is a number greater than 4 but smaller than 10. What is the fraction Alia is thinking of? A.

4/8

33. Find the value of A.

B. 8/4 P

− Q + R

S

C. 12/8

D. 16/12 1P 19

.

)

38

3

72954

(

−38

349 −3 Q 2

B. 4

75 −

C. 6

38

3 R 4 −

D. 7

S 2

34. The movie tickets of 8 people cost A.

`

342

300

B.

`

5000

` 1000.

What will be the cost of 24 tickets? C.

`

Space for Rough Work

3000

D.

`

4500



























8th I IM MO - SET B

7

35. The given gure (not drawn to scale) is made up of square PQRS and a rectangle LMNO. LR is thrice the length of LQ. LM = RO. (a) Find the sum of PS and RO. (b) Find the length of LM. (a) (b) A. B. C. D.

12 cm 16 cm 12 cm 14 cm

6 8 8 6

cm cm cm cm Space for Rough Work



























Class 4 th

9

Set A Year 2015



























LOGICAL REASONING

1.

Some letters are given which are numbered 1, 2, 3, 4, 5 and and 6 followed by four options options containing combinations of these numbers. Find the combination of numbers so that letters are arranged accordingly to form a meaningful word.

A. 2.

6, 2, 3, 5, 4, 1

L

E

D

G

1

2

3

4

5

6

B. 5, 4, 1, 6, 2, 3

C. 3, 4, 1, 6, 5, 2

D. 1, 6, 5, 4, 3, 2

B.

C.

D.

If ‘Chocolate’ means ‘Toffee’, ‘Toffee’, ‘Toffee’ ‘Toffee’ means ‘Cake’ and ‘Cake’ means means ‘Butter’, then what is cut on birthday? A.

4.

O

Select Select the odd one out. A.

3.

N

Cake

B. Butter

C. Toffee

How many many possible possible combinations combinations of 1 color color and 1 dress dress is possible from the given colors and dresses? A.

12

B. 35 C. 21

D. Chocolate Dress

Color

Frock

Blue

Saree

Red

Suit

Black White

D. 49 5.

Which of the following gure gure is obtained when Figure (X) is folded along the dotted dotted line?

Figure (X) A.

B.

C.

SPACE FOR ROUGH WORK

D.





























6.

Find the mirror image of Figure (X), if the mirror mirror is placed along MN. M

Figure (X) N A.

7.

B.

C.

D.

In which of the following gures, Figure (X) is exactly exactly embedded as one of its part?

Figure (X) A.

8.

B.

C.

Study the adjoining diagram carefully. carefully.

D.

Police Station

Library

Mohit is facing towards Park. If Theatre and Hospital interchange their positions, and Mohit takes

Hospital

1

turn anticlockwise,

4

then he will be facing towards ________. A.

Mohit

Office

Park

Book Store

B. Theatre C. Police Station

MTG Mall

D. Hospital 9.

Park

Mall

Find the missing missing number, number, if a certain rule is followed in all the three gures. 15 6

12 12

8

13

10 ?

14

Theatre





























10. Read the information carefully. ● Manu is taller than Chinku. ● Tanu is taller than Chunnu. ● Chunnu is taller than Manu. Who among the following is the tallest? A.

Manu

B. Chinku

C. Tanu

D. Chunnu

MATHEMATICAL MA THEMATICAL REASONING REAS ONING

11. Find P, Q, R and S respectively. A.

P

1, 6, 1, 4

44

B. 1, 4, 6, 1 C. 1, 4, 1, 6

4

_

6 2 5 4 S

_

R 8 5 1 7 Q 9

D. 4, 1, 1, 6 12. How many multiples of 10 are there from 20 to 150? A.

13

B. 14

C. 15

D. 12

13. 94560 in words is written as _________. A.

Ninety-four hundred and fty-six

B. Nine thousand, four hundred hundred and fty six

C. Nine thousand, ve hundred and sixty

D. Nine Ninety ty-f -fou ourr thou thousa sand nd,, ve ve hund hundre red d and and sixt sixty y

14. What fraction of the owers are red? A.

9/20

B. 1/2 C. 1/4 D. 19/40 15. If

+

+

+

+

= 125 and

=

+ 4, then then nd the value value of





























16. If the weight weight of each A.

is same, then weight of

is ______ ______ g.

33

B. 22 C. 28

20

D. 9 17. The bar graph shows the savings of ve children. Akansha Aka nsha needs nee ds to save another ano ther ______ ____ __ so that she has twice as much money as Mohit. A.

`

50

B.

`

150

C.

`

100

D.

`

200

0 g

25

15

5

25

10

20

0 g

15

5 10

Kiran Jyoti Mohit Akansha Shalini 0

50 100 100 150 150 200 200 250 250 300 300 350 350 400 400 Amount (in `)

18. How long did Varun take to complete his homework? A.

1 hr 45 mins

B. 1 hr 30 mins C. 1 hr 50 mins D. 1 hr 40 mins

Start doing homework

19. The given gure is made up of three rectangles. Find the length of CD. A.

Completed homework

5 cm A

B

4 cm E

F

10 cm ?

B. 7 cm C. 8 cm

D

C

G

H

D. 13 cm

17 cm

20. Figures (i) and (ii) shows two identical rectangles X and Y which are arranged differently. What is the difference between the perimeters of both the gures? A.

2 cm

B. 6 cm

X

Y





























EVERYDAY MATHEMATICS

21. The ight from Chennai to Dubai took off at 4:45 hours. It landed at Dubai at 9:15 hours. How long was the ight? A.

4 hrs 50 mins

B. 3 hrs 55 mins

C. 4 hrs 30 mins

D. 4 hrs 10 mins

22. Mrs. Latika bought 2 L 500 mL of milk. She used 750 mL to make coffee and fed her cat with 350 mL of milk. Find the quantity of milk that is left over. A.

1 L 100 mL

B. 2 L 50 mL

C. 2 L

D. 1 L 400 mL

23. The contents in Anaya’s school bag are given below. Text books – 675 g, Notebooks – 415 g, Pencil box – 175 g. If the empty bag weighs 205 g, calculate how much does the school bag weigh with its contents? A.

1 kg 520 g

B. 1 kg 470 g

C. 1 kg 220 g

D. 2 kg

24. In a bag, there were 5600 red beads and 6540 white beads. Kavya sold 3680 beads. How many beads were left in the bag? A.

12140

B. 6240

25. Charu had 36 cookies. She gave

C. 4620 1 9

D. 8460

of the cookies to her brother. brother. How many cookies had

she left with her? A.

32

B. 28

C. 30

D. 16

26. Megha collected 324 seashells. She collected 78 more seashells than Beena. How many seashells did they both collected altogether? A.

246

B. 570

C. 492

D. 726

27. The total number of children in a class is 40. 7 children were absent on Monday. What fraction of the class was present on Monday?





























28. To decorate a banquet hall, 354 electric bulbs were bought. If the cost of each bulb is ` 28, what is the total cost of 354 electric bulbs? A.

`

9912

B.

`

7660

C.

`

4944

D.

` 9940

29. Garima travels 504 km to her ofce in a month. If she works for 28 days in the month, nd the distance she travels in one day. A.

9 km

B. 12 km km

C. 18 km

D. 22 km

30. A music store sold 192 CDs every week. Find the number of CDs sold in 38 weeks. A.

5376

B. 6144

C. 8064

D. 7296

ACHIEVERS SECTION

31. Fill in the blanks. A multipl mult iple e of a number numb er is __P ____ smaller small er than the number. A multiple o f an even number n umber is __Q ____ odd. 1 is the __R ____ of every number. P

Q

R

Never

Factor

B. Never

Never

Factor

C. Always

Always

Multiple

D. Never

Always

Multiple

A.

Sometimes

32. The figure shows the amount of water in 3 beakers at rst. Karan poured 150 mL of water from beaker P to beaker Q. He then poured 200 mL of water from beaker Q to beaker R. Finally, Finally, he poured 100 mL of water from beaker R to beaker P. Which one of the following statements is true? A.

500 mL

500 mL

500 mL

400

400

400

300

300

300

200

200

200

100

100

100

P

Q

R

Beaker P contained more water than the other beakers at the end.

B. Beaker Q contained more more water than the the other beakers at the end. end.































33. Find P, Q, R and S respectively. A.

IX, XI, IV, IV, II

_

B. II, III, VIII, IV

C. IV, VII, VIII, II

P 8 5 Q 3 R S 5 5

D. VIII, VII, IV, II

4 3 2

34. The gure is obtained by removing some small identical squares from a big rectangle. The length of each side of a small identical square in the obtained gure is 2 cm. Find the perimeter of the gure. A.

40 cm

B. 56 cm

C. 64 cm

2 cm

D. 128 cm

2 cm

35. The table shows the number of points scored by different teams at a sports meet. Which two teams had a total of 538 points?

A.

Team(s)

Yellow

Green

Red

Blue

Purple

Points

351

187

308

402

298

Yellow and Purple B. Red and Purple

C. Yellow and Green D. Red and Green

SPACE FOR ROUGH WORK





























Class 4 9th





























logical reasoning

1.

Which of the following series is following the given rule? Rule : Number of letters skipped in between adjacent letters in the series decreases by one. A.

2.

TOJEZUP

B. VOIDZWU

C. IGECAYW IGECAYW

D. NKHEBV

There is a denite relationship between between gures (i) and (ii). Establish the same relationship between gures (iii) and (iv) by selecting a suitable gure from the options that would replace the (?) in g. (iv). ? (i) A.

3.

(ii)

B.

(iii)

(iv)

C.

D.

Which of the following will be the next term in the given number pattern pattern ? A.

90

B. 65 C. 120

1

2

6

24

?

D. 29 4.

In a certain code, '14567' is written as 'LXRZA' 'LXRZA' and '9823' is written as 'VPIC'. How will '94623' be written in the same code?





























6.

Find the option which will complete the given gure pattern.

?

A.

7.

B.

C.

D.

In which of the following gures, Fig. (X) is exactly embedded as one of its part?

Fig. (X) A.

8.

B.

C.

Garima faces Mango tree, goes straight and takes a left turn to reach Orange tree. She again takes a left turn to reach Apple tree. In which direction is she facing now? A.

D.

Orange tree

Island

North

B. East C. West

Mango tree

Garima Apple tree





























10. Select the CORRECT match. Figure

Number of lines of symmetry

Figure

Number of lines of symmetry

A.

2

B.

1

C.

1

D.

4

mathematical ma thematical reasoning reas oning

11. Which of the given gures has the least perimeter? A.

Fig. P

4 cm 5 cm

B. Fig. Q

2 cm

P 5 cm

C. Fig. R

2 cm 2 cm

Q

2 cm

2 cm

4 cm

R

4 cm

4 cm

D. Can’t be determined 12. Which of the following gures has 2 pairs of parallel lines and 2 pairs of perpendicular lines? A.

B.

13. Which of the following gures represents A.

B.

C.

3 5

D.

− 2 shaded fraction? 5

C.

D.































15. Shailesh is celebrating Diwali with his friends. He knew that recrackers can be burst only till 10 p.m. The time shown by the clock is the starting time when Shailesh starts bursting crackers in the night. For how much time can Shailesh and his friends enjoy bursting crackers? A.

20 minutes

B. 45 minutes

C. 40 minutes

D. 56 minutes

16. There are ___________ even factors of 48. A.

4

B. 5

C. 6

D. 8

17. Read the menu of a hotel and answer the question. mu

Item

Cost (in ` )

Item

Cost (in ` )

Soup

30.00

Chips

10.00

Juice

10.00

Coffee

3.00





























20. Find the symbol in the box. CX + XXXVI – XXIII A.

>

LX – XXXVIII + XI B. <

C. =

D. Can’t be determined everyday mathematics

21. Shikha has

22

7

3

3

m of green ribbon and Priya has

m of yellow ribbon. Who has more

ribbon and by how much? A.

Shikha, 5 m

B. Priya, 5 m

C. Shikha, 7 m

D. Priya, 7 m

22. Samrat was given one week time to complete his geometry project. He realized that 3 days and 17 hours had already gone by. How much time is left for Samrat to complete his project? A.

3 days 7 hours

B. 3 days 9 hours

C. 4 days

D. 3 days 6 hours

23. Varun undertook a pilgrimage on foot. He walked 3 km 550 m on the rst day, 5 km on





























28. Parking space in theatre P is for 79,407 cars, while the same in theatre Q is for 58,868 cars. How many more cars can be parked in theatre P than in theatre Q? A.

38,275

B. 21,549

C. 21,461

D. 20,539

29. 990 cold drink bottles are to be placed in crates. Each crate can hold 18 bottles. How many crates would be needed? A.

50

B. 55

C. 60

D. 65

30. A library has 35 shelves. Each shelf has 455 books. Find the number of books in the library. A.

15925

B. 15625

C. 14825

D. 13965

achievers section

31. Pinku, Ravi, Brijesh and Raghu are friends. The graph shows the toy cars each of them have. What can we conclude from the given graph? Pinku A. Brijesh has one-third the number of toy cars Pinku has. Ravi





























33. Which of the following statements is INCORRECT ? A.

1 is a factor of every number. number.

B. Every multiple of a number is greater than or equal to the number. number. C. The greatest factor of every number is the number itself. D. Number of factors of any number are always one more than the number. number. 34. Rahul took 162 sweets to school on his birthday. He distributed all sweets to the 32 children in his class equally. How many sweets did each child get? How many sweets were left with him? A.

5, 2

B. 2, 8

C. 9, 5

D. 5, 7

35. Which of the following gures have same perimeter? 42 cm 18 cm

18 cm

(i)

6 cm

(ii)

8 cm

8 cm 28 cm

22 cm

2 cm

2 cm

4 cm 14 cm

12 cm

(iii)

2 cm 16 cm

16 cm



























































LOGICAL REASONING

1.

Which of the following gures is same as the Problem Figure? Problem Figure

A.

B.

C.

D.





























5.

6.

Select the INCORRECT match. A.

–

B.

–

C.

–

D.

–

Which of the following words can be formed from the letters of the the given word? word? MEASUREMENT A.

7.

MASTER

B. MANTLE

C. SUMMIT

D. ASSURE

In a certain code language, the letters are coded as follows : S

B

C

P

N

E

O

H

R

M





























MATHEMATICAL REASONING

11. The adjoining list shows the names names of the students who are in the Environmental Club.

Students in the Environmental Club

What fraction of names are starting with alphabet M? A.

2 8

B.

3 8

C.

1 8

Ananya

Jesha

Sanya

Mrinal

Mohit

Sidak

Mehul

Parul

D. 0





























16. If

+ +

A.

= 19 kg,

+

+

+

= 22 kg, then the weight of

4 kg

B. 3 kg

+

+

+

+

C. 2 kg

D. 5 kg 12 c m

18 cm

160 cm

B. 142 cm C. 138 cm

= 94 kg and

= ?.

17. Find the perimeter of the given gure. A.

+

9 cm

12 cm





























EVERYDAY MATHEMATICS

21. For a wedding the decorators have to x 1250 owers in the hall. If they had already xed 985 owers, how many more owers do they have to x? A.

270

B. 265

C. 272

D. 358

22. A farm has 437 rows of mango trees with 108 trees in each row. How many mango trees are there in the farm? A.

48196

B. 57301

C. 47196

D. 52305































29. Sonika went to her friend’s house at 1:15 p.m. Her father told her to be back home in 1 hour and 45 minutes. What time does Sonika needs to be at home?





























33. How many more squares of side 1 cm must be added to the given gure to form a square of side 5 cm? A.

9

B. 11

1 cm

























































LOGICAL REASONING

1.

Thee is a denite elationship elationship between between gues gues (i) and (ii). Establish a simila elationship





























5.

Kunal folds a piece of pape and cuts cuts out a shape as shown below. below.













































































































































































Years Solved Papers: Class

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