THEMATA OLYMPIADAS

1 2000 : 50

' 1. 6. 3, 4, 5

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66,72,78, 84, 90, 96, 102, 108, 114, 120, 126, ... 3, 4, 5 6; . 12 . 18 . 42 . 60 . 90

2. (. ); . 19 . 39 . 63 . 87 . 93

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2 2001 : 60 ' 1.. 5 2 1+1+1+1+1+1+1+1+1+1= . 4 2 .

2 2

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1999-1996 = 99 [ ] . 6 ] . 210 . 11 . 20 . 19 . 99 . 96

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B. 105

. 104

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B. 6:55 ..

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. 7:05 ..

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18. 72 cm2, ;

. 12 cm2

. 18 cm2

. 6 cm2

. 4 cm2

.

1 cm2 4

19. 20 58. ;

A. 144

B. 2

. 0

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E. 14...

6

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23. 64 cm 4 cm. ;

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(4 x ) 22 = 46, ;. 16 . 17 . 22 . 68

. 6 25.

512 cm3, :. 256 cm . 128 cm . 8 cm . 4 cm

. 16 cm

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...

6th CYPRUS MATHEMATICAL OLYMPIAD

4th Grade

English Version 4th Grade

1. Find the answer.0,9 (0,4 + 0,6)= . 0,9 . 9 C. 1,9 D. 0,09 . 1

2.John multiplied a number by 10 instead of dividing it by 10. He obtained the result100. What would have been the correct result if he hadnt done this mistake? .

1 10

. 1

C. 10000

D. 100

. 1000

3.There are some pupils on a school bus. At the first bus stop 3 pupils get of the busand 7 get in. At the second bus stop Maria and her 2 little cousins get of the bus. The remaining 12 pupils that are still on the bus leave at the third bus stop. How many were the pupils before the first bus stop?

. 10

. 11

C. 12

D. 13

. 14

4.The digit * in the following sum is equal to:

. 1

. 2

C. 6

D. 7

. 9

5. How many matchsticks will you need to construct the fourth shape in the row?

47


4th Grade

. 9

. 18

C. 30

D. 42

. 45

6. Which of the following numbers is a prime number?A. 27 B. 39 C. 17 D. 35 E. 91

7. If ((x 1) 1) + 1 = 105, what is the value of x;A. 106 B. 105 C. 104 D. 103 E. 102

8. Below is the beginning of a pattern. The number under each triangle shows thetotal number of dots on the triangle. The number inside the triangle shows the number of dots on each side of the triangle.

If we continue the pattern, which number will be shown inside the triangle, when the number under the triangle will be 27?

A. 10

B. 33

C. 9

D. 36

E. 12

9.

The objects have the following masses:

Which combination of objects below makes up 2,05 kilograms?

. C. .

. D.

48

...


4th Grade

10. A supermarket advertises the following promotion: If you buy 4 jars of jam at. 1,32 B. 1,27 C. 1,25 D. 0,96 . 1,09

the normal price, the fourth one costs only 10 cent". Helen paid 7,70 and bought 8 jars of jam. What is the normal price for one jar of jam?

11. Peter built a model of a small house. The small house had no floor and no doors.

Which of the following shows the shapes that Peter used to build the house?

12.. 0

1+ 2 + 3 + 4 equals 1 2 5 B. 1 C. 2 D. 3 . 4

13. What is the missing number in the square?

49


4th Grade

. 5

B. 20

C. 21

D. 10

. 25

14. If you multiply 11 13 15, what is the units digit of the product?. 1 B. 3 C. 5 D. 7 . 9

15. What is the result of the following operations?. 0,78 . 1,3 C. 0,189 D. 3,9 . 0,39

16. If you divide 2001 by 200, the remainder is:. 1 . 10 C. 99 D. 9 . 0

17. You are planning to go to the cinema to watch a 60-minute movie. The movie

you want to watch starts at 7:30 p.m. You want to get to the cinema 10 minutes before the movie starts, so that youll have plenty of time to buy your tickets. If it takes you 20 minutes to get to the cinema from your house, at what time should you leave your house? B. 6:55 p.m. C. 7:00 p.m.2

A. 6:50 p.m.

D. 7:05 p.m.

E. 8:05 p.m.

18. If the area of the hexagon is 72 cm , what is the area of the shaded part of thehexagon?

. 12 cm2

. 18 cm2

C. 6 cm2

D. 4 cm2

.

1 cm2 4

19. Four consecutive natural numbers add up to 58. Which is the smallest of thesefour numbers? A. 150

B. 2

C. 16

D. 13

E. 14...


4th Grade

20. Which of the following has the biggest sum?A. 0,3 + 0,11 B. 0,09 + 0,21 C. 0,4 + 0,10 D. 0,27 + 0,14 E. 0,41 + 0,03

21. How many different 4-digit numbers can be constructed using the digits 1, 2, 3and 4, if each digit is only used once in each number? . 8 C. 20 . 4 D. 12 . 24

22. Nikos and Niki had 1 1 chocolates to divide evenly between them. What part of 2the chocolate does each one get? A.5 8

B. 1

1 4

C.

3 4

D.

1 4

E.

1 2

23. The length of a rectangle is 64 cm and its width is 4 cm. Which of the followingsquares has the same area as the rectangle? . Square with a side of 8 cm C. Square with a side of 256 cm . Square with a side of 16 cm . Square with a side of 2 cm D. Square with a side of 12 cm

24. If (4 x ) 22 = 46, find the value of ;. 6 . 16 C. 173

D. 22

. 68

25. If the volume of a cube is 512 cm , then the side of the cube is:. 16 cm . 256 cm C. 128 cm D. 8 cm . 4 cm

26. I need 4 pins to fix a rectangular picture on the board, and 6 pins to fix twopictures, as it is shown in the picture below.

51


4th Grade

How many pins do I need to fix 10 pictures in the same manner? . 24 . 22 C. 20 D. 18 . 16

27. What is the value of X?2 30 3 5 8 96 6 2 4 80 4

XD. 5 . 4

. 8

. 12

C. 9

28. I used 5 squares in order to construct the following shape. The perimeter of theshape is 72 cm.

How many square centimeters is the area of the shape? . 36 . 180 C. 108 D. 360 . 5

29. The sum of 7 one-digit numbers is 17. Six of these numbers are the same. Whatis the value of the seventh number? . 7 . 1 C. 3 D. 6 . 5

30. What part of the hexagon is shaded;

.

1 2

.

5 12

C.

4 12

D.

1 3

.

3 12

52

...

. 1 9

7 2006 : 60

1. ;

2. 27 5 . ; . 4 . 6 . 9 . 15 . 81

3. 101 101 101 :. 101 112 . 10 211 . 11 111 . 11 211 . 10 121

5 2 6 . 57 . 21 . 67 . 32

4. 4 1, 3; . 42

10 . 5 , 2 . 29 . ; . 5 . 6 . 7 . 8 . 9

5.

7

. 2 9

78 . , , , ... , ;; . 5 . 8 . 12 . 13 . 10

6.

. 48 cm. ; ( , , ).

7.

A . 48 . 60 . 50 . 80

B . 10

8. , . . 9 . 2 . 1

A B + , ; . 8 . 0

9. ;. 28 7 > 3 1 . 9 6 < 7 8 . 8 0 < 7 7 . 63 7 > 64 8 . 48 6 < 36 9

. 3 9

10. , , , 5 ;

1 2 3 4 5 6A. 1 B. 2 . 3 . 4 E. 6

11. (( 6) 6) + 6 = 66 6, .A. 16 B. 36 . 56 . 66 E. 366

12. , ;

. 90 B. 40 . 100 . 1 20 . 1 18

13. .

. 648 cm2

B. 324 cm2

. 162 cm2

. 36 cm2

. 18 cm2

7

. 4 9

14. ;

. 8

B. 7

. 9

. 10

. 12

15. :

100, 3; 5; , . B. 75 . 36 . 45 . 25

. 30

16. M N . M + N;

A. 14

B. 12

. 15

. 13

E. 11

17. ;268 + 1375 + 6179 - 168 - 1275 - 6079 . 300 B. 0 . -100 . 100 . -300

. 5 9

18. , ;

A

B

7

. 6 9

1 9 , , , *; ( ).

19.

A. 8

B. 5

. 9

. 6

E. 7

20. ;

. 1

B. 3

. 5

. 7

. 9

3 21. 7 ; 18 A. 49 27 B. 56 33 . 70 42 . 91 48 E. 112

. 7 9

, ;

22.

---------------------------------------------------------------------

.

.

.

.

.7

. 8 9

. 25 cm 2 10 cm 2 , . ;

23. 4 :

A. 5 cm

B. 6 cm

. 7 cm

. 8 cm

E. 9 cm

24. ;A. . B. E. .

.

25. X, , ,

A. 8

B. 7

. 6

. 3

E. 10

26. ;(999+999+999+999+999) 999 = 9 A. 3 B. 4 . 5 . 6 E. 7

. 9 9

27. 100 + 0,01 0,001 =A. 100,09 B. 100,9 . 99,09 . 100,009 . 100

28. 16 , 16 =4 4. 2 101;A. 7 B. 8 . 9 . 10 E. 11

. ;A. 15 B. 16 . 17 . 21 E. 37

29. 42 . 5 30. 2500 .. 1, 10 60.

, 22 ,

124;

A

7

8 2007 : 60

' 1. .0,9 (0,4 + 0,6)=. 0,9 . 9 . 1,9 . 0,09 . 1

2. 10. .

10 100. , ;

1 10

. 1

. 10000

. 100

. 1000

3. . . 10 . 11 . 12 . 13 . 14

3 7. 2 . 12 . ;

4. * ;

. 1

. 2

. 6

. 7

. 9

8

5. ;

. 9

. 18

. 30

. 42

. 45

. .

6.

;

2 3+ 7. 1 +1 + 5 4 : 2 . 0 B. 1 . 2 . 3 . 4

8

8. ;

. 5

B. 20

. 21

. 10

. 25

9. 11 13 15, ; . 1 B. 3 . 5 . 7 . 9

10. ;. 0,78 . 1,3 . 0,189 . 3,9 . 0,39

11. . 4 . 8 . 20 . 12 . 24

1, 2, 3 4, ;

12. 1 1 . 2 ;. A.5 8

B. 1

1 4

.

3 4

.

1 4

E.

1 2

13. 64 cm 4 cm. ; . 8 cm . 2 cm . 256 cm . 12 cm . 16 cm

8

14. (4 x ) 22 = 46, ;. 6 . 16 . 17 . 22 . 68

15.

512 cm3, :. 16 cm . 256 cm . 128 cm . 8 cm . 4 cm

16. 78 . . 5 . 8 . 12 . 13 . 10

, , , ... , ;;

17. . , ,

48 cm. ; ( ).

A. 48 . 60 . 50 . 80

B. 10

18. , . . 9 . 2 . 1

A B + , ;

. 8

. 0

8

19. ;. 28 7 > 3 1 . 9 6 < 7 8 . 8 0 < 7 7 . 63 7 > 64 8 . 48 6 < 36 9

20. , , 1 2 3 4 5 6A. 1 B. 2 . 3 . 4 E. 6

, 5 ;

21. M N . M + N;

A. 14

B. 12

. 15

. 13

E. 11

22. ;268 + 1375 + 6179 - 168 - 1275 - 6079 . 300 B. 0 . -100 . 100 . -300

8

23. , ;

A

B

8

24. 1 9 ,

, , *; ( ).

A. 8

B. 5

. 9

. 6

E. 7

25. ;

. 1

B. 3

. 5

. 7

. 9

26. ;(999+999+999+999+999) 999 = 9 A. 3 B. 4 . 5 . 6 E. 7

8

27. 100 + 0,01 0,001 =A. 100,09 B. 100,9 . 99,09 . 100,009 . 100

28. 16 , 16 =4 4. 2 101;A. 7 B. 8 . 9 . 10 E. 11

29. 42 . 5 . ;A. 15 B. 16 . 17 . 21 E. 37

30. 2500 .. 1, 10 60. , 22 ,

124;

A

CYPRUS MATHEMATICAL S0CIETY 8th CYPRUS MATHEMATICAL OLYMPIAD April 2007 TIME: 60 MINUTES

4th GRADE - D Demotikou1. Find the answer.0,9 (0,4 + 0,6)= . 0,9 . 9 C. 1,9 D. 0,09 . 1

2.John multiplied a number by 10 instead of dividing it by 10. He obtained the result 100.What would have been the correct result if he hadnt done this mistake? .

1 10

. 1

C. 10000

D. 100

. 1000

3.There are some pupils on a school bus. At the first bus stop 3 pupils get of the bus and 7. 10 . 11 C. 12 D. 13 . 14

get in. At the second bus stop Maria and her 2 little cousins get of the bus. The remaining 12 pupils that are still on the bus leave at the third bus stop. How many were the pupils before the first bus stop?

4.The digit * in the following sum is equal to:

. 1

. 2

C. 6

D. 7

. 9


4th GRADE - D Demotikou

5. How many matchsticks will you need to construct the fourth shape in the row?

. 9

. 18

C. 30

D. 42

. 45

6.Peter built a model of a small house. The small house had no floor and no doors.

Which of the following shows the shapes that Peter used to build the house?

7.. 0

1+ 2 + 3 + 4 equals 1 2 5

B. 1

C. 2

D. 3

. 4



8.What is the missing number in the square?

. 5

B. 20

C. 21

D. 10

. 25

9.If you multiply 11 13 15, what is the units digit of the product?. 1 B. 3 C. 5 D. 7 . 9

10. What is the result of the following operations?

11. How many different 4-digit numbers can be constructed using the digits 1, 2, 3 and 4,if each digit is only used once in each number?

. 4

. 8

C. 20

D. 12

. 24

12. Nikos and Niki had 1 1 chocolates to divide evenly between them. What part of the 2chocolate does each one get?

A.

5 8

B. 1

1 4

C.

3 4

D.

1 4

E.

1 2

13. The length of a rectangle is 64 cm and its width is 4 cm. Which of the followingsquares has the same area as the rectangle?

. Square with a side of 8 cm C. Square with a side of 256 cm . Square with a side of 16 cm

. Square with a side of 2 cm D. Square with a side of 12 cm



14. If (4 x ) 22 = 46, find the value of ;. 6 . 16 C. 173

D. 22

. 68

15. If the volume of a cube is 512 cm , then the side of the cube is:. 16 cm . 256 cm C. 128 cm D. 8 cm . 4 cm

16. There are 78 seats in a bus. The bus leaves the station empty and takes one passenger. 5 . 8 C. 12 D. 13 . 10

from the first bus stop, two passengers from the second bus stop, three from the third bus stop etc. If no passenger gets off the bus, after how many bus stops will the bus be full?

17.

Shapes A and B have the same area. The perimeter of shape A is 48 cm. What is the , are squares).

perimeter of shape B? (The small shapes like this one

A

B

. 48

. 60

C. 50

D. 80

. 10

18.

A, B and C are different numbers. If

A B + , what is the value of C?

. 9

. 2

C. 1

D. 8

. 0



19.

Which one of the following statements is false?

. 28 7 > 3 X 1 . 9 X 6 < 7 X 8 C. 8 X 0 < 7 7 D. 63 7 > 64 8 . 48 6 < 36 9

20. If the figure below is folded, it becomes a cube. Which number will be on the bottomof the cube, if 5 is on the top of the cube?

1 2 3 4 5 6A. 1 B. 2 C. 3 D. 4 E. 6

21. In the subtraction shown, M and N each represent a single digit. What is the value ofM + N?

A. 14

B. 12

C. 15

D. 13

E. 11

22. What is the value of:. 300 B. 0

268 + 1375 + 6179 - 168 - 1275 6079=

C. -100

D. 100

. -300



23. If I from the construction below I remove the three cubes indicated with X, which oneof the following will be the new construction created?

A

B

C

D

E



24. The digits from 1 to 9 inclusive are to be placed in the figure shown below. Only onedigit goes in every square. If the sum in each of the four lines is the same which digit should replace *?

A. 8

B. 5

C. 9

D. 6

E. 7

25. Which is the missing number in the shape below;

. 1

B. 3

C. 5

D. 7

. 9

26. Find the value of .(999+999+999+999+999) 999 = 9 -

A. 3

B. 4

C. 5

D. 6

E. 7



27. 100 + 0,01 0,001 =A. 100,09 B. 100,9 C. 99,09 D. 100,009 E. 100

28. Sixteen is called a square number, because 16 = 4 4. How many square numbersare there between 2 and 101?

A. 7

B. 8

C. 9

D. 10

E. 11

29. Aunt Anna is 42 years old. Eleni is 5 years younger than Niki, and iki is half the ageof Aunt Anna. How old is Eleni?

A. 15

B. 16

C. 17

D. 21

E. 37

30. In Mesopotamia in 2500 B.C.,This sign was used to represent 1, This sign was used to represent 10 and This sign was used to represent 60. Thus, 22 would be written like this:

How would 124 be written?

A D

C

1

' 13 2008 1. (. ); . 93 . 87 . 39 . 63 . 19

2. 1x4x16=2x8x . 8

: . 4 . 3 . 2 . 1

3. 28 . 4 3 : . 7 . 12 . 14 . 16 . 20

4. 12. . 16 . ; . (12x3)16= . (3x16)12= . 3x(1612)=

. 16(3x12)=

. 12+3+16=

5. 0,9 0,99 : . 1,98 . 1,89 . 1,08 . 0,999 . 0,98

6. 5 2 1 3 , o 10 : A. 6 B. 9 . 10 . 12 E. 20

7. . . ; A. 5 B. 6 . 15 . 10 E. 9

8. , 10 10. 500. , ; A. 0,5 B. 5 . 50 . 5000 E. 50000

9 2008

2

9. 3 100 + 9 10 + 27 : . 39, . 23, . 22, . 12, .

10. 16cm2. , :

. 7 cm . 4 cm . 3 cm2 . 6 cm2 . 11. 7 4. . 1 . 100 . 6 . 7 . 9

2

2

12. . 5

1 1 . 7 2 2

1 303 : 6 1 . 50 .1,818 . 2

13. 35% ; 1 1 3 . . . 4 3 5

.

5 5

.

3 8

14. .

. 8 cm2 . 16cm2 . 4 cm2 . 35 cm2 .

9 2008

15.

3

A ( ), . .6 16. .4 .5 .7 .

: 3 6 1 1 . . . . . 3 5 16 2 17.

1m. ; . 20m . 21m . 22m . 23m . 24m

9 2008

18. 4 5 . 456; . 470 . 580 . 480 . 570 .

4

19. . 1,5

5 : 9 . 0,7 . 1,8 . 0,8

.

20.

1 2

2 3 17 . 24

.

1 3

.

1 4

.

7 12

.

3 4

21. 5 5 5 2 2 2 2 2 4 A.125 B. 125 2

:. 125 4 . 125 8

E: 22. . 44 100, 4 5 8. ; A. 48 B. 50 . 58 . 80 E. 85

23. . 10 . ; . 5 .10 .9 .20 .

24. . ; . 2 . 3 .5 .4 .

25. . 100 100 ; .100 . 5 .20 .10 .

9 2008

5

26. 1 . 2 . , 3, ;

1 .

2 .

3

81 256

.

27 64

9 16

.

3 4

.

27. 6cm X 8cm X 10cm . 2cm x 2cm x 2cm. ; . 6 28. . 12 . 8 . 16 . 4 6 x 18 34

3 4 6 x 18

x . 8 . 9 . 10 . 11 . 12

29. 6 . . ; U V W X Z A. Z

B.U

.V

.W

.Y

9 2008

30. AB , A = A B = B. E = 70 . .

6

70

A

E

B

.40

.60

. 55

.45 .

9 2008

4th Grade-D Dimotikou

1

4th Grade-D Dimotikou1. Which of the following numbers is prime (that is, is divided only with itself and the unit)? A. 93 B. 87 C.39 D. 63 E. 19

2. If 1x4x16=2x8x

, the missing number in the box is A. 8 B. 4 C. 3 D. 2 E. 1

3. In a class there are 28 children. 4 boys correspond to 3 girls. How many are the boys in the class? A. 7 B. 12 C. 14 D. 16 E. 20

4. Mimis has 12. Timos has 3 times more money than Mimis. Fotis has 16 less money than Timos. If z represents Fotis money which of the following relations is true? A. (12x3)-16=z B. (3x16)-12=z C. 3x(16-12)=z D. 16-(3x12)=z E. 12+3+16=z

5. The sum of the numbers 0,9 and 0,99 is: A. 1,98 B. 1,89 C. 1,08 D. 0,999 E. 0,98

6. If 5 oranges cost as much as 2 pears and 1 pear costs as much as 3 apples, then 10 oranges cost as much as ... apples. A. 6 B. 9 C. 10 D. 12 E. 20

7. Five teams participate in a football championship. Every team plays with all the other teams only once. What is the total number of matches that will be played? A. 5 B. 6 C. 15 D. 10 E. 9

CYPRUS MATHEMATICAL SOCIETY

9th MATHEMATICAL OLYMPIAD

4th Grade-D Dimotikouby 10. The wrong answer was 500. What is the correct answer? A. 0,5 B. 5 C. 50 D. 5000 E. 50000

2

8. A student by mistake, multiplied a number by 10, instead of dividing it

9. If we add the digits of the number 3 100 + 9 10 + 27 , the answer will be: A. 39 B. 23 C. 22 D. 12 E. none of the previous

10. The area of the following square is 16cm2. If K and M are the midpoints of AB and AD respectively, then the shaded area equals:

A. 7cm2

B. 4cm2

C. 3cm2

D. 6cm2

E. none of the previous

11. How many integers are there, which when divided by 7 give a quotient 4? A. 1 B. more than 1001 303 you will find : 6

C. 6

D. 7

E. 9

12. If you simplify

A. 5

1 1 B. 7 2 2

C. 50

1 2

D.1,818


13. Which of the following fractions is closest to 35% ? A.1 4

B.

1 3

C.

3 5

D.

5 5

E.

3 8




3

14. Find the difference of the two non-shaded surfaces inside the squares.

A. 8 cm2 B. 16cm2 C. 4 cm2 D. 35 cm2 E. none of the previous

15.

A If we can only go left and up (not diagonal), in how many ways we can get from A to B. A.6 B.4 C.5 D.7 E. none of the previous



4th Grade-D Dimotikou16.

4

The quotient of the division of the shaded area to the non-shaded area is: A.3 5

B.

6 16

C.

1 3

D.

1 2


17.

The shape above shows a wall which fixes a corridor of 1m of width. What is the length of the wall? A. 20m B. 21m C. 22m D. 23m E. 24m

18. In a school, 4 boys correspond to 5 girls. How many are the girls if the boys are 456? A. 470 B. 580 C. 480 D. 570 E. none of the previous



4th Grade-D Dimotikou19. The fraction A. 1,55 equals: 9

5

B. 0,7

C. 1,8

D. 0,8

E. none of the previous1 2 and smaller than ? 2 3

20. Which of the following fractions is greater than17 24 1 3 1 4 7 12

A.

B.

C.

D.

E.

3 4

21. If 5 5 5 2 2 2 2 2 4 , complete the box with one of the following: A.125 B. 125 2 C. 125 4 D. 125 8 E. none of the previous

22. During the summer, Gianna noted the kilometres she covered with her bicycle. The number of the kilometres she covered is between 44 and 100, it is a multiple of 4 and it is divisible exactly by 5 and 8. How many kilometres did Gianna covered with her bicycle? A. 48 B. 50 C. 58 D. 80 E. 85

23. A water lily floats in the middle of a lake and every day it doubles its size. In 10 days the entire lake will be covered with it. In how many days the water lily will cover half of the lake? A. 5 B.10 C. 9 D. 20 E. none of the previous

24. A brick weights 1 kilo plus half brick. How many kilos do two bricks weight? A. 2 B. 3 C.5 D.4 E. none of the previous

25. Five dogs catch five cats in five minutes. How many dogs catch 100cats in 100 minutes? A.100 B. 5 C.20 D.10 E. none of the previous




6

26. The following shapes show a sequence of equilateral triangles that have area of 1 square unit. The non-shaded triangle of shape 2, has its vertices in the middle of the bigger triangle. If the same motive continues, what is the area of the shaded triangles in shape 3, in square units?

Shape 1 A.81 256

Shape 227 64

Shape 3 E. none of the previous

B.

C.

9 16

D.

3 4

27. A Wooden solid of rectangle of parallelepiped 6cm X 8cm X 10cm is painted green in all sides. Then its been carved into cubes. 2cm x 2cm x 2cm. How many cubes where not painted at all? A. 6 B. 12 C. 8 D. 16 E. none of the previous

28.

Entrance 3 4 6 x 18

Exit 4 6 x 18 34

Based to the logical sequence of the table, number x is A. 8 B. 9 C. 10 D. 11 E. 12



4th Grade-D Dimotikou29. A piece of paper has six connected squares in which there is a letter, like the following shape. We fold the paper, so as to make a cube. Which letter is opposite the letter X?

7

U V W X Z A. Z B.U C.V D.W E.Y

30. The following triangle ABC has, AD = A and B = B, also angle DCZ=70o. Calculate the angle D in degrees. C 70 D

A

E

B

A. 40

B. 60

C. 55

D. 45 E. none of the previous



10 2009 : 60

1 21, : x9 -24

21

;

10

810

45

90

2 1 34. 3 ; 7 8 9 10 11

3 ; 8 0 < 7 7 63 7 > 64 8 9 6 < 78 48 6 < 36 9

28 7 > 3 1

4 ; . . . . 1

10

5 ;

1cm

20

19

18

16

9

6 @ ; @ 0 @ 9

+

2

0

9

11

12

13

14

7 69. ;17 14

13

11 22 4 7 19

22

12

6

13

8 73205 ; 37 32 73 50 2

10

9 1cm 1cm 1cm

, ;

2cm

2cm 4cm

.

12

24

16

26

40

10 , 60 . 7:30.. 10 , . 20 , ; 8:05 .. 6:50 .. 7:05 .. 6:55 .. 7:00 ..

11 To 24 km. . . , : 6 km 8 km 12 km 18 km

12 ;

6 16

10 16

5 8

5 3

3 5

10

3

13 1,166666661 : 60 1 =0,16666666. , 6

0,16666660

0,16060606

0,01666666

0,001666666

14 . 8 , 5 10 . 7 , ; 6 .. 3 . . 11 .. 9 ..

15 :

1 + 2 + 3 +..+ 23 + 24 + 25 78 650 325 312

16 . , . . . 2 . ; 32 30 28 16

17 6, : 0 1 7 6 1 2 3 4 5 6 7

18 100 199, ; 8 16 24 32 4

10

19 16 9 , . :

21

24

22

20

20 : 96 97

5, 6, 10, 15, 24, 38, 61, ..

98

99

100

21 . 7; .

1 2 1 2 5 6

3 4 7 8

1

2

3

A. . 3. 4, .

24

32

49

98

22 . 100 ;

2 3 4

1

8

2

23 ;B. 7 . (1000 9) + (30 9) + (4 7) 7;

0

4

7

8

95

: _______________ . 50 . 10 50, .

24 ;

8

9

10

11

12

25 ; 8673 7683 6284 4351 8095

26 , .

18 20 26

14

, ; 12 16 24 28 30

27 , , , 5 ;

1 2 3 4 5 6 1 2 3 4 66

10

28 . ;

0

100

200

300

400

500

600

29 :3 2

3

2

8

9

10

11

16

30 ; 888888 864198 975309 885309

10

7

10 April 2009 Time: 60 minutes

- IV PRIMARYQUESTION 1 A number was entered in the following calculator and we got the outcome 21, as it is indicated: Number Outcome entered x9 half -24

21

What number was entered?

10

810

45

90

None of the previous

QUESTION 2 The houses in a road are numbered from 1 up to 34. How many times the digit 3 was used in this numbering of the houses? 7 8 9 10 11

QUESTION 3 Which of the following propositions is wrong? 8 0 < 7 7 63 7 > 64 8 9 6 < 78 48 6 < 36 9

28 7 > 3 1

QUESTION 4 Which of the following propositions is NOT right? A Square is a rectangle. A square is a rhombus. A rectangle is a rhombus. A rhombus is a parallelogram. A parallelogram is a quadrilateral.

10

1

QUESTION 5 How many square centimeters of paper do we need to cover the solid consisting of four cubes as it is shown in the following figure?

1cm

20

19

18

16

9

QUESTION 6 What is the sum of the digits represented by @ and ? @ 0 @ 9

+

2

0

9

11

12

13

14

QUESTION 7 The letters and represent two numbers so that the sum of the numbers in each circle is equal to 69. What number is represented by the letter ?17 14

13

11 22 4 7 19

22

12

6

13

QUESTION 8 What number do we have to add to 73205 so that the outcome can be read backwards as well ? 37 32 73 50 None of these2

10

QUESTION 9How many cubes do we need to fill the following box?

.

12

24

16

26

40

QUESTION 10 You want to go to the cinema to watch a film of 60 minutes duration. The film starts at 7:30p.m. You want to be at the cinema 10 minutes earlier, so that you have the time to buy a ticket. If you need 20 minutes to go to the cinema from your home, at what time do you have to leave? 8:05 p.m. 6:50 p.m. 7:05 p.m. 6:55 p.m. 7:00 p.m.

QUESTION 11 The length of the road connecting the cities A and B is 24 km. On this road and in between the two cities there is a village. The length of the road connecting the village with the city B is triple the length of the road connecting the village with the city A. Then the length of the road connecting the village with the city A is : 6 km 8 km 12 km 18 km None of these

QUESTION 12 What part of the un-shaded area is the shaded area of the figure?

6 16

10 16

5 8

5 3

3 5

10

3

QUESTION 13The outcome given on a calculator for

1 1 =0,16666666. Then the outcome for is: 6 60

1,16666666

0,16666660

0,16060606

0,01666666

0,001666666

QUESTION 14 Peter is ill. His doctor told him that he has to take pill A every 8 hours, pill B every 5 hours and pill C every 10 hours. If he took all the pills at 7 in the morning of Tuesday, then he will take again all three pills simultaneously at: 6 a.m Wednesday QUESTION 15 Find the following sum: 3 p.m. Friday 11 p.m. Wednesday 9 a.m. Thursday None of these

1 + 2 + 3 +..+ 23 + 24 + 25 78 650 325 312 There are not enough data

QUESTION 16 Maria was given a bag of sweets by her grandfather. Maria, who was greedy, ate half of the sweets in one hour. In the next hour she ate half of the remaining ones and in the third hour half of what was left. In the fourth hour she ate again half of what was left. Now Maria has 2 sweets in her bag. How many sweets did Maria eat? 32 30 28 16 None of these

QUESTION 17 The sum of the digits of a 7-digit number is 6. Then the product of its digits is: 0 1 7 6 1 2 3 4 5 6 7

QUESTION 18 How many of the integers between 100 and 199, with all their digits different, are odd? 8 16 24 32

10

4

QUESTION 19 A square contains two squares and with areas 16 square metres and 9 square metres respectively, as shown in the following figure. The perimeter in metres of the section of the figure is:

21metres

24 metres

22 metres

20 metres

None of these

QUESTION 20 Find the next term of the sequence: 96 97

5, 6, 10, 15, 24, 38, 61, ..

98

99

100

QUESTION 21 The three figures below, called 1, 2 and 3, are divided into small equal triangles. . called 3? How many such triangles are there in the Figure

1 2 1 2 5 6

3 4 7 8

1

2

3

A. . 3. 4, .

24

32

49

98

None of these

QUESTION 22 Today is Sunday. What day will it be after 100 days?

Sunday

Tuesday

2 Wednesday3 4

1

Thursday8

2

Friday

QUESTION 23 What is the last digit of the number representing the following sum?B. 7 . (1000 9) + (30 9) + (4 7) 7;

0

4

7

8

95

: _______________ . 50 . 10 50, .

QUESTION 24 How many squares can be found in the following figure?

8

9

10

11

12

QUESTION 25 Which of the following four digits numbers has the digit of its hundreds as double of the digit of its units and the digit of its tens as greater than the digit of its thousands? 8673 7683 6284 4351 8095

QUESTION 26 In the following magic square the sum of the numbers in each row, column and diagonal is the same:

18 20 26

14

When we complete the numbers in the square which of the following numbers IS NOT going to be used?

12

16

24

28

30

QUESTION 27 The following figure is folded in order to construct a cube. Which number lies at the bottom of the cube if the number 5 lies on the upper face?

1 2 3 4 5 6 1 2 3 4 6

10

6

QUESTION 28 The following graph represents the contributions to the RADIOMARATHONIO of the classes of a primary school. What class contributed the one fifth of the total contribution, given that the word represents class and the phrase represents contribution in euro?

0

100

200

300

400

500

600

QUESTION 29 The area of the shaded region of the following figure, in square units, is:3 2

3

2

8

9

10

11

16

QUESTION 30 What is the difference between the largest six-digit number, with all of its digits different, and the smallest six-digit number, with all of its digits different as well? 888888 864198 975309 885309 None of these

10

7

: 60

, . . 4 . 1 . . , . . .

53

54

...

55

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THEMATA OLYMPIADAS