2009 Junior Test | Test and Chat

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2009 Junior (Grade 9 - 10)

Questions: 30 | Answered: 0

Q1. Which of the following number is divisible by 3? 9

3 points

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Question 1

Q2. What is the minimum number of points which have to be removed from the adjacent diagram so that in the rema ining picture no three points lie in one line?

3 points

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Question 2

Q3. 2009 people are taking part in a public fun run. The number of people Hans beat is three times as big as the number of people that have finished before him. In which place did Hans finish the race?

3 points

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Question 3

Q4. Harry does his paper round in Long Street. He has to deliver one newspaper to each house with an odd number. The first house with an odd number is 15 and the final house has the number 53. H ow many houses does Harry have to visit?

3 points

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Question 4

Q5. The product of four different natural numbers is 100. What is the sum of the four numbers?

3 points

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Question 5

Q6. What is the value of ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ 1000 ?

3 points

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Question 6

Q7. A long number is build by writing the number 2009, 2009 times in a line. How big is the sum off all odd number within this number that are immediately to the left of an even number?

3 points

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Question 7

Q8. The diagram on the right shows a solid made up of 6 triangles. Each vertex is assigned a number, two of which are indicated. The total of the three numbers on each triangle is the same. What is the total of all five numbers?

3 points

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Question 8

Q9. For how many positive whole numbers a do a² and a³ have the same amount of digits?

3 points

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Question 9

Q10. The area of the shown triangle equals 80m². Each circle has a radius of 2m and it ’ s centre is in one of the vertices of the triangles. What is the area of the grey shaded region (in m²)?

3 points

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Question 10

Q11. Leonhard made up a sequence where, starting with the third term, each term is the sum of the previous two numbers. The fourth number is 6 and the sixth number is 15. What is the seven th number in the sequence?

4 points

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Question 11

Q12. In the triangle illustrated one internal angle measures 68°. The three angle bisectors of the triangle are shown. What is the size of the angle indicated with a question mark?

4 points

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Question 12

Q13. Maria can achieve 0, 1, 2, 3, 4 or 5 points in a test. After 4 tests she has a mean of exactly 4. One of the following sentences can therefore not be true. Which one is it?

4 points

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Question 13

Q14. The “ Borromaic Rings ” have an extraordinary property. Although no two are interlocked, they are strongly connected within each other. If one ring is cut through, the other two fall apart. Which of the following diagrams shows the picture of “ Borromaic Rings ” ?

4 points

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Question 14

Q15. On the island of the nobles and liars 25 people are stanging in a queue. The first person in the line claims tha t everybody behind him is a liar. Each of the other people claims that the person in front of him is a liar. How many liars are actually in the queue? (Nobles are always telling the truth and liars are always lying.)

4 points

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Question 15

Q16. If a b = ab + a + b and 3 5 = 2 x, then x equals

4 points

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Question 16

Q17. The centres of the four illustrated circles are in the corners of the square. The two big circles touch each other and also the two little circles. With which factor do you have to multiply the radii of the little circles to obtain the radius of the big circles? 2

4 points

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Question 17

Q18. The difference of n a nd 10 is less than 1. How many whole numbers n are there with this characteristic?

4 points

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Question 18

Q19. Friday writes different positive whole number that are all less than 11 next to each other in the sand. Robinson Crusoe looks at the se quence and notices with amusement that adjacent numbers are always divisible by each other. What is the maximum amount of numbers he could possibly have written in the sand?

4 points

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Question 19

Q20. There are three great circles on a sphere that intersect each other in a right angle. Starting in point S a little bug moves along the great circles in the direction indicated. At crossings it turns alternately to the right or left. How many quarter circles does it crawl along until it is back in poin t S?

4 points

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Question 20

Q21. How many 0s have to replace the Star * in the decimal number 1.*1 to

5 points

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Question 21

Q22. How many 10 - digit numbers exist that are solely made up of the numbers 1, 2 and 3 (but not necessary all of them) and where adjacent numbers always differ by exactly 1?

5 points

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Question 22

Q23. If a = 2 , b = 8 and c = 3 then

5 points

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Question 23

Q24. All factors of a number N (with the exception of 1 and N itself) are written down one after the other. It turns out that the biggest factor is 45 times as big as t he smallest number. For how many numbers N is that true?

5 points

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Question 24

Q25. Kangoo has 2009 unit dice that he is putting together to a big cuboid. He has also got 2009 square unit sticker with the measurements 1 × 1 with which he tries to paste up the surface area of the cuboid. He manages to do that and even has got some spare stickers. How many are there left over?

5 points

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Question 25

Q26. Robert wants t o place stones on a 4 × 4 gameboard so that the number of stones in each row and column is different; i.e. there are

5 points

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Question 26

Q27. A number of oranges, peaches, apples and bananas are put down in a row. What is the minimum number of fruits needed to lay them down so that each fruit lies next to each other fruit at least once in that row?

5 points

ABCDE

Question 27

Q28. What is the smallest whole number n for which the expression 2 2 2 2 (2 - 1) ◊ (3 - 1) ◊ (4 - 1) ◊ … ◊ (n - 1) is a square number?

5 points

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Question 28

Q29. A kang aroo is sitting in the origin of a kartesian co - ordinate system. With each bounce it can jump one unit in the horizontal or vertical direction. How many points are there, where the kangaroo could be after 10 jumps?

5 points

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Question 29

Q30. A single digit prime number is called „ strange “ . A prime number with more than one digit is called „ strange ” if the numbers that are obtained by cancelling the first and the last digit respectively are both strange prime numbers again. How ma ny strange prime numbers are there?

5 points

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Question 30

2009 Junior Test | Test and Chat