2016 Junior Test | Test and Chat

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2016 Junior (Grade 9 - 10)

Questions: 30 | Answered: 0

Q1. The arithmetic mean of four numbers is 9. What is the fourth number i f the three other numbers are 5, 9 a nd 12?

3 points

ABCDE

Question 1

Q2. semi finals a nd one f inal ). The results for s ix of the seven matches are known ( but not necessarily in this order ): Bella beats Ann, Celine beats Donna, Gina beats Holly, Gina beats Celine, Celine beats Bella, Emma beats Farah. Which result is missing ?

3 points

ABCDE

Question 2

Q3. Ruth takes part in the kangaroo competition where 30 questions have to be answered. She answers every question and each answer is either right or wrong. She has 50% more right than wrong answers. How many of her answers are right ?

3 points

ABCDE

Question 3

Q4. Five points are given i n a Cartesian coordinate system : P( - 1, 3), Q(0, - 4), R( - 2, - 1), S(1, 1), T(3, - 2). Four of these five points are vertices of a square. Which point does not belong there ?

3 points

ABCDE

Question 4

Q5. If a positive whole number x is divided by 6 , the remainder is 3. What is the remainder if 3  x is divided by 6?

3 points

ABCDE

Question 5

Q6. 2016 hours are how many weeks ?

3 points

ABCDE

Question 6

Q7. Lukas invents his own notation for negative numbers. When counting backwards he writes : ... 3, 2, 1, 0, 00, 000, 0000, ... What is the result of the calculation 000 + 0000 in his notation ?

3 points

ABCDE

Question 7

Q8. I have some unusual dice . On their faces are the digits 1 to 6 as usual, however the odd numbers are negative ( so - 1, - 3, - 5 instead of 1, 3, 5). I throw two such dice at the same time . W hich of the following sums can I definitely not achieve with one such throw ?

3 points

ABCDE

Question 8

Q9. S tep by step the word VELO is changed int o the word LOVE . In every step two adjacent letters are allowed to be swapped around . What is the minimum amount of steps needed ?

3 points

ABCDE

Question 9

Q10. Sven writes five different single - digit positive whole numbers on a board . He realises that no sum of two of these numbers is equal to 10. Which of the following numbers has Sven definitely written on the board ?

3 points

ABCDE

Question 10

Q11. F or the real numbers 푎 , 푏 , 푐 , 푑 the following holds true: 푎 + 5 = 푏 − 1 = 푐 + 3 = 푑 − 4 . Which of the numbers a, b, c, d is biggest ?

4 points

ABCDE

Question 11

Q12. A 3 × 3 field is made up of 9 unit squares . In two of these squares , circles are inscribed as shown in the diagram . How big is the shortest distance between these circles ?

4 points

ABCDE

Question 12

Q13. A knock - out tennis tournament is taking place . There are seven matches (4 quarter finals ,

4 points

ABCDE

Question 13

Q14. W hat percentage of the area of the triangle is coloured in grey in the adjacent diagram ?

4 points

ABCDE

Question 14

Q15. Jilly makes up a multiplication magic square using the numbers 1, 2, 4, 5, 10, 20, 25, 50 a nd 100. The products of the numbers in each row, column and diagonal should be equal . In the diagram it can be seen how she has started . W hich number goes into the cell with the question mark ?

4 points

ABCDE

Question 15

Q16. Jack wants to keep six tubes each of diameter 2 cm together using a rubber band. He chooses between the two possible variat ions shown . How are the lengths of the rubber bands related to each other ?

4 points

ABCDE

Question 16

Q17. Peter wants to colour in the cells of a 3 × 3 square so that every row, every column and both diagonals each have three cells with three different colours . W hat is the smallest number of colours with which Peter can achieve this ?

4 points

ABCDE

Question 17

Q18. Eight cards with the numbers 1, 2, 4, 8, 16, 32, 64, 128 are each in an unmarked envelop e . Eva randomly chooses some of these eight envelopes. Ali takes the remaining ones . Both add their numbers together . They find out that Eva ’ s sum is 31 bigger tha n Ali ’ s sum . How many envelopes has Eva chosen ?

4 points

ABCDE

Question 18

Q19. I n the diagram we see a cube and four marked angles . How big is the sum of those angles ?

4 points

ABCDE

Question 19

Q20. In an enclosure there are 2016 kangaroos . Each of them is either red or grey, and there is at least one red and at least one grey kangaroo amongst them . F or each kangaroo K w e calculate the fraction obtained , if you take the number of kangaroos of the other colour divided by the kangaroos of the own colour (including K itself) . Determine the sum of these 2016 fractions .

4 points

ABCDE

Question 20

Q21. A creeping plant twists exactly 5 times around a post with circumference 15 cm (as shown in the diagram) and thus reaches a height of 1 m. While the plant grows the height of the plant also grows with constant speed . How long is the creeping plant ?

5 points

ABCDE

Question 21

Q22. W hat is the biggest remainder one can obtain by dividing a two - digit number by the sum of its digits ?

5 points

ABCDE

Question 22

Q23. We consider a 5 × 5 square that is split up into 25 fields. Initially all fields are white. In each move it is allowed to change the colour of two fields that are horizontally or vertically adjacent (i.e. white fields turn black and black ones turn white). W hat is the smallest number of moves needed to obtain the chessboard colouring shown in the diagram?

5 points

ABCDE

Question 23

Q24. A motorboat drives in the middle of a stream. Downstream it needs four hours to get from X to Y. In order to drive back from Y to X it needs six hours. T ree trunks are also floating o n the stream. How many hours does it take for a tree trunk to float in the middle of the stream from X to Y ?

5 points

ABCDE

Question 24

Q25. In th e Kangaroo Republic , every month has 40 days, which are numbered through from 1 to 40. Every day with a number that is divisible by 6 is a publi c holiday, and likewise every day with a prime number. How often per month does it occur that there is exactly one working day between two public holidays ?

5 points

ABCDE

Question 25

Q26. Two heights of a triangle have lengths 10 cm a nd 11 cm. W hich of the following lengths cannot be the length of the third height ?

5 points

ABCDE

Question 26

Q27. Jakob writes down four consecutive positive whole numbers. He calcula tes all possible sums of three of those numbers und realises that none of those sums is a prime number. W hat is the smallest number that Jakob could have written down ?

5 points

ABCDE

Question 27

Q28. Four sportswomen and sportsmen are sitting around a round table for dinner. They do four different sports: ice skating, skiing, hockey and sledging . The person who skies sits to the left of Sandra. The person who ice sk ates sits opposite Benjamin. Eva and Philipp sit next to each other. A woman sits next to the person who play s hockey. Which sport does Eva do?

5 points

ABCDE

Question 28

Q29. A date can be written in the form DD.MM.YYYY ; e .g. today ’ s date is 17. 03.2016. We call a date “ surprising ” if all 8 digits used in this notation are different. In which month does the next surprising date occur ?

5 points

ABCDE

Question 29

Q30. Exactly 2016 people are taking part in a conference. They are registered as P1 to P2016 in the system. Each person from P1 to P2015 has shaken exactly the amount of other hands that his/her own system number indicates. How many people did P2016 sha k e hands with ?

5 points

ABCDE

Question 30

2016 Junior Test | Test and Chat