2017 Kangaroo Math Junior Test

Q1. cm², 4 cm², 9 cm² and 16 cm² respectively. She places the sta rs on top of each other as shown in the diagram and glues them together. How big is the total area of the visible grey parts?

3 points

Q2. Peter writes the word KANGAROO on a see-through piece of glass, as seen on the right. What can he see when he first flips over the glass onto its back along t he right-hand side edge and then turns it about 180° while it is lying on the table?

3 points

Q4. Maria has 24 Euros. Each of her 3 sisters has 12 Euros. How much does she have to give to each sister so that all four of them have the same amount of Euros?

3 points

Q5. A wheel rolls along a zigzag curve as can be seen below. Which of the following pictures shows the curve that is described by the centre of the wheel?

3 points

Q6. Some girls are standing in a circle. The teacher makes them do a headcount. Bianca says one, her neighbour says two and so on. If they count in a clockwise direction, Antonia says six. If they count in an anticlockwise direction, Antonia says nine. How many girls are forming the circle?

3 points

Q7. A circle with radius 1 rolls along a straight line from point K to point L , as shown, with KL = 11  In which position is the circle when it has arrived in L ?

3 points

Q9. At a wedding one eighth of the guests is underage. Three sevent hs of the adult guests are men. How big is the fraction of adult women amongst all guests? ଵ ଵ ଵ ଵ ଷ

3 points

Q10. A whimsical teacher has a box wi th 203 red, 117 white and 28 bl ue buttons. He asks his students to each take one button out of the box without looking. What is the minimum numb er of students who have to take a button so that definitely at least three of the buttons picked have the same c olour?

3 points

Q11. A BCD is a trapezium with parallel sides AB and CD . Let AB = 50 and CD = 20. Point E lies on side AB in such a way that the straight line DE divides the trapezium into two shapes of equal area. How long is the straight line AE ?

4 points

Q13. In an equilateral triangle with a rea 1, we draw the six perpend icular lines from the midpoints of each side to the oth er two sides as seen in the di agram. How big is the area of the grey hexagon that has been created t his way? ଵ ଶ ସ ଵ ଶ

4 points

Q15. A belt system is made up of wheels A , B and C , which rotate without sliding. B rotates 4 times around, while A turns 5 times around, and B rotates 6 times around, while C turns 7 times around. The circumference of C is 30 cm. How big is the circumference of A ?

4 points

Q16. Tycho plans his running training. Each week he wants to go for a run on the same weekdays. He never wants to go for a run on two consecutive days. But he wants to go for a run three days a week. How many different weekly plans meet those conditions?

4 points

Q17. Four brothers have different heights. Tobias is as many centime ters smaller than Viktor, as he is taller than Peter. Oskar on the other hand is equally many centimeters smaller tha n Peter. Tobias is 184 cm tall, and on average the four brothers are 178 cm tall. How tall is Oskar?

4 points

Q18. During our holidays it rained on 7 days. If it rained before no on, then there was no rain in the afternoon. If it rained in the afternoon, there was no rain before noon. There w ere 5 days without rain before noon and six days without rain in the afternoon. How many days long was our holid ay?

4 points

Q19. Jenny wants to write numbers into the cells of a 3x3-table so t hat the sum of the numbers in each of the four 2x2-squares are equa lly big. As it is shown in the diagram, she has already inserted three numbers. What number does she have to write into the cell in th e fourth corner?

4 points

Q20. Seven positive whole numbers a, b, c, d, e, f, g are written down next to each other in this order. The sum of all seven numbers is 2017. Every two adjacent numbers always differ by 1. Which number can be equal to 286?

4 points

Q21. In the primate enclosure in a z oo there are four gorillas. They are all younger than 18 years old. No two have the same age, and all their ages are whole numbers. The product of their ages is 882. How big i s the sum of their ages?

5 points

Q22. The numbers -3, -2, -1, 0, 1, 2 are written on the six faces of a die. The die is rolled twice. The num bers that were rolled are multi plied. How big is the probability that this product is negative? ଵ ଵ ଵଵ ଵଷ ଵ

5 points

Q23. In a convex quadrilateral ܣܤܥܦ the diagonals are perpendi cular to each other. The length of the edges are ܣܤ ൌ 2017 , ܤܥ ൌ 2018 and ܥܦ ൌ 2019 (diagram not to scale). How long is side ܣܦ ?

5 points

Q24. A popular two-digit number is made up of the digits a and b . If the number pair is written down three times one after the other, a six-digit number is obtained. This new numbe r is always divisible by

5 points

Q25. My friend Heinz wants to use a special password that is made up of seven digits. Each digit used in the password appears as many times in the pas sword as is the value of the di git. Additionally, equal digits are always next to each other. Therefore he can fo r example use 4444333 or 1666666 as p asswords. How many possible passwords can he choose from?

5 points

Q26. Paul wants to write a positive whole number onto every tile in the number wall shown, so that every number is equal to the sum of the two numbers on the tiles that are directly below. What is the maximum number of odd numbers he can write on the t iles?

5 points

Q27. Lisa places some points on a circle and then connects them in s equence to make a polygon. She adds up the interior angles of the polygon. By mistake she misses out one a ngle and obtains the sum 2017. How big is the angle that she has overlooked?

5 points

Q28. dancers are standing in a circle facing the centre. The danc e instructor shouts “Left” and many of them turn 90° to the left. Unfortunately, s ome are confused and turn righ t, so that some dancers are now directly facing each other. All of the ones that are facing each other are shaking t heir head. It turns out that 10 dancers shake their head. Then the dance instructor says “ Turn around” and all of them tu rn 180° to look in the opposi te direction. Again, all of the ones that are directly faci ng each other shake their head. How many dancers are shaking their head second time round?

5 points

Q29. Three weights are randomly place d on each tray of a beam balanc e. The balance dips to the right hand side as shown on the picture. The masses of the weights are 101, 102, 103,

5 points

Q30. The points A and B lie on a circle with centre M . The point P lies on the straight line through A and M . PB touches the circle in B . The lengths of the segments PA and MB are whole numbers, and PB = PA + 6. How many possible values for MB are there?

5 points

2017 Junior (Grade 9 - 10)

Q1. cm², 4 cm², 9 cm² and 16 cm² respectively. She places the sta rs on top of each other as shown in the diagram and glues them together. How big is the total area of the visible grey parts?

Q2. Peter writes the word KANGAROO on a see-through piece of glass, as seen on the right. What can he see when he first flips over the glass onto its back along t he right-hand side edge and then turns it about 180° while it is lying on the table?

Q3. Angelika crafts a piece of jewellery out of two grey and two wh ite stars. The stars have areas of

Q4. Maria has 24 Euros. Each of her 3 sisters has 12 Euros. How much does she have to give to each sister so that all four of them have the same amount of Euros?

Q5. A wheel rolls along a zigzag curve as can be seen below. Which of the following pictures shows the curve that is described by the centre of the wheel?

Q6. Some girls are standing in a circle. The teacher makes them do a headcount. Bianca says one, her neighbour says two and so on. If they count in a clockwise direction, Antonia says six. If they count in an anticlockwise direction, Antonia says nine. How many girls are forming the circle?

Q7. A circle with radius 1 rolls along a straight line from point K to point L , as shown, with KL = 11  In which position is the circle when it has arrived in L ?

Q8. Martina plays chess. This season she has already played 15 game s, nine of which she has won. She still has to play

Q9. At a wedding one eighth of the guests is underage. Three sevent hs of the adult guests are men. How big is the fraction of adult women amongst all guests? ଵ ଵ ଵ ଵ ଷ

Q11. A BCD is a trapezium with parallel sides AB and CD . Let AB = 50 and CD = 20. Point E lies on side AB in such a way that the straight line DE divides the trapezium into two shapes of equal area. How long is the straight line AE ?

Q12. How many positive whole numbers n have the property that exactly one of the two numbers n and n + 20 has four digits?

Q13. In an equilateral triangle with a rea 1, we draw the six perpend icular lines from the midpoints of each side to the oth er two sides as seen in the di agram. How big is the area of the grey hexagon that has been created t his way? ଵ ଶ ସ ଵ ଶ

Q14. The sum of the squares of three consecutive positive whole numb ers is 770. What is the biggest of these numbers?

Q15. A belt system is made up of wheels A , B and C , which rotate without sliding. B rotates 4 times around, while A turns 5 times around, and B rotates 6 times around, while C turns 7 times around. The circumference of C is 30 cm. How big is the circumference of A ?

Q16. Tycho plans his running training. Each week he wants to go for a run on the same weekdays. He never wants to go for a run on two consecutive days. But he wants to go for a run three days a week. How many different weekly plans meet those conditions?

Q17. Four brothers have different heights. Tobias is as many centime ters smaller than Viktor, as he is taller than Peter. Oskar on the other hand is equally many centimeters smaller tha n Peter. Tobias is 184 cm tall, and on average the four brothers are 178 cm tall. How tall is Oskar?

Q18. During our holidays it rained on 7 days. If it rained before no on, then there was no rain in the afternoon. If it rained in the afternoon, there was no rain before noon. There w ere 5 days without rain before noon and six days without rain in the afternoon. How many days long was our holid ay?

Q19. Jenny wants to write numbers into the cells of a 3x3-table so t hat the sum of the numbers in each of the four 2x2-squares are equa lly big. As it is shown in the diagram, she has already inserted three numbers. What number does she have to write into the cell in th e fourth corner?

Q20. Seven positive whole numbers a, b, c, d, e, f, g are written down next to each other in this order. The sum of all seven numbers is 2017. Every two adjacent numbers always differ by 1. Which number can be equal to 286?

Q21. In the primate enclosure in a z oo there are four gorillas. They are all younger than 18 years old. No two have the same age, and all their ages are whole numbers. The product of their ages is 882. How big i s the sum of their ages?

Q22. The numbers -3, -2, -1, 0, 1, 2 are written on the six faces of a die. The die is rolled twice. The num bers that were rolled are multi plied. How big is the probability that this product is negative? ଵ ଵ ଵଵ ଵଷ ଵ

Q23. In a convex quadrilateral ܣܤܥܦ the diagonals are perpendi cular to each other. The length of the edges are ܣܤ ൌ 2017 , ܤܥ ൌ 2018 and ܥܦ ൌ 2019 (diagram not to scale). How long is side ܣܦ ?

Q24. A popular two-digit number is made up of the digits a and b . If the number pair is written down three times one after the other, a six-digit number is obtained. This new numbe r is always divisible by

Q26. Paul wants to write a positive whole number onto every tile in the number wall shown, so that every number is equal to the sum of the two numbers on the tiles that are directly below. What is the maximum number of odd numbers he can write on the t iles?

Q27. Lisa places some points on a circle and then connects them in s equence to make a polygon. She adds up the interior angles of the polygon. By mistake she misses out one a ngle and obtains the sum 2017. How big is the angle that she has overlooked?

Q29. Three weights are randomly place d on each tray of a beam balanc e. The balance dips to the right hand side as shown on the picture. The masses of the weights are 101, 102, 103,

Q30. The points A and B lie on a circle with centre M . The point P lies on the straight line through A and M . PB touches the circle in B . The lengths of the segments PA and MB are whole numbers, and PB = PA + 6. How many possible values for MB are there?