2025 Junior Test | Test and Chat

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2025 Junior (Grade 9 - 10)

Questions: 30 | Answered: 0

Q1. In which of the following hexagons is exactly one third of the area black and half of the area white?

3 points

ABCDE

Question 1

Q2. The base of a triangle is extended by 50% and its h eight is reduced by one third. What is the ratio of the area of the new triangle to the area of the original triangle?

3 points

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Question 2

Q3. The left and right part of a three-part brochure ea ch contain four transparent windows. If these two parts are folded onto the mid dle part, some of the numbers written on the middle part are visible through the windows. What is the sum of the visible numbers when the bro chure is folded?

3 points

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Question 3

Q4. Every year, the third Thursday in March is Kangaroo Day. What is the earliest calendar day that can be a Ka ngaroo Day?

3 points

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Question 4

Q5. In a recipe, Ruben needs 1 1 cups of water for 1 cup of rice. Ruben wants to us e 1 1 cups of rice. 2 2 How many cups of water does he need? 3

3 points

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Question 5

Q6. Lisa has four wooden digits. She can use them to m ake the number 2025. How many different numbers greater than 2025 can sh e make with these digits?

3 points

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Question 6

Q7. Sarah has a bag of 18 balls numbered from 1 to 18. What is the smallest number of balls Sarah must rem ove from the bag to be sure that she has removed at least th ree prime numbers?

3 points

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Question 7

Q8. Luka has dogs, rabbits and cats as pets. Eight of t hese pets are not dogs, five of these pets are not rabbits and seven of these pets are not cats. How many pets does Luka have?

3 points

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Question 8

Q9. Katrin and Thomas are both celebrating their birth day today. Thomas notices that 1 of Katrin's age is the same as 19

3 points

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Question 9

Q10. Consider a circle with centre O and radius 10 cm. A square OPQR is drawn inside the circle so that Q lies on the circle (see diagram). What is the area of the grey triangle PQR ?

3 points

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Question 10

Q11. On a standard die, the sum of the number of points on opposite sides is always 7. We want to tilt the die shown several times along its edges so that all six sides are on top once. Which of the given sequences of top numbers is not possible?

4 points

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Question 11

Q12. Alexander folds a square sheet of paper along its diagonal to form a triangle. He then folds the paper again s o that one of the two shorter sides of the triangle lies o n the longer side of the triangle to form the smaller tri angle AXC (see diagrams). What is the size of the angle  CXA ?

4 points

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Question 12

Q13. The four-digit number 80 is missing its last two digits. We know that this number is divisible by 8 and 9. What is the product of the last two digits?

4 points

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Question 13

Q14. An athlete has a collection of 2 gold medals and 5 silver medals. They are numbered in a certain order from 1 to 7. The images show black an d white pictures of the medals. Each of the six pictures shows exactly one gold medal. What is the sum of the numbers on the two gold meda ls?

4 points

ABCDE

Question 14

Q15. Anna is looking at a picture on her smart phone. T he format is 16:9 and fills the entire screen. If she turns the smart phone, the picture b ecomes smaller. What proportion of the screen is needed for the smaller picture?

4 points

ABCDE

Question 15

Q16. Paul shoots a ball at two targets (see diagram) a total of 27 times. When he aims for the upper left target, he hits 50% of the time, and when he aims for the bottom right target, he hits 80% of the time. I n total, 9 of his shots miss their target. How many times does Paul hit the top left target?

4 points

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Question 16

Q17. There are some cards on a table with various differ ent positive integers written on them. All of these are smaller than 20 and their pr oduct is 2025. What is the maximum number of cards on the table?

4 points

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Question 17

Q18. The number N is the largest 6-digit number, for which the produ ct of all its digits is 180. What is the sum of the digits of the number N?

4 points

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Question 18

Q19. Five bricks form a wall (see figure). Peter can on ly remove a brick if there is no other brick directly above it. On each turn, he ran domly selects one of the removable bricks with equal probability and removes it. What is the probability that the brick numbered 4 is the third to be removed?

4 points

ABCDE

Question 19

Q20. Daniel numbers some squares on a piece of squared paper. He starts with a random square and numbers the squares 1, 2, 3, 4, 5, ..., 2025 anti-clockwise (see illustration). At the end he considers the figure that results fro m all 2025 numbered squares. Each square has a side length of 0.5 cm. What is the perimeter of the figure?

4 points

ABCDE

Question 20

Q21. We want to place the numbers 1 through 8 in the eig ht squares of the figure shown in such a way that consecutive numbers are never in ad jacent squares (not even diagonally adjacent). Which numbers can we write in the square marked with an X ?

5 points

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Question 21

Q22. The two small rectangles in the diagram are congrue nt and each has an area of 4 cm 2 . What is the area of rectangle ABCD in cm 2 ?

5 points

ABCDE

Question 22

Q23. The product of three prime numbers is 11 times the ir sum. What is the maximum sum of the three numbers?

5 points

ABCDE

Question 23

Q24. The square ABCD contains two shaded rectangles (see diagram). The d imensions are as shown and the area of the overlapping region is 18 cm 2 . What is the perimeter of the square ABCD ?

5 points

ABCDE

Question 24

Q25. A four-digit number ABCD is multiplied by its units digit D . The result is a different four-digit number DXYA , whose units- and thousands- digits are swapped co mpared to the original number (see illustration). Different letters can stand for the same digits. How many four-digit numbers ABCD have this property?

5 points

ABCDE

Question 25

Q26. The six-digit number ABCDEF consists of the digits 1, 2, 3, 4, 5 and 6, with e ach digit occurring exactly once. The number AB consisting of the first two digits is a multiple o f 2. The number ABC is a multiple of 3. The number ABCD is a multiple of 4. The number ABCDE is a multiple of 5 and the entire number ABCDEF is a multiple of 6. What values can the digit F take?

5 points

ABCDE

Question 26

Q27. A number is to be written in each circle of the di agram in such a way that the sum of the numbers in three touching circles is always the same. Some of the numbers are already given. What is the sum of all the numbe rs in the middle row?

5 points

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Question 27

Q28. In the diagram we see two touching circles and the diameter through their common point. The outer circle has a chord parallel to thi s diameter with length 16, which touches the inner circle. What is the area of the grey region?

5 points

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Question 28

Q29. The number 8 and another number x are written on a board. Eight children go to the bo ard, one after the other. Each child writes down the ave rage of all the numbers already on the board. The last child writes the number 26. What is the value of x ?

5 points

ABCDE

Question 29

Q30. There are 12 children at a party, including 3 pair s of twins. How many different ways are there to di stribute six blue hats and six red hats to the children, so that each pair of twins wears hats of the same colour?

5 points

ABCDE

Question 30

2025 Junior Test | Test and Chat