IKMC 2024 - Grades 7-8 - Set 2 - Self-study

Which of the following strings cannot be transformed into the string on the right without cutting?

The diagram on the right is made up of five-sided tiles of equal size. Which tile can be inserted in the missing spot so that two closed lines are formed?

The first diagram shows a rhombus. The area of the first diagram is increased by adding two right-angled triangles, as shown. By what percentage has the area increased?

What is the value of $\frac{20\times24}{2\times0+2\times4}$?

Julio cuts off four corners of a regular tetrahedron. How many corners does the object now have?

Ria has three counters marked 1, 5 and 11, as shown. She wants to place them side by side to make a four-digit number. How many different four-digit numbers can she make?

A fruit bowl contains five types of fruit: apples, grapes, cherries, strawberries and bananas. Al likes apples. Bok likes apples, cherries, strawberries and bananas. Cam likes grapes, cherries, strawberries and bananas. Don likes apples, grapes and cherries. Eva likes apples and cherries. The fruit is shared so that everyone gets a different type of fruit and everyone gets a type of fruit that they like. Who gets cherries?

The weight restriction notice for an elevator says it can carry either 12 adults or 20 children. According to the weight restrictions, what is the largest number of children that can ride in the elevator with nine adults?

Four different positive whole numbers are written into the grid and are then covered up. The products of the two numbers in each row or column, respectively, are stated next to or below the grid. What is the sum of the four covered numbers?

All trolleys in a shop are the same. Four trolleys slid together have a total length of 108 cm (see diagram). Ten trolleys slid together have a total length of 168 cm. How long is one trolley?

Carina has baked a cake and cut it into 10 equal pieces. She ate one piece of cake and rearranged the remaining pieces evenly (see diagram). How big is the angle between two neighbouring pieces?

Werner forms a $4\times4$ square from the three pieces shown and another piece. The sum of the four numbers in every row and every column is the same. What does the fourth piece look like?

A square has side-length 10 m. It is divided into parts by three straight line segments, as shown. The areas of the two shaded triangles are A and B. What is the value of A − B?

Paula the penguin goes fishing every day and always brings back twelve fish for her two chicks. Each day, she gives the first chick she sees seven fish and gives the second chick five fish, which they eat. In the last few days one chick has eaten 44 fish. How many has the other chick eaten?

Johan had a large number of identical cubes. He made the structure on the right by taking a single cube and then sticking another cube to each face. He wants to make an extended structure in the same way so that each face of his original structure will have a cube stuck to it. How many extra cubes will he need to complete his extended structure?

A kangaroo jumps up a mountain and back down again on the same path. Upwards, it covers 1 metre per jump. Downwards, it covers 3 metres per jump. In total it jumped 2024 times. How many metres did it cover in total?

Gerard cuts a large rectangle into four smaller rectangles. The perimeters of three of these smaller rectangles are 16, 18 and 24, as shown in the diagram. What is the perimeter of the fourth small rectangle?

Fresh mushrooms consist of 80 percent water. In dried mushrooms, however, the amount of water is only 20 percent of its mass. By what percentage does the mass of a mushroom decrease during drying?

Tiler Teri wants to cover a square floor with a regular pattern (see diagram) using six-sided and three-sided tiles. She estimates that she will be needing approximately 3000 six-sided tiles for the entire floor. Approximately, how many three-sided tiles will she be needing?

Nine cards numbered from 1 to 9 were placed facedown on the table. Aleksa, Bart, Clara and Deindra each picked up two of the cards. Aleksa said “My numbers add up to 6”. Bart said “The difference between my numbers is 5”. Clara said “The product of my numbers is 18”. Deindra said “One of my numbers is twice the other one”. All four made a true statement. Which number was left on the table?