IKMC 2017 - Grades 7-8 - Self-study

What is the time 17 hours after 17:00?

A group of girls stands in a circle. Xena is the fourth on the left from Yana and the seventh on the right from Yana. How many girls are there in the group?

What number must be subtracted from −17 to obtain −33?

The diagram shows a stripy isosceles triangle and its height. Each stripe has the same height. What fraction of the area of the triangle is white?

Which of the following equalities is correct?

The diagram shows two rectangles whose sides are parallel. What is the difference in the lengths of the perimeters of the two rectangles?

Bob folded a piece of paper twice and then punched one hole in the folded piece of paper. When he unfolded the paper, he saw the arrangement shown in the diagram. How had Bob folded his piece of paper?

The sum of three different positive integers is 7. What is the product of the three integers?

The diagram shows four overlapping hearts. The areas of the hearts are 1 cm², 4 cm², 9 cm² and 16 cm². What is the shaded area?

Yvonne has 20 euros. Each of her four sisters has 10 euros. How many euros does Yvonne have to give to each of her sisters so that each of the five girls has the same amount of money?

Annie the Ant started at the left end of a pole and crawled $2/3$ of its length. Bob the Beetle started at the right end of the same pole and crawled $3/4$ of its length. What fraction of the length of the pole are Annie and Bob now apart?

One sixth of the audience in a children’s theatre were adults. Two fifths of the children were boys. What fraction of the audience were girls?

In the diagram, the dashed line and the black path form seven equilateral triangles. The length of the dashed line is 20. What is the length of the black path?

Four cousins Ema, Iva, Rita and Zina are 3, 8, 12 and 14 years old, although not necessarily in that order. Ema is younger than Rita. The sum of the ages of Zina and Ema is divisible by 5. The sum of the ages of Zina and Rita is also divisible by 5. How old is Iva?

This year there were more than 800 runners participating in the Kangaroo Hop. Exactly 35% of the runners were women and there were 252 more men than women. How many runners were there in total?

Ria wants to write a number in each box of the diagram shown. She has already written two of the numbers. She wants the sum of all the numbers to equal 35, the sum of the numbers in the first three boxes to equal 22, and the sum of the numbers in the last three boxes to equal 25. What is the product of the numbers she writes in the grey boxes?

Simon wants to cut a piece of thread into nine pieces of the same length and marks his cutting points. Barbara wants to cut the same piece of thread into only eight pieces of the same length and also marks her cutting points. Carl then cuts the thread at all the cutting points that are marked. How many pieces of thread does Carl obtain?

Two segments, each 1 cm long, are marked on opposite sides of a square of side 8 cm. The ends of the segments are joined as shown in the diagram. What is the shaded area, in cm²?

Tycho wants to prepare a schedule for his jogging. He wants to jog exactly twice a week, and on the same days every week. He never wants to jog on two consecutive days. How many such schedules are possible?

Emily wants to write a number into each cell of a 3×3 table so that the sum of the numbers in any two cells that share an edge are the same. She has already written two numbers, as shown in the diagram. What is the sum of all the numbers in the table?