IKMC 2019 - Grades 7-8 - Self-study

Which cloud contains four even numbers?

How many hours are there in ten quarters of an hour?

A 3×3×3 cube is built from 1×1×1 cubes. Then some cubes are removed from front to back, from left to right and from top to bottom, as shown. How many 1×1×1 cubes are left?

Three rings are linked as shown in the diagram. Which diagram also shows the three rings linked in the same way?

Which diagram cannot be drawn without lifting your pencil off the page and without drawing along the same line twice?

Five friends met. Each of them gave a cupcake to each of the others. They then ate all the cupcakes they had been given. As a result, the total number of cupcakes had decreased by a half. How many cupcakes did the five friends have at the start?

In a race, Lotar finished before Manfred, Victor finished after Jan, Manfred finished before Jan and Eddy finished before Victor. Who finished last of these five runners?

The pages of the book Juliet is reading are all numbered. The numbers used on the pages contain digit 0 exactly five times and digit 8 exactly six times. What is the number of the final page?

A large square is divided into smaller squares. What fraction of the large square is coloured grey?

Andrew divided some apples into six equal piles. Boris divided the same number of apples into five equal piles. Boris noticed that each of his piles contains two more apples than each of Andrew’s piles. How many apples did Andrew have?

Four-digit integers are written on each of three pieces of paper. The pieces are arranged so that three digits are covered, as shown. The sum of the three four-digit integers is 10126. Which are the covered digits?

In the diagram, PQ=PR=QS and angle QPR=20°. What is the size of angle RQS?

Which of the following 4×4 tiles cannot be formed by combining the two given pieces?

Alan, Bella, Claire, Dora and Erik met at a party and shook hands exactly once with everyone they already knew. Alan shook hands once, Bella twice, Claire three times and Dora four times. How many times did Erik shake hands?

Jane is playing basketball. After 20 shots, she had scored 55% of the time. Five shots later, her scoring rate increased to 56%. On how many of the last five shots did she score?

Cathie folded a square sheet of paper exactly in half twice and then cut it in the middle twice, as shown. How many of the pieces she obtains are squares?

Michael keeps dogs, cows, cats and kangaroos as pets. He tells Helen that he has 24 pets in total and that $1/8$ of them are dogs, $3/4$ are NOT cows and $2/3$ are NOT cats. How many kangaroos does Michael keep?

Some identical rectangles are drawn on the floor. A triangle of base 10 cm and height 6 cm is drawn over them, as shown. The region inside the rectangles and outside the triangle is shaded. What is the area of the shaded region?

Julio has two cylindrical candles with different heights and diameters. The first lasts 6 hours, the second 8 hours. He lights both at the same time; three hours later they have the same height. What was the ratio of their original heights?

Aylin wants to create a path of matches using as few matches as possible. She places each match along a dotted line on the paper, like the one shown. The path returns to the left-hand end of the original match. Numbers in cells equal the number of matches around that cell. How many matches are in this path?