IKMC 2027 - Grades 7-8 - Self-study SET 6 - Thematic Batch 3

A bus leaves the airport for the city centre every 3 minutes. A car leaves the airport at the same time as one bus. A bus takes 60 minutes to reach the centre, while the car takes 35 minutes. How many buses does the car pass on its journey, excluding the bus that starts with it?

Editorial assumption: All vehicles follow the same route at constant speeds, with the regular bus service already running.

PQR is an equilateral triangle. The source writes “ray SR” as the bisector of $\angle PRQ$. Take T on RS so that $\angle TQR:\angle TQS=2:1$. Find $\angle STQ$.

Editorial note: The diagram identifies S on PQ and the intended bisector as ray RS from R; the Vietnamese source wording is retained.

Betty orders a drink with three parts. The liquid is matcha or chocolate; the topping is white pearls, black pearls or pearl strips; and the cream is vanilla or strawberry. How many complete drinks can she order?

In the world of geometric solids, an ant is made from solids with triangular faces. It weighs 20 g. If its linear dimensions become 100 times as large, how much will it weigh?

Editorial assumption: The ant is enlarged geometrically in all three dimensions, with unchanged material density.

Mic, Max, Min, Mac and Mai join clubs for football, volleyball, baseball, table tennis and basketball. The meeting times clash, so each friend joins only one club.
– Mic does not join volleyball or football.
– Max does not join football, baseball or basketball.
– Min does not join volleyball, basketball or baseball.
– Mac does not join table tennis, basketball or baseball.
– Mai does not join basketball or volleyball.
Which club does Mai join?

Original printed choices: A) Football; B) Baseball; C) Table tennis; D) Football or baseball; E) Baseball or table tennis

Editorial task: Solve the literal problem, identify any missing condition, and distinguish the intended interpretation.

The Champions League group stage has 8 groups of 4 teams. Each team plays two matches against the other teams in its group. How many matches are played in the whole group stage?

Editorial interpretation: Each pair of teams in a group plays twice.

A sector equal to 15% of a circular cake is cut out as shown. Find $\alpha$.

Ann places the integers 1 through 9, each once, in the nine circles shown. The sum on every straight line of three circles must be divisible by 9. Which listed number can occupy the centre marked “?”?

In the dance final, each judge awards the five contestants the scores 0, 1, 2, 3 and 4, each exactly once. Adam knows all contestant totals and the individual scores shown in the table. What score did judge III give Adam?

Four identical cubes are shown in different orientations. They are placed together to make the large square top face shown. Which option is the face opposite that top face?

A class has a mean mathematics test score of 6. The 60% of pupils who pass have a mean score of 8. What is the mean score of the pupils who fail?

One hundred trees stand along one side of a road. Every third tree is a linden; every fifth tree is a maple or a linden. All other trees are poplars. How many poplars are there?

In the figure, A is the area of the square and B is the total area of the six semicircles. Find A − B.

The figure is the net of a triangular prism. Before it was unfolded, which edge coincided with UV?

Laura writes $(1-2)-(3-4)-(5-6)-\cdots-(2015-2016)-(2017-2018)$. What is its value?

A 3 × 3 × 3 cube is assembled from white, grey and black unit cubes as shown. The separate white and black parts are displayed on the right. Which option is the grey part?

This winter Tom will keep horse Hor, goat Goa and sheep Shee together in one stable. They take 2, 3 and 6 days respectively to eat one cartload of hay. Winter lasts three months of 30 days each. How many cartloads must he prepare at minimum?

Two cars start at the same time and travel in the same direction at 40 km/h and 50 km/h. How many hours after starting will they be 18 km apart?

Editorial assumption: The two cars leave the same point and keep their stated constant speeds.

A faulty printing machine damages every fifteenth magazine it prints. A customer orders 2500 undamaged magazines. What is the minimum total number the printer must print?

Let v be the total area of the vertically hatched regions and w the total area of the horizontally hatched regions in the figure. The four circle diameters are 6, 4, 4 and 2. Which statement is true?