IKMC 2014 - Grades 9-10 - Self-study

The Kangaroo competition is held on the third Thursday in March each year. What is its earliest possible date in March?

The MSC Fabiola holds a record as the largest container ship to enter San Francisco Bay. Its 12500 containers would stretch about 75 km placed end to end. Roughly how long is one container?

If a, b, c are the lengths of the three lines in the picture, which ordering is correct?

Which number is halfway between $2/3$ and $4/5$?

In 2014, the last digit is larger than the sum of the other three digits. How many years earlier did this last happen?

The large regular hexagon has sides twice as long as the small regular hexagon. The small hexagon’s area is 4 cm². What is the large hexagon’s area?

What is the negation of “Everybody solved more than 20 problems”?

Tom draws a square with one diagonal on the x-axis, whose endpoints are (−1,0) and (5,0). Which coordinates belong to another vertex?

In a village, the ratio of adult men to adult women is 2:3, and the ratio of adult women to children is 8:1. What is the ratio of all adults to children?

The bicycle’s large wheel has circumference 4.2 m, and its small wheel 0.9 m. Both valves are initially at the lowest point. The bicycle rolls left. After how many metres do both valves first return to their lowest points together?

A grandmother, her daughter, and her granddaughter have ages summing to 100 this year. Each age is a power of 2. In which year was the granddaughter born?

Paul hangs rectangular paintings. Each nail is 2.5 m above the floor, and a 2 m string is attached to the two upper corners of each painting. Which hangs closest to the floor? Choices give width×height in cm.

Six girls share two bathrooms, starting at 7:00. Each bathroom serves one girl at a time. Their required times are 9,11,13,18,22,23 minutes. They breakfast together once all finish. What is the earliest possible time?

The figure is a regular octagon. Its shaded top region has area 3 cm². Find the area of the whole octagon.

A newly discovered crocodile has tail length one third of its whole length. Its head is 93 cm long and is one quarter of its length excluding the tail. How long is the crocodile?

On this special die, opposite faces always have the same sum. The three unseen numbers are all prime. Which number is opposite 14?

Ann walks 8 km at 4 km/h, then runs at 8 km/h. How long must she run so her overall average speed is 5 km/h?

A chess player plays 40 games and scores 25 points: a win gives 1, a draw 1/2, and a loss 0. How many more games did he win than lose?

Triplets Jane, Danielle, Hannah want identical hats. They lack respectively one third, one quarter, and one fifth of the price. After each hat becomes 9.40 EUR cheaper, they pool their savings and buy one each, with nothing left. What was the original price per hat?

Positive integers p, q, r satisfy $p+\frac1{q+1/r}=\frac{25}{19}$. Find pqr.