2006 xIMC keystage2-EMIC individual

When Anura was $8$, his father was $31$. His father is now twice Anura’s age. How old is Anura now?

Nelly measures three sides of a rectangle and gets $88$ cm. Raffy measures three sides of the same rectangle and gets $80$ cm. Both measurements are correct. Find its perimeter in cm.

Which number should be removed from $1,2,\ldots,11$ so the average of the remaining numbers is $6.1$?

Every house on one side of a street is directly opposite a house on the other. They are numbered consecutively up one side and back down the other. House $37$ is opposite $64$. How many houses are there altogether?

Six basketball players weigh $540$ kg in total. Fourteen cheerleaders average $40$ kg each. Find the average weight of all twenty people, in kg.

How many natural numbers less than $1000$ have first and last digits summing to $13$?

Two bikers $A,B$, initially $370$ km apart, travel towards each other at constant speeds. Starting together, they meet after $4$ hours. If $B$ starts $\frac12$ hour later, they are still $20$ km apart after $A$ has ridden $4$ hours. Find $A$’s speed in km/h.

Rectangle $ABCD$ has $AB=12$, $AD=5$. Points $P,Q,R,S$ divide diagonal $AC$ into five equal parts: $AP=PQ=QR=RS=SC$. Find the total shaded area in the original diagram.

In triangle $ABC$, $P\in AC$, $Q\in AB$, $R\in BC$, $AP=AQ$, $BQ=BR$, and $\angle ACB=70^\circ$ as shown. Find $\angle PQR$ in degrees.

$N=\square+\square-\square$ must be a positive integer. Choose three distinct cards from $1,2,3,5$ and put one in each box. How many different values of $N$ result? With cards $1,2,3$ alone the two values are $2,4$.

A $20$-problem exam awards $5$ points for a correct answer, deducts $1$ for an incorrect answer, and gives zero for a blank. Jolie scores $31$. What is the maximum number she could have answered, correctly or incorrectly?

Joni has a day off after every nine workdays, Dini after every six workdays. Today Joni is off, and tomorrow Dini is off. At least how many days from today until their next shared day off?

Bava, Juan and Suren hold distinct positions: director (D), manager (M), teller (T). The teller is an only child and earns least. Suren is married to Bava’s sister and earns more than the manager. Which position does Juan hold?

Each outer equilateral triangle has area $1$. Pattern $1$ is fully shaded. In pattern $2$ the midpoint triangle is unshaded. In each later pattern repeat this removal inside every surviving shaded triangle, as pattern $3$ shows. Find the shaded area in pattern $5$.

Five circles have three different diameters and touch as shown. The unshaded parts total $20$ cm$^2$. Find the total shaded area in cm$^2$.