Question bank IMAS 2022

Among the 16 hexagons shown, what is the largest number having the same symbols with the same counts, not necessarily in the same order?

Three types of toy each have a fixed price. Row and column totals are shown except in the last row and column. What is the value of *?

What is the value of (1234+2341+3412+4123)÷5?

Construct the 9 by 9 multiplication table of all products of two positive one-digit integers. How many entries are two-digit numbers?

How many different triangles can you find in the diagram below?

Eight friends share a restaurant bill equally. Tom left his money at home, so each of the other seven paid 25 dollars extra to cover his share. What was the total bill?

The dartboard scores the number in the hit zone. Hitting the centre scores 90; hitting a boundary scores the higher of the two adjacent zones. With three darts on the board, how many different score combinations total exactly 100?

The segments $OA$, $OB$, $OC$ satisfy $\angle AOB=22^\circ$ and $\angle BOC=56^\circ$. Segment $OD$ bisects $\angle AOC$. Find $\angle BOD$ in degrees.

Your height this year is 10% more than last year; last year it was 20% more than the year before. What percentage did it increase over the two years?

The number 638*977 is a multiple of 7. How many different possible values of
the middle digit represented by the symbol * are there?

Place digits 1 to 9 exactly once in the nine circles, one per circle, so that the sums on the three lines are equal. What is the smallest possible common sum?

Two squares of side 8 cm overlap, with a corner of one at the centre of the other. Given $BC=DE$, find the shaded area in cm².

Three avocados cost the same as five oranges; four oranges cost the same as eleven apples; five apples cost the same as twenty-four bananas. How many bananas cost the same as two avocados?

Four diagrams A–D each have eight unit squares. Using three copies of the yellow V-shaped piece of three squares, with rotations, flips and overlaps allowed, which diagram cannot be covered?

How many odd multiples of 3 lie between 1800 and 2022?

The average of 50 numbers is 38. If two of these numbers, namely 37 and 63, are
discarded, what will be the average of the remaining numbers?

A rectangle ABCD is divided into nine smaller rectangles as shown in the
diagram below. The number written inside a small rectangle denotes its perimeter,
in cm. Notice that the perimeter of one of the small rectangles has an unknown
value, *. If the perimeter of rectangle ABCD is 50 cm, what is the value of the
symbol *? Note that the diagram is not drawn to scale.

The digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 are arranged in a circle, where every chain of
three consecutive digits in the clockwise direction forms a three-digit number.
What is the maximum value of the sum of all nine such numbers?

For her birthday, Alice brought a box of candies, which she wanted to share with
her classmates. If she gave each child 2 candies, there would be 6 candies left in
the box. If she gave each child 3 candies, then exactly 5 children would be left
without candies. How many candies were there in the box?

The figure shows a cube net. Which of the five cubes A–E cannot be folded from it?