Question bank IMAS 2016

What is the value of 2016-20×16?

Cubes of side length 1 cm are available in two colors. They are used to form a large cube of side length 3 cm, and two small cubes sharing a common face have different colors. What is the positive difference between the numbers of cubes in the two colors?

How many different rectangles (including squares) in different positions are there in the diagram below?

In a 6 by 6 table, each row and each column contains the letters A, B, C, D, E and F exactly once. All but four of the squares have been filled in. Which of the following should be chosen to fill in the blank squares?

The letters IMAS are spelt out with the same size of black and white circles as shown in the diagram below. If the total area of the black circles is 50 cm², what is the total area, in cm², of the white circles?

Barry is flying from A to B on a 13:00 flight. The distance between A and B is 1800 km, and the speed of the plane is 600 km per hour. If the flight is delayed for 2 hours and no time difference between A and B, when will Barry arrive at B?

Jane feeds her cat at regular intervals. The first feeding is at 7:00 and the sixth feeding is at 22:00. Which of the following is not a feeding time for the cat?

If Mary buys 3 dolls, she will have 150 dollars left. If she buys 4 dolls, she will be 50 dollars short. All the dolls are at the same price. How much money does Mary have on her?

How many four-digit numbers using each of 0, 2, 4 and 5 once are divisible by 5?

Four teachers predict the order of finish among five classes, as shown in the table below. Every prediction is wrong! In which place does Class 2 finish?

| | $ 1^{{st}} $ | $ 2^{{nd}} $ | $ 3^{{rd}} $ | $ 4^{{th}} $ | $ 5^{{th}} $ |
| --- | --- | --- | --- | --- | --- |
| Teacher A | Class 4 | Class 3 | Class 2 | Class 5 | Class 1 |
| Teacher B | Class 4 | Class 2 | Class 5 | Class 3 | Class 1 |
| Teacher C | Class 3 | Class 1 | Class 4 | Class 2 | Class 5 |
| Teacher D | Class 1 | Class 5 | Class 2 | Class 4 | Class 3 |

A new arithmetic operation “∇” is such that $6\nabla3=218$, $8\nabla4=232$ and $ 9\nabla3 = 327 $. What is the value of $ 10\nabla2 $?

A bamboo stick is lowered vertically into water to a depth of 50 cm, and a mark is made on the stick at the point of immersion. The stick is then taken out and turned upside down. Then it is lowered vertically into water to a depth of 50 cm, and a mark is made on the stick at the point of immersion. If the distance between the two marks is 25 cm, what are the possible lengths, in cm, of the bamboo stick?

If a boy is chosen as captain, then the number of boys among the other members is equal to the number of girls. If a girl is chosen as captain, then the number of girls among the other members is one half the number of boys. How many boys are there?

Use all of the numbers 1, 2, 3, 4, 5, 6, 7 and 8 to fill in the circles in the diagram below so that the sum of the numbers in the four circles of each of the two squares and each of the four trapezoids is constant. What is this constant sum?

Four identical dice are stacked on a desk, as shown in the diagram below. How many spots are on the face of the bottom die touching the top of the desk?

C and D are two points on the segment AB, as shown in the diagram below. If AD is 30 cm longer than BD and AC is 14 cm shorter than BC, what is the length, in cm, of CD?

Simultaneously, X and Y start going from A to B while Z goes from B to A, each at a different constant speed. Z's speed is 3 times that of X. Ten minutes after their start, Y meets Z, and 10 minutes later, X meets Z. How many minutes will it take for Y to complete the whole trip?

Hanna makes four straight cuts on a round cake. Into at most how many pieces can she cut it?

Eight children are sharing 61 balloons. Each gets at least one, and everyone receives a different number. What is the smallest number of balloons that can go to the child receiving more balloons than the others?

In how many ways can we choose six different numbers from 1, 2, 3, 4, 5, 6, 7 and 8 so that their sum is a multiple of 4?