Question bank IMAS 2017

What is the simplified value of $ 25 \times 99 + 55 \times 5 $?

In the arithmetic expression $ \overline{1A} + \overline{B1} = 100 $, what is the value of the digit B?

As shown in the figure below, there is a $ 7 \times 7 $ grid paper where each small square has an area of $ 1 \, cm^2 $, what is the area, in $ cm^2 $, of the shaded part?

Students are arranged in a square formation with 8 rows and 8 columns. Now, 3 rows and 3 columns are removed, how many students were reduced?

A train travels between City A to City B. There are 4 other stops in-between these two cities. How many different kinds of tickets are there? (Note: The ticket from City A to City B and City B to City A must not be the same).

In the figure shown below, a square is embedded in a rectangle. If AB=9cm and CD=15cm, then what is the perimeter, in cm, of the rectangle?

In a class, 22 students take painting course, 28 students take piano course, 10 students take both courses and 5 students take none of the courses. Find the number of students in the class.

As shown in the figure below, points C and D are on segment AB. The length of AC is 6 cm longer than the length of CD. The length of BD is twice as the length of AC. How much, in cm, is BD longer than AD?

The sum of four consecutive odd integers is 72. What is the largest integer among the four integers?

Each of the digits 1, 2, 3, 4, 5 and 6 are printed on one of the 6 cards. Choose two different cards to form a 2-digit number. List down all possible 2-digit numbers in increasing order on a sheet of paper, what is the $21^{st}$ number in the list?

If $ (\Delta \div 2 - 2) \times 2 + 2 = 222 $, then what is the value of the symbol $ \Delta $?

Positive integers are arranged in the array as shown below. What is the sum of all the integers located on the fourth row?

$$\begin{array}{ccccc}&&1&&\\&2&3&4&\\5&6&7&8&9\\&&\cdots&&\end{array}$$

Define a new operation “*” such that $ 4 * 2 = 86 $, $ 6 * 3 = 189 $, $ 8 * 4 = 3212 $ and $ 9 * 3 = 2712 $. Find $ 10 * 2 $.

The average score of Peter in several math exams is 88. On the last exam, he must get 98 in order to raise his average score to 90. How many exams has he taken in total?

How many different ways are there to place 2 identical black balls and 2 identical white balls in three different boxes A, B and C such that each box should contain at least one ball?

As shown in the figure below, there is a $ 3 \times 3 $ grid paper where each small square has an area of $ 1 cm^{2} $. Find the area, in $ cm^{2} $, of the shaded part.

The sum of the digits of a 2-digit number is equal to 9. If the 2-digit number is multiplied by 5, the sum of all digits is still 9. How many such 2-digit numbers are there?

As shown in the figure below, an ant starting from point A crawl along the path to point B. It is required that both point C and point D can only pass once, how many different paths can the ant crawl?

Arrange black and white beads according to the pattern shown in the figure below. If the total number of beads is 97, how many black beads are there?

There are 6 persons A, B, C, D, E and F attend a meeting. Some of them shake hands with one another. In the final count up, A shakes 5 hands, B shakes 4, C shakes 3, D shakes 2 and E shakes 1. How many does F shake?