Question bank IMAS 2021

Five identical pencils are positioned on the table as shown below. Which two pencils are lying on the same plane?

Five children ride on a seesaw. The diagrams below show weight comparisons between two persons. Who has the heaviest weight?

Tom and Tim play a badminton match. The first player to reach 21 points wins a
game and the first player to win two games wins the match. If Tom wins the first
and third games and gets a total of 60 points for the whole match, what score did
Tom get in the second game?

Which of the following is closest to 2021 kg?

Let $ \star $ be a positive integer such that $ (\star-2)\times(\star+2)=2021 $, what is the value of $ \star $?

What is the value of $2021-2020+2019-2018+2017+\ldots-2+1$?

Josh has 3 dogs, namely Jack, Sparrow and Tom, where each of them has different weights. If Jack and Sparrow weigh 12 kg together, Sparrow and Tom weigh 16 kg together and Tom and Jack weigh 14 kg together, then what is the total weight, in kg, of all 3 dogs?

A certain year in the 21st Century is a perfect square number. What year is it? (Note: $ 1=1^{2} $, $ 4=2^{2} $, $ 9=3^{2} $, ..., so we call 1, 4, 9, ... perfect square numbers.)

Peter keeps all of his socks in a messy non-transparent drawer under his bed. He has 8 black socks and 6 white socks. He takes the socks out from the box, one sock at a time. How many attempts does he need to make sure that he gets 2 socks of the same colour? (Note: There is no difference between a left and a right sock.)

The puzzle shown in the diagram below has one rule: Always follow the direction of the arrows. How many allowable routes from “in” to “out” adhere to the rule?

The diagram below contains five pairs of figures (square, triangle, circle, heart and star) that are placed on a grid. We must connect any two same figures using a single path such that all connecting paths must run only along the grey segments of the grid and no connecting paths may intersect.



Jane draws five sets of connecting paths, as shown in the options. Exactly four of them are satisfying the conditions. Which option is NOT a correct set of connecting paths?

There are four pairs of square patterns as shown below. Inside each square, there
is a wire element. In one of the squares (marked with a question mark), the wire
element is missing. Which of the following is its pattern?
?

Alan and Benjie use the staircase shown in the diagram below to play a game
where the goal is to reach a certain level on the staircase first. At the beginning,
both of them will start in step 1, and in each turn, they will be playing the “Rock,
Paper and Scissors” game to move around the staircase. The winner in each game
gets to move 4 consecutive steps upward (or downward or a combination of both)
for showing a rock; 5 consecutive steps for showing scissors and 6 consecutive
steps for showing a paper. So, for example, when someone reaches step 10, he
must go down to the step 9 and so on, finally returning to the step 1 and then
goes back up doing the same procedure again until somebody wins. To illustrate
further, when a person shows a rock on the first game and wins and then in the
second game shows a paper and wins, he will then move and land on step 9.










Since Alan is curr ently on step 1 of the stairs, what is the least number of times
he has to win in order to reach step 2? Note: If a game is a tie (where both
players show the same hand, i.e. paper and paper), then they don’t move.

A young-looking mother took her child to the park to play. People thought she was the child's elder sister. Curiously, one person asked her age and her smart child replied: "Four years ago, my mother was 7 times my age, but now she is 4 times my age." How old is the mother?

The diagram below is a square that is divided into four parts. Which two of them have the same area?

Select two numbers from 2, 3, 4, 5, 6, 7 and 8 to form a simplified proper fraction. If the product of any two such simplified proper fractions is $ \frac{1}{2} $, they are considered as one pair. How many pairs are there in total?

Let's play a game where we start counting from the thumb with the number 1, the index finger is 2, the middle finger is 3, the ring finger is 4 and the little finger is 5, then after which we count in backward order, where the ring finger is 6, the middle finger is 7, the index finger is 8, and the thumb is 9; then we count in forward order again, and we keep on counting in this manner, as shown on the diagram. Which finger will it land into when I count to 2021?

The diagram below is made up of nine identical squares which form the letter "I". How many different rectangles located in different positions (including squares) are there in the diagram?

Four persons A, B, C and D will participate in a 100-meter race. The following table shows the predicted rankings of each of these four participants before the race. Line ① is participant B's prediction. After the race, all four of them checked the final ranking and after comparing it with their predictions, they found out that nobody predicted their own personal ranking correctly. It is known that everyone has correctly predicted the winner of at least one from the first to third placers, none of them correctly predicted who finished last and exactly two participants correctly predicted the third place winner. Who are the participants that predicted line ②, line ③ and line ④? Note: write the answer in this order.

| | First Place | Second Place | Third Place | Four Place |
| --- | --- | --- | --- | --- |
| ① | D | B | C | A |
| ② | D | A | B | C |
| ③ | A | B | C | D |
| ④ | C | A | B | D |

The three circles below have some number of points on their circumference. Connect all the points on the same circle using straight lines and count the number of regions these segments have partitioned the circle into.



2 points,

2 regions.



3 points,

4 regions.



4 points,

8 regions.

If there are 5 points on the circumference of a circle, how many regions have been partitioned at the most?