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IMAS 2019 — Middle Primary Grades 3–4 — Round 1

Question 1

What is the value of $13+12+11+\cdots+3+2+1+2+3+\cdots+11+12+13$?
  1. 181
  2. 182
  3. 183
  4. 184
  5. 185

Question 2

If $ (\Delta \times 2 + 1) \times 3 = 2019 $, then what is the value of $ \Delta $?
  1. 335
  2. 336
  3. 337
  4. 3028
  5. 3029

Question 3

In the figure below, each unit square has side length of 1 cm. What is the area, in cm², of the shaded region?

Question illustration
  1. 6
  2. 8
  3. 10
  4. 12
  5. 14

Question 4

A square piece of paper, with a perimeter of 48 cm, is to be cut into three rectangles of the same size as shown in the figure below. What is the perimeter, in cm, of each rectangle that was cut out?

Question illustration
  1. 12
  2. 18
  3. 24
  4. 32
  5. 40

Question 5

In the equation below, fill in the five numbers 7, 50, 51, 55, and 63 into the five circles to make the equality true. What is the sum of the numbers in the first three circles?

$ ○+○+○-○=○ $

Question illustration
  1. 105
  2. 106
  3. 113
  4. 114
  5. 118

Question 6

How many different 3-digit numbers are there such that the sum of its digits is equal to 4?
  1. 7
  2. 8
  3. 9
  4. 10
  5. 11

Question 7

There are a total 80 pandas in a zoo, all of which are housed in three different halls. The number of pandas in Hall 1 is twice that in Hall 2, and the number of pandas in Hall 2 is three times that in Hall 3. How many pandas are there in Hall 2?
  1. 16
  2. 24
  3. 36
  4. 48
  5. 60

Question 8

Every page of a book is either all text or all illustrations and that there are exactly three pages of illustrations between every two pages of text, that is, if the last page of the book is text only, then one page before and after the three-page illustration are all-texts. If the last page is an illustration, in addition to the illustrations on the last few pages, one page before and after the other three pages of illustrations is text. If the first page of the book is text, and it has a total of 136 pages, how many pages are there in this book are illustrations only?
  1. 104
  2. 103
  3. 102
  4. 68
  5. 34

Question 9

For any positive integer, we compute by following the operating rules: If the number is an even number, then we divide it by 2; and if it is odd, then we add 1 to it. We continue to do these operations until we arrive with the value of “1” for the first time. How many numbers will leave a value of “1” after four operations?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 10

Among the numbers from 0 to 200, what is the average of all numbers that are multiples of 3?
  1. 95
  2. 96
  3. 99
  4. 100.5
  5. 101

Question 11

What is the tens digit of the simplified value of the following expression: $ 1+12+123+1234+12345+123456+1234567+12345678+123456789 $ ?
  1. 0
  2. 2
  3. 4
  4. 6
  5. 8

Question 12

In the figure below, the largest rectangle has dimensions 9 cm long by 8 cm wide, with a cross-section formed by two shaded rectangles in the middle. If the total area of the shaded parts is exactly equal to the area of the un-shaded parts, then what is the value, in cm, of x?

Question illustration
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 13

Use the digits 2, 0, 1, and 9 exactly once to form different 4-digit numbers. How many of these 4-digits numbers will be greater than 1905?
  1. 12
  2. 13
  3. 15
  4. 17
  5. 19

Question 14

After deleting one of the six numbers 2, 3, 12, 26, 29 and 41, the five remaining numbers can be divided into two groups with the same sum. What is the number that was deleted?
  1. 3
  2. 12
  3. 26
  4. 29
  5. 41

Question 15

As shown in the diagram, three of the seven areas enclosed by the three circles are each filled with a number, and it is known that the numbers 13, 15, 17, and 18 can be filled inside the four blank areas such that the sum of the four numbers in each circle are all equal. What is the sum?

Question illustration
  1. 58
  2. 59
  3. 60
  4. 61
  5. 62

Question 16

In the figure below, each unit square has a side length of 1 cm. How many squares and rectangles are there?

Question illustration
  1. 9
  2. 12
  3. 14
  4. 15
  5. 16

Question 17

A theater has nine rows of seats. The first row has a total of 19 seats and starting from the second row, each row has two more seats than the previous row. How many seats does this theater have in total?
  1. 173
  2. 187
  3. 243
  4. 261
  5. 280

Question 18

Divide the six positive integers 2, 3, 7, 13, 18, and X into three groups so that the first group contains one number, the second group contains two numbers, and the third group contains three numbers, where X must belong in the third group. If the number in the first group is greater than the sum of the numbers in the second group, and that the sum of the numbers in the second group is greater than the sum of the numbers in the third group, then what is the maximum possible value of $X$?
  1. 4
  2. 5
  3. 6
  4. 7
  5. 8

Question 19

In the figure below, rectangle $ ABCD $ has a perimeter of 32 cm, where both $ ABFE $ and $ EGHD $ are squares. If the perimeter of $ GFCH $ is 12 cm, then what is the area, in cm², of rectangle $ ABCD $?

Question illustration
  1. 28
  2. 39
  3. 48
  4. 55
  5. 60

Question 20

As shown in the figure below, an ant starting from vertex A of the cuboid needs to move along the edges to reach its destination, vertex B. If the ant can only pass through three edges, how many possible paths can the ant crawl to reach the destination?

Question illustration
  1. 3
  2. 6
  3. 9
  4. 12
  5. 15