IMAS 2018 — Upper Primary Grades 5–6 — Round 1

What is the least common denominator of these three fractions: $\frac14$ , $\frac56$ and $\frac38$ ?

What is the largest possible integer that can be placed in the □ below such that the inequality is satisfied? $9\times\square\lt2018$

Bob got a score of 94 on foreign language test, and his average score on the native language and math tests is 97. What is his average score on these three tests?

If we add 6 to the denominator of $\frac23$ , then what number should be added to its numerator such that the value of the fraction remains unchanged?

There are 240 kg of flour in a restaurant, which is planned to be used for 8 days. After some modifications in the menu recipe, daily consumption of flour is now reduced by 6 kg. How many days will the stock of flour last?

A train left town A at 8:30 AM some day and arrived at town B at 1:50 AM of the next day. There is no time difference between the two places. How long did the train travelled for the trip?

Three hundred pairs of shoes were shipped to a department store. The shoes were packed into 2 wooden boxes and 9 carton boxes. Each wooden box contains the same number of shoes, while each carton box also contains the same number of shoes. If 3 carton boxes contain the same number of shoes as 1 wooden box, how many pairs of shoes does each wooden box contain?

Which of the following statements below is true:

The fraction below each figure indicates the ratio of the area of the shaded region compared to the area of the whole figure. Which of the following options is always correct?

Mike placed 4 identical squares, each with side length 5 cm and are non-overlapping, to form a new figure as shown below. Find the perimeter, in cm, of this new figure.

When dividing, Mike mistakenly wrote 54 instead of 45. The resulting quotient is now 18 with remainder 18. What should be the correct quotient?

The figure below shows a statistical pie chart of the number of History, Math and Science books in the library of Sun Light Elementary School. It is known the total number of books of these three subjects is 1200. How many more History Books are there than Science Books?

Cut a right cylinder starting from the diameter of its top face along an up and down direction, such that it is divided into two identical pieces. The cross section is a square. How many times of height of the cylinder is the circumference of its top face?（Use $\pi=3.14$ ）

Two sectors are located in a circle as shown in the figure below. The first sector has a central angle 30° and has an area of 37.68 cm² , while the second sector has an area of 56.52 cm² . Find the measure, in degrees, of the central angle of the second sector. （Use $\pi=3.14$ ）

A palindrome number is a positive integer that is the same when read forwards or backwards. The numbers 909 and 1221 are examples of palindromes. How many three-digit palindrome numbers are divisible by 9?

The table below shows an attendance sheet (which is incompletely filled-out) of a company on Oct. 30.
|Department|Total number of Employees|Employees on Duty|Percentage|
|---|---|---|---|
|Department1|150| |96%|
|Department2| | | |
|Total| |234|97.5%|

What is the total number of employees in Department 2 on Oct. 30?

When some three-digit number is divided by 37, it gives a result of quotient a with remainder b, where a and b are non-negative integers. What is the maximum possible value of $a+b$ ?

The side lengths of a right triangle are 3 cm, 4 cm and 5 cm, respectively. A quarter-circle is placed inside this triangle and touches the hypotenuse, as shown in the figure below. What is the area, in cm² , of the shaded region? ( $\pi=3.14$ , round-off to one decimal place)

The greatest common divisor of n and 24 is 2, while the greatest common divisor of $n+1$ and 24 is 3. Which of the following numbers cannot be n?

In the figure below, six identical squares are used to form a $3\times2$ rectangle, wherein the diagonals of five of these squares are drawn. How many right isosceles triangles are there in the figure?