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IMAS 2017 — Upper Primary Grades 5–6 — Round 1

Question 1

What is the simplified value of $\frac{20\times17}{2+0+1+7}$ ?
  1. 340
  2. $\frac{34}{2017}$
  3. 10
  4. 20
  5. 34

Question 2

What is the remainder when 2017 is divided by 9?
  1. 0
  2. 1
  3. 2
  4. 3
  5. 7

Question 3

Positive integers are arranged in the array as shown below, what is the sum of all the integers located on the fifth row ? $\begin{array}{ccccccc}&&&1&&&\\&&2&3&4&&\\&5&6&7&8&9&\\10&11&12&13&14&15&16\\&&&\vdots&&&\end{array}$
  1. 91
  2. 164
  3. 172
  4. 189
  5. 215

Question 4

Arrange the numbers $2.\overline{718}$, $2.7\overline{18}$, $2.71\overline8$, $2.71828$ in increasing order. (Repeating decimals are denoted by drawing a horizontal bar above the recurring figures.)
  1. $2.7\overline{18}$ < $2.\overline{718}$ < $2.71828$ < $2.71\overline8$
  2. $2.71828$ < $2.\overline{718}$ < $2.7\overline{18}$ < $2.71\overline8$
  3. $2.7\overline{18}$ < $2.71828$ < $2.\overline{718}$ < $2.71\overline8$
  4. $2.71828$ < $2.7\overline{18}$ < $2.71\overline8$ < $2.\overline{718}$
  5. $2.7\overline{18}$ < $2.\overline{718}$ < $2.71\overline8$ < $2.71828$

Question 5

The figure below plots the body temperature records of one patient in a day. The records started at 00:00 AM and were taken every 4 hours. After how many hours did the patient recorded his highest temperature?

Question illustration
  1. 0
  2. 4
  3. 12
  4. 16
  5. 24

Question 6

On a $5\times5$ table below, place into each cell the sum of its row number and column number. For example, value of a below is $2+3=5$ . How many odd numbers are filled into the table?
|Row/Column|1|2|3|4|5|
|---|---|---|---|---|---|
|1| | | | | |
|2| | |a| | |
|3| | | | | |
|4| | | | | |
|5| | | | | |

Question illustration
  1. 5
  2. 10
  3. 12
  4. 18
  5. 25

Question 7

There are 23 kids seated in a row. They call out the numbers from left to right as 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, … for the first round. They call out 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, … from right to left for the second round. How many kids call out the same number in two rounds?
  1. 11
  2. 12
  3. 15
  4. 18
  5. 23

Question 8

Salted water with 3.2% concentration weights 500 g. How many salt, in grams, is left if the water is vaporized completely?
  1. 16
  2. 32
  3. 64
  4. 100
  5. 128

Question 9

In the figure below, Tom combined some squares of the same size into a shape of umbrella. Find the least number of squares he would use.

Question illustration
  1. 5
  2. 9
  3. 12
  4. 15
  5. 20

Question 10

The shape enclosed by solid lines in the figure below is composed of unit squares. What is the maximum area of a rectangle that can be cut from the shape along grid lines?

Question illustration
  1. 80
  2. 96
  3. 100
  4. 112
  5. 128

Question 11

Given six cards with numbers 1, 2, 3, 4, 5 and 6 one card for each number. Each time Lee takes 2 cards, he computes the difference (larger one minus small one) and discards the two cards. Find the maximum possible sum of the three differences after all cards are discarded.
  1. 3
  2. 5
  3. 7
  4. 8
  5. 9

Question 12

The houses of Mary and Jerry are connected by a trail. One day, they started from their respective house at the same time, and walked towards the other's house. The speed of Mary is 1.5 times that of Jerry and they met 12 minutes later. On the next day, Mary left his house and walked to Jerry's house with the same speed. How long would he take to reach Jerry's house?

Question illustration
  1. 15
  2. 18
  3. 20
  4. 24
  5. 30

Question 13

In the figure below, the area of square ABCD is 36 cm² , the area of rectangle CDEF is 18 cm² and the area of ADGH is 48 cm² . What is the perimeter, in cm, of BFEDGH?

Question illustration
  1. 18
  2. 36
  3. 46
  4. 48
  5. 56

Question 14

There are two routes starting in a bus stop. A bus departs for the first route every 8 minutes and departs the second route every 10 minutes. At 6:00 in the morning, two buses depart for the two routes at the same time. Among the choices below, when will the buses depart for the two routes simultaneously?
  1. 7:30
  2. 8:20
  3. 9:40
  4. 10:00
  5. 11:00

Question 15

Let a, b, c, d, e and f are distinct digits such that the expression $\overline{ab}+\overline{cd}=\overline{ef}$ . What is the least possible value of $\overline{ef}$ ?
  1. 30
  2. 34
  3. 36
  4. 39
  5. 41

Question 16

Henry starts working at 9：00 in the morning and finishes at 5：00 in the afternoon. How many more degrees does the minute hand rotates than the hour hand does on the clock during this period?
  1. 120
  2. 1200
  3. 1320
  4. 2640
  5. 2880

Question 17

The average score of a class in an exam is 70. Two students got 0 for absence and the average of remaining students is 74. What is the total number of students in the class?
  1. 25
  2. 28
  3. 30
  4. 35
  5. 37

Question 18

The price criteria of the subway ticket of a city is as follows: \$2 for within 4 km, \$1 more per 4 km for distances between 4 km and 12 km, \$1 more per 6 km for distances over 12 km. It costs \$8 to take subway from station A to station B. Which of the following is closest to the distance between A and B?

Question illustration
  1. 12 km
  2. 18 km
  3. 24 km
  4. 36 km
  5. 48 km

Question 19

The figure below shows the floor plan of a library. Each room is connected to adjacent rooms. One starts from room 1 and walks through all rooms without repetitions (going back). How many unique paths are there?

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

Question 20

In the figure below, 55 unit cubes were stacked in a pile. Paint the surface of the pile of cubes but the face on the ground is not painted. How many unpainted unit cubes are there when the stack is separated?

Question illustration
  1. 6
  2. 9
  3. 13
  4. 14
  5. 18