Đề thi Toán quốc tế Kangaroo (IKMC) lớp 5-6 năm 2017

www.mathkangaroocanada.com
INTERNATIONAL CONTEST-GAME
MATH KANGAROO
CANADA, 2017
INSTRUCTIONS
GRADE 5-6
1. You have 75 minutes to solve 30 multiple choice problems. For each problem, circle only
one of the proposed five choices. If you circle more than one choice, your response will be
marked as wrong.
2. Record your answers in the response form. Remember that this is the only sheet that is
marked, so make sure you have all your answers transferred here by the end of the contest.
3. The problems are arranged in three groups. A correct answer of the first 10 problems is
worth 3 points. A correct answer of problems 11-20 is worth 4 points. A correct answer of
problems 21-30 is worth 5 points. For each incorrect answer, one point is deducted from
your score. Each unanswered question is worth 0 points. To avoid negative scores, you start
from 30 points. The maximum score possible is 150.
4. Calculators and graph paper are not permitted. You are allowed to use rough paper for draft
work.
5. The figures are not drawn to scale. They should be used only for illustration.
6. Remember, you have about 2-3 minutes for each problem; hence, if a problem appears to
be too difficult, save it for later and move on to the other problems.
7. At the end of the allotted time, please submit the response form to the contest supervisor.
Please do not forget to pick up your Certificate of Participation!
Good luck! Canadian Math Kangaroo Contest team
2017 CMKC locations: Algoma University; Bishop's University; Brandon University; Brock University; Carlton
University; Concordia University; Concordia University of Edmonton; Coquitlam City Library; Dalhousie University;
Evergreen Park School; F.H. Sherman Recreation & Learning Centre; GAD Elementary School; Grande Prairie
Regional College; Humber College; Lakehead University (Orillia and Thunder Bay); Laurentian University; MacEwan
University; Memorial University of Newfoundland; Mount Allison University; Mount Royal University; Nipissing
University; St. Mary’s University (Calgary); St. Peter’s College; The Renert School at Royal Vista; Trent University;
University of Alberta-Augustana Campus; University of British Columbia (Okanagan); University of Guelph;
University of Lethbridge; University of New Brunswick; University of Prince Edward Island; University of Quebec at
Chicoutimi; University of Quebec at Rimouski; University of Regina; University of Toronto Mississauga; University of
Toronto Scarborough; University of Toronto St. George; University of Windsor; The University of Western Ontario;
University of Winnipeg; Vancouver Island University; Walter Murray Collegiate, Wilfrid Laurier University; YES
Education Centre; York University; Yukon College.
2017 CMKC supporters: Laurentian University; Canadian Mathematical Society; IEEE; PIMS.

Grade 5-6 2017
Copyright © Canadian Math Kangaroo Contest. All rights reserved.
This material may be reproduced only with the permission of the Canadian Math Kangaroo Contest Corporation. Page 1
Canadian Math Kangaroo Contest
Part A: Each correct answer is worth 3 points
1. A fly has 6 legs, a spider has 8 legs. Together, 3 flies and 2 spiders have as many legs as 9 chickens and
several cats. How many cats are there?
(A) 2 cats (B) 3 cats (C) 4 cats (D) 5 cats (E) 6 cats
2. Alice has 4 pieces of this shape: . Which picture can she not make from these four pieces?
(A) (B) (C)
(D) (E)
3. Kalle knows that 1111 × 1111 = 1234321. What is the answer of 1111 × 2222?
(A) 3456543 (B) 2346642 (C)2457642 (D) 2468642 (E) 4321234
4. There are 10 islands and 12 bridges, as depicted in the figure. All bridges
are open for traffic right now. What is the smallest number of bridges that
must be closed in order to stop the traffic between A and B?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
5. Martin wants to colour the squares of the rectangle so that 1/3 of all
squares are blue and half of all squares are yellow. The rest of the squares
are to be coloured red.
How many squares will he colour red?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
6. When the car wheels make one full rotation the car moves forward by about 1.8 meters. Approximately
how many kilometres will the car move forward after 10,000 full rotations of the wheels?
(A) 1.8 (B) 18 (C) 180 (D) 1 800 (E) 18 000

Grade 5-6 2017
7. There are 32 students in Mrs. Vicky’s class. Part of the students took one pencil each from the box with
pencils on the teacher’s desk. Then a third of the remaining students took 3 pencils each, and there were
no more pencils left in the box. How many pencils were there in the box at first?
(A) 16 (B) 24 (C) 32 (D) 43 (E) 64
8. Three rhinoceroses Jane, Kate and Lynn go for a walk: Jane first, Kate in the middle, and Lynn – last. Jane
weighs 500 kg more than Kate. Kate weighs 1000 kg less than Lynn. Which of the following pictures may
show Jane, Kate and Lynn in the order they walked?
(A) (B)
(C) (D)
(E)
9. Peter and Nick are both working on "Kangaroo" contest problems. For every two problems that Peter
solves, Nick manages to solve three problems. In total, the boys solved 30 problems. How many problems
did Nick solve more than Peter?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
10. Bob folded a piece of paper, used a hole puncher and punched exactly one hole in the folded paper.
Then, he unfolded the piece of paper, which looked as shown below.
Which of the following pictures shows the lines along which Bob folded the piece of paper?
(A) (B) (C) (D) (E)

Grade 5-6 2017
Part B: Each correct answer is worth 4 points
11. A special die has a number on each of its six faces. The sums of the numbers on opposite faces are all
equal. Five of the numbers are 5, 6, 9, 11 and 14. What number is on the sixth face?
(A) 4 (B) 7 (C) 8 (D) 13 (E) 15
12. Tom wrote all the numbers from 1 to 20 in a row and obtained the 31‐digit number
1234567891011121314151617181920.
Then he deleted 24 of the 31 digits, so that the remaining number was as large as possible.
Which number was it?
(A) 9671819 (B) 9567892 (C) 9781920 (D) 9912345 (E) 9818192
13. Peter went hiking in the mountains for 5 days. He started on Monday and his last trip was on Friday. Each
day he walked 2km more than the day before. The total distance he walked during the five days was 70km.
What distance did Peter walk on Thursday?
(A) 12 km (B) 13 km (C) 14 km (D) 15 km (E) 16 km
14. In a chocolate store, one chocolate costs $3. One day the store had a deal: “Buy two and get a third one
free” and Adam decided to take 49 chocolates. How much did he pay for the chocolates?
(A) $75 (B) $98 (C) $99 (D) $102 (E) $147
15. Eight kangaroos stood in a line as shown in the diagram.
At some point, two kangaroos standing side by side and facing each other exchanged places by jumping
past each other. This was repeated until no further jumps were possible.
How many exchanges were made?
(A) 2 (B) 10 (C) 12 (D) 13 (E) 16
16. The Modern Furniture store is selling sofas, loveseats, and chairs made from identical modular pieces as
shown in the picture. Including the armrests, the width of the sofa is 220 cm and the width of the loveseat
is 160 cm.
What is the width of the chair?
(A) 60 cm (B) 80 cm (C) 90 cm (D) 100 cm (E) 120 cm
sofa loveseat chair
220 cm 160 cm

Grade 5-6 2017
17. There are five padlocks and 5 keys – one for each of them (see the figure). The number code on each key
has been modified into a letter code on the corresponding padlock. Equal digits have been replaced by
the same letter, and different digits – by different letters. What is the number code on the fifth key?
(A) 382 (B) 282 (C) 284 (D) 823 (E) 824
18. Boris has an amount of money and three magic wands that he can use only once. Wand A adds $1. Wand S
subtracts $1. Wand D doubles the amount. In which order must he use these wands to obtain the largest
amount of money?
(A) DAS (B) ASD (C) DSA (D) ADS (E) SAD
19. A vase weighs 600 g when one third of it is filled with water. The same vase weighs 800 g when two thirds
of it are filled with water. What is the weight of the vase when it is empty?
(A) 100 g (B) 200 g (C) 300 g (D) 400 g (E) 500 g
20. Rafael has three squares. The first one has side length 2 cm. The second one
has side length 4 cm and a vertex is placed in the centre of the first square.
The last one has side length 6 cm and a vertex is placed in the centre of the
second square, as shown in the picture. What is the area of the figure?
(A) 32 cm2
(B) 51 cm2
(C) 27 cm2
(D) 16 cm2
(E) 6 cm2
Part C: Each correct answer is worth 5 points
21. The natural numbers are arranged in the form of a triangle: 1 is in the first row, 2 and 3 are in the second
row, 4, 5 and 6 are in the third row, and so on. What is the sum of the numbers written in the 10‐th row?
(A) 490 (B) 495 (C) 500 (D) 505 (E) 510
1
2 3
4 5 6
.
.
.

Grade 5-6 2017
22. There are eight balls numbered with the numbers 40, 80, 100, 101, 190, 200, 260 and 292 in a bag.
Martina takes four balls out of the bag and calculates the sum of the numbers on these balls. It appears
that this sum is half of the sum of the numbers on the balls that remain in the bag. What is the greatest
number written on the balls taken out?
(A) 101 (B) 200 (C) 260 (D) 190 (E) 292
23. The structure on the figure is made of unit cubes glued together. Morten wants to
put it into a rectangular box. What are the dimensions (length, width and height)
of the smallest box he can use?
(A) 3 × 3 × 4 (B) 3 × 5 × 5 (C) 3 × 4 × 5 (D) 4 × 4 × 4 (E) 4 × 4 × 5
24. Four players scored goals in a handball game. All of them scored a different number of goals. One of the
players, Mike, scored the least number of goals. The other three players scored 20 goals in total. What is
the largest number of goals Mike could have scored?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
25. Ala likes even numbers, Beata likes numbers divisible by 3, Celina likes numbers divisible by 5. Each of
these three girls went separately to a basket containing 8 balls with numbers written on them, and took all
the balls with numbers she liked. It turned out that Ala collected balls with numbers 32 and 52, Beata ‐ 24,
33 and 45, Celina ‐ 20, 25 and 35. In what order did the girls approach the basket?
(A) Ala, Celina, Beata (B) Celina, Beata, Ala (C) Beata, Ala, Celina
(D) Beata, Celina, Ala (E) Celina, Ala, Beata
26. The picture of a kangaroo in the first (leftmost) triangle was reflected across the dotted lines, as in mirrors.
The first two reflections are shown.
What does the reflection look like in the shaded triangle?
(A) (B) (C) (D) (E)
27. The numbers 1, 2, 3, 4, and 5 must be written in the five cells in the figure, respecting the following rules:
 If a number is just below another number, it must be greater.
 If a number is just to the right of another number, it must be greater.
In how many ways can this be done?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 8

Grade 5-6 2017
28. John wrote a natural number in each of the four boxes in the bottom row of the diagram. Then he wrote in
each of the other boxes the sum of the two numbers in the boxes immediately underneath. What is the
largest number of odd numbers that could appear in the completed diagram?
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
29. Julia has four pencils of different colours and wants to use some or all of them to paint the map of an
island divided into four countries, as in the picture. Any two countries with a common border must be
coloured differently on the map. How many different colourings of this map are possible? (Two
colourings are considered different if at least one of the countries is coloured differently).
(A) 12 (B) 18 (C) 24 (D) 36 (E) 48
30. A bar consists of two grey cubes and one white cube glued together as shown in the figure.
Which cube can be built from nine such bars?
(A) (B) (C) (D) (E)

www.mathkangaroocanada.com
International Contest-Game
Math Kangaroo Canada, 2017
Answer Key
Grade 5-6
1 A B C D E 11 A B C D E 21 A B C D E

Đề thi Toán quốc tế Kangaroo (IKMC) lớp 5-6 năm 2017

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