CSAR Learning Solutions Pvt. Ltd.
MATH KANGAROO
WORK BOOK
Prepare yourself for
No.1
Work Book
WORLD’S MOST CELEBRATED
Math Challenge!
Benjamin
Grade 5 & 6
A division of CSAR Learning Solutions Pvt. Ltd.
I O A
Medals and Merit Certificates

Gold medals will be awarded to the top 5% of competitors; silver medals will be awarded to the next top
10% of competitors, and bronze medals will be awarded to the next top 10% of competitors. All medalists
will be presented with merit certificates. Others will receive a participation or appreciation certificate.

Only an e-certificate will be given for appreciation and participation.

In the second round of competition, the first-round perfect scorer will compete. Students who score
higher than 95% in the second round will receive a Perfect Score Award, a Gold Medal, and $100 in cash.
ORGANISED BY
International Olympiad Academy
www.internationalolympiadacademy.com
ACKNOWLEDGEMENT
The Math Kangaroo work book is an initiative of International Olympiad
Academy. International Olympiad Academy acknowledges the
contribution of all its authors, content writers and designers in the creation
of the book
Copyright © International Olympiad Academy (IOA)
All rights reserved with the publisher. No part of the work may be
reproduced, stored in retrieval system or transmitted in any form or by any
means, electronic, mechanical, photocopying, microfilming, recording or
otherwise, without the prior written permission of the publisher.
The publisher apologizes to its readers for any errors or omissions and
would be grateful for notification of corrections that should be
incorporated in the future reprints.
Published by:
International Olympiad Academy (IOA)
Registered Office:
A-409, Durga Vihar, East of Sainik Farms, New Delhi-110080
Website:
www.internationalolympiadacademy.com
PREFACE
This workbook is designed to enable students to explore math effectively.
Designed in accordance with the requirements of the Math Olympiads/Contests,
the workbook is an efficient tool to achieve comprehensive success at not only at
the Math Kangaroo and other math Olympiads/Contests but also develop a deeper
understanding of the subject and be able to appreciate the ubiquitous role that
mathematics plays in our daily life.
This book consists of three sections: SECTION - A: PRE-Foundation, SECTION - B:
Foundation and SECTION - C: Exploration. Questions in SECTION- A aim to
strengthen the basic concepts, SECTION- B poses questions of medium difficulty
level aiming to enhance the understanding level, and finally questions of SECTIONC are of a higher difficulty level and aims to build the proficiency of students in the
application of the basic concepts.
Sanjay K Singh
(Director)
CONTENTS
SECTIONS
PAGE NUMBERS
A: Pre-Foundation
(3 Point Problems)
1 to 48
B: Foundation
(4 Point Problems)
49 to 119
C: Exploration
(5 Point Problems)
120 to 164
INTERNATIONAL OLYMPIAD ACADEMY
Our education system has, for long, focused only on the core concepts that science and
mathematics can offer. This has spurred the need for an external platform that provides the
opportunity to apply these concepts and build a deep understanding of the core concepts
learned in school. Olympiads are competitive examinations conducted nationally and
internationally and have proved to be such platforms that allow students to test their mettle in
different subjects.
These exams focus on the application of concepts learned in the
classroom. The exams are designed in such a way that the students are
forced to apply multiple concepts simultaneously to arrive at the answers.
This not only sharpens their skill, it also builds in them the deep
appreciation of the subject.
We, at International Olympiad Academy, recognize the need for such
periodic tests that pushes the students out of their comfort zone and
helps them build them their logical reasoning and analytical abilities.
Our Olympiads, picks students from all across the globe to compete
against their peer groups. We aim to foster a healthy environment
which is competitive yet enriching.
We also provide mentoring programs that guide the students throughout the
process of preparing for such exams. Our mentors are highly qualified
professionals who have been a part of the education system for over twenty
years. Their extensive experience allows them to assess the potential of students quickly
and customize the program to mentor students with different capabilities in a manner that
suits each student exclusively. Currently in collaboration with HIPPO International Language
Competition, International Science Olympiad and Mathematical Kangaroo (also known as
International Mathematical Kangaroo, or Kangourou sans frontières in French), IOA aims to
identify young geniuses and bring out the best in them.
I O A
CSAR Learning Solutions Pvt. Ltd.
Prepare for World's Most Celebrated Contests!
JOIN OUR ONLINE
PREPARATORY CLASSES
For
MATH KANGAROO
COMPETITION
SINGAPORE & ASIAN
SCHOOLS MATH
OLYMPIAD
VANDA
INTERNATIONAL
SCIENCE
COMPETITION
HIPPO ENGLISH
OLYMPIAD
PROGRAM HIGHLIGHTS:
Structured Teaching of Fundamental Concepts by Mentors of International Repute
Worksheets on Each Topic
Test Based Analysis for Topics
Safe and Secured Online Platform for Seamless Delivery
Previous Year Exam Papers
Doubt Clearing Sessions
Mock Tests on Full Course
Medium of Teaching: English
Secured Payment Gateway for All International/National Payments
Diagnostic Assessment
ENROLL NOW
HOW TO REGISTER:
For Registration through School: Please Contact Your School Administration
For Individual Registration please visit: www.internationalolympiadacademy.com
MATH KANGAROO WORK BOOK
1.
What is 2005 × 100 + 2005?
(A) 2005002005 (B) 20052005
(C) 2007005
(D) 202505
2.
Ali and Amna have 10 sweets, but Amna has 2 more than Ali. How many
sweets does Amna have?
(A) 8
(B) 7
(C) 6
(D) 4
3.
In the diagram any of the eight kangaroos can jump to
another square. What is the least number of kangaroos
that must jump so that each row and each column has
exactly two kangaroos?
(A) 1
(B) 2
(C) 3
(D) 4
4.
Ali lives with his father, mother, brother and also one dog, two cats, two parrots
and four goldfish. How many legs do they have altogether?
(A) 13
(B) 28
(C) 24
(D) 22
5.
A butterfly sat down on my correctly solved exercise. What number is the
butterfly covering?
2005 − 205 = 25+
(A) 1825
(B) 2185
(C) 1775
(D) 1800
6.
The diagram shows a cube with sides of length 12 cm. An ant is
walking across the cube’s surface from A to B on the route
shown. How far does it walk?
(A) 40 cm
(B) 48 cm
(C) 60 cm
(D) It is impossible to determine
7.
Saima cut a sheet of paper into 10 pieces. Then she took one of the pieces and
cut it into 10 pieces also. She repeated this twice more. How many pieces of
paper did she have in the end?
(A) 27
(B) 30
(C) 37
(D) 40
1
Grade – 5 & 6
MATH KANGAROO WORK BOOK
8.
Aisha chose a whole number and multiplied it by 3. Which of the following
numbers could not be her answer?
(A) 103
(B) 105
(C) 204
(D) 444
9.
3 × 2006 = 2005 + 2007 + . Find the missing number.
(A) 2005
(B) 2006
(C) 2007
(D) 2008
10. Six numbers are written on the cards,
as shown. What is the largest number
you can form with the given cards by
placing them in arrow?
(A) 9 876 543 210
(B) 4 130 975 682
(C) 7 568 413 092
(D) 7 685 413 092
41
5
309
7
68
2
11. Four people can sit at a square table. For the school party the students put
together 10 square tables in order to make one long table. How many people
could sit at this long table?
(A) 20
(B) 22
(C) 30
(D) 32
12. Choose the picture where the angle between the hands of a watch is 1500.
(A)
(B)
(C)
(D)
13. On the left side of Main Street one will find all odd house-numbers from 1 to 39.
On the right side the house-numbers are all the even numbers from 2 to 34.
How many houses are there on the Main Street?
(A) 35
(B) 36
(C) 37
(D) 38
14. With how many ways one can get a number 2006 while
following the arrows on the figure?
(A) 6
(B) 7
(C) 8
(D) 9
15. One half of one hundredth is
(A) 0.005
(B) 0.05
(C) 0.02
(D) 0.5
2
Grade – 5 & 6
MATH KANGAROO WORK BOOK
16. The cube in the figure has one of the following nets:
(A)
(B)
(C)
(D)
17. Asia walks from the left to the right and puts the numbers in her basket. Which
of the following numbers can be in her basket?
(A) 1, 2 and 4
(B) 2, 3 and 4
(C) 2, 3 and 5 (D) 1, 5 and 6
18. Which piece fits together with the given one to form a rectangle?
(A)
(B)
(C)
(D)
19. A kangaroo takes 6 seconds for every 4 jumps. How long does it take her to do
10 jumps?
(A) 15
(B)12
(C) 10
(D) 18
20. 2007÷ (2 + 0 + 0 + 7) − 2 × 0 × 0 × 7 = ?
(A) 9
(B) 214
(C) 223
(D) 2007
21. Usman, who is older than Ali by 1 year minus 1 day, was born on January 1,
2002. What is the date of Ali’s birth?
(A) January 2, 2003
(B) January 2, 2001
(C) December 31, 2000
(D) December 31, 2002
3
Grade – 5 & 6
MATH KANGAROO WORK BOOK
22. The Carpenter’s shop has two machines A and B. A is a “printing machine” and
B is a “turning machine”. What’s the right sequence to obtain
?
(A) BBA
(B) ABB
(C) BAB
starting from
(D) BA
23. If you cut a 1 meter cube into 1 decimeter cubes and put one on the other, what
height this structure will have?
(A) 100 m
(B) 1 km
(C) 10 km
(D) 10 m
24. Uzma cut a paper in the shape of a square with perimeter 20 cm into two
rectangles. The perimeter of one rectangle was 16 cm. What was the perimeter
of the second rectangle?
(A) 8 cm
(B) 9 cm
(C) 12 cm
(D) 14 cm
25. Which is the smallest?
(A) 2 + 0 + 0 +8
(C) 2 x 0 x 0 x 8
26. By what
×
(A) 2
(B) 200/8
(D) 8 + 0 + 0 – 2
can be replaced to have:
= 2 × 2 × 3 × 3?
(B) 3
(C) 2 × 3
(D) 2 × 2
27. Javed likes to multiply by 3, Parvaiz likes to add 2, and Naveed likes to subtract
1. In what order should they perform their favorite actions to convert 3 into 14?
(A) JPN
(B) PJN
(C) JNP
(D) NJP
28. To make the equality 1 + 1♣1 – 2 = 100 correct, we should replace ♣ with
(A) +
(B) –
(C) 0
(D) 1
29. Numbers 2, 3, 4 and one more number are written in the cells of 2 × 2 table. It
is known that the sum of the numbers in the first row is equal to 9, and the sum
of the numbers in the second row is equal to 6. The unknown number is
(A) 5
(B) 6
(C) 7
(D) 8
30. Before the snowball fight, Ali had prepared a few snowballs. During the fight, he
made another 17 snowballs and threw 21 snowballs at the other boys. After the
fight, he had 15 snowballs left. How many snowballs had Ali prepared before
the fight?
(A) 53
(B) 33
(C) 23
(D) 19
4
Grade – 5 & 6
MATH KANGAROO WORK BOOK
31. This is a small piece of the multiplication table.
4 3
5 20 15
7 28 21
And this is an other one, in which, unfortunately, some numbers are missing.
35 63
30 ?
What is the number in the square with the question mark?
(A) 54
(B) 56
(C) 65
(D) 36
32. In a shop selling toys a four-floor black and white “brick flower” is displayed.
(picture 1). Each floor is made of bricks of the same colour. On picture 2, the
flower is shown from the top. How many white bricks were used to make the
flower?
(A) 9
(B) 10
(C) 12
(D) 14
33. Knowing that ▲ + ▲ + 6 = ▲ + ▲ + ▲ + ▲, which number is hidden by ▲?
(A) 2
(B) 3
(C) 4
(D) 6
34. The number 4 is next to two mirrors so it reflects twice as shown. When the
same thing happens to number 5, what do we get instead for the question
mark?
(A)
(B)
(C)
(D)
5
Grade – 5 & 6
MATH KANGAROO WORK BOOK
35. Kalim goes directly from zoo to School. He counts each flower on the way.
Which zoo school of the following number cannot be his result?
(A) 9
(B) 10
(C) 11
(D) 12
36. A ladder has 21 stairs. Nadeem and Mahmood are counting stairs; one – from
bottom to top, another – from top to bottom. They met on a stair that was called
the 10th by Nadeem. What number will Mahmood give to this stair?
(A) 13
(B) 11
(C) 12
(D) 10
37. Adil has connected all the upper points to all the lower
points. How many lines Adil has drawn?
(A) 20
(B) 25
(C) 30
(D) 35
38. A fly has 6 legs, while a spider has 8 legs. Together, 2 flies and 3 spiders have
as many legs as 10 birds and
(A) 3 cats
(B) 4 cats
(C) 5 cats
(D) 6 cats
39. There are seven bars in the box. It is possible to slide the bars
in the box so there will be space for one more bar. At least how
many bars have to be moved?
(A) 1
(B) 2
(C) 3
(D) 4
40. A square sheet of paper has grey upper side and white
lower side.
Sadia has divided it in nine little squares.
Along which does she have to cut?
(A) 1, 3, 5 and 7;
(B) 2, 4, 6 and 8;
(C) 2, 3, 5 and 6;
(D) 3, 4, 6 and 7;
6
Grade – 5 & 6
MATH KANGAROO WORK BOOK
41. Basil wants to paint the word KANGAROO. He paints one letter each day. He
starts on Wednesday. On what day will he paint the last letter?
(A) Monday
(B) Tuesday
(D) Thursday
(E) Friday
(C) Wednesday
42. A motorcyclist rode a distance of 28 km in 30 minutes at a constant speed.
At what speed did he drive, in km per hour?
(A) 28
(B) 36
(C) 56
(D) 58
(E) 62
43. A square of paper is cut into two pieces using a single straight cut.
Which of the following cannot be the shape of either piece?
(A) A square triangle
(B) A rectangle
(C) A right-angled triangle
(D) A pentagon
(E) An isosceles triangle
44. Hamster Fridolin sets out for the Land of Milk and Honey. His way to the
legendary Land passes through a system of tunnels. There are 16 pumpkin
seeds spread through the tunnels, as shown in the picture.
What is the highest number of pumpkin seeds Fridolin can collect if he is not
allowed to visit any junction more than once?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
45. In Crazytown, all the houses on the right side of Number Street have odd
numbers. However, Crazytowners don't use numbers containing the digit 3,
though they use every other number. The first house on the right side of the
street is numbered 1, and the houses are numbered in increasing order. What
is the number of the fifteenth house on the right side of the street?
(A) 29
(B) 41
(C) 43
(D) 45
(E) 47
7
Grade – 5 & 6
MATH KANGAROO WORK BOOK
46. The picture shows a partially built cuboid.
Which of the following pieces will complete the cuboid?
(A)
(B)
(C)
(D)
(E)
47. We pour 1000 litres of water into the top of the pipe work shown in the picture.
Every time a pipe forks, the water splits into two equal parts. How many litres of
water will reach container Y?
(A) 500
(B) 660
(C) 666.67
(D) 750
(E) 800
48. The date 01-03-05 (1 March 2005) consists of three consecutive odd numbers
in increasing order. This is the first date with this feature in the 21st century.
Including 01-03-05, how many dates in the 21st century, when expressed in the
form dd-mm-yy, have this feature?
(A) 5
(B) 6
(C) 16
(D) 13
(E) 8
49. The picture shows four cardboard pieces.
All four pieces are put together without gaps or overlaps to form various
shapes. Which of the following shapes cannot be made in this way?
(A)
(B)
(C)
(D)
(E)
8
Grade – 5 & 6
MATH KANGAROO WORK BOOK
50. When Liza the cat just lazes around, she drinks 60 ml of milk per day. But each
day that she catches mice, she drinks a third more milk. In the last two weeks
she has been catching mice every other day. How much milk did she drink in
the last two weeks?
(A) 840 ml
(B) 980 ml
(C) 1050 ml
(D) 1120 ml
(E) 1960 ml
51. Basil wants to paint the slogan VIVAT KANGAROO on a wall. He wants
different letters to be coloured differently, and the same letters to be coloured
identically. How many colours will he need?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 13
52. A blackboard is 6 m wide. The width of the middle part is 3 m. The two other
parts have equal width. How wide is the right-hand part?
(A) 1 m
(B) 1,25 m
(C) 1,5 m
(D) 1,75 m
(E) 2 m
53. Sally can put 4 coins in a square built with 4 matches (see picture). At least how
many matches will she need in order to build a square containing 16 coins that
do not overlap?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 16
54. In a plane, the rows are numbered from 1 to 25, but there is no row number 13.
Row number 15 has only 4 passenger seats, all the rest have 6 passenger
seats. How many seats for passengers are there in the plane?
(A) 120
(B) 138
(C) 142
(D) 144
(E) 150
55. When it is 4 o’clock in the afternoon in London, it is 5 o’clock in the afternoon in
Madrid and it is 8 o’clock in the morning on the same day in San Francisco. Ann
went to bed in San Francisco at 9 o’clock yesterday evening. What was the time
in Madrid at that moment?
(A) 6 o’clock yesterday morning
(B) 6 o’clock yesterday evening
(C) 12 o’clock yesterday afternoon
(D) 12 o’clock midnight
(E) 6 o’clock this morning
9
Grade – 5 & 6
MATH KANGAROO WORK BOOK
56. The picture shows a pattern of hexagons. We draw a new pattern by
connecting all the midpoints of any neighbouring hexagons. What pattern do we
get?
(A)
(B)
(C)
(D)
(E)
57. To the number 6 we add 3. Then we multiply the result by 2 and then we add 1.
Then the final result will be the same as the result of the computation
(A) (6 + 3 • 2) + 1
(B) 6 + 3 • 2 + 1
(D) (6 + 3) • 2 + 1
(E) 6 + 3 • (2 + 1)
(C) (6 + 3) • (2 + 1)
58. The upper coin is rotated without slipping around the fixed lower coin to a
position shown on the picture. Which is the resulting relative position of
kangaroos?
(A)
(B)
(C)
(D)
(E) depends on the rotation speed
10
Grade – 5 & 6
MATH KANGAROO WORK BOOK
59. One balloon can lift a basket containing items weighing at most 80 kg. Two
such balloons can lift the same basket containing items weighing at most 180
kg. What is the weight of the basket?
(A) 10 kg
(B) 20 kg
(C) 30 kg
(D) 40 kg
(E) 50 kg
60. Vivien and Mike were given some apples and pears by their grandmother. They
had 25 pieces of fruit in their basket altogether. On the way home Vivien ate 1
apple and 3 pears, and Mike ate 3 apples and 2 pears. At home they found out
that they brought home the same number of pears as apples. How many pears
were they given by their grandmother?
(A) 12
(B) 13
(C) 16
(D) 20
(E) 21
61. We put 2, 0, 1, 3 into an adding machine, as shown. What is the result in the
box with the question mark?
2
0
1
3
+
+
?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
62. Nathalie wanted to build the same cube as Diana had (picture 1). However,
Nathalie ran out of small cubes and built only the part of the cube, as you can
see in the picture 2. How many small cubes must be added to fig. 2 to form fig.
1?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
11
Grade – 5 & 6
MATH KANGAROO WORK BOOK
63. Find the distance which Mara covers to get to her friend Bunica.
(A) 300 m
(B) 400 m
(C) 800 m
(D) 1 km
(E) 700 m
64. Nick is learning to drive. He knows how to turn right but cannot turn left. What is
the smallest number of turns he must make in order to get from to , starting
in the direction of the arrow?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 10
65. The sum of the ages of Ann, Bob and Chris is 31 years. What will the sum of
their ages be in three years time?
(A) 32
(B) 34
(C) 35
(D) 37
(E) 40
66. What digit must be placed in all three boxes ⧠⧠ · ⧠ = 176, in order to make the
multiplication work?
(A) 6
(B) 4
(C) 7
(D) 9
(E) 8
67. Michael has to take a pill every 15 minutes. He took the first pill at 11:05. What
time did he take the fourth pill?
(A) 11:40
(B) 11:50
(C) 11:55
(D) 12:00
(E) 12:05
68. By drawing two circles, Mike obtained a figure, which consists of three regions
(see picture).At most how many regions could he obtain by drawing two
squares?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
12
Grade – 5 & 6
MATH KANGAROO WORK BOOK
69. The number 36 has the property that it is divisible by the digit in the unit
position, because 36 is divisible by 6. The number 38 does not have this
property. How many numbers between 20 and 30 have this property?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
70. Ann has a lot of pieces like the one in the picture.
She tries to put
as many as possible in the 4 by 5 rectangle.
The pieces
may not overlap each other. What is the largest possible number of pieces Ann
can put in the rectangle?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
71. Arno spelled the word KANGAROO with cards showing one letter at a time.
Unfortunately some cards were tipped. Tipping back twice he can correct the
letter K and tipping once he can correct the A - see the figures. How many
times does he need to tilt for all of the letters to be correct?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
72. A cake weights 900 g. Paul cuts it in 4 pieces. The biggest piece is as heavy as
the 3 others weight altogether. What’s the weight of the biggest piece?
(A) 250 g
(B) 300 g
(C) 400 g
(D) 450 g
(E) 600 g
73. Two great rings, one grey, one white, are linked in each other. Peter, in front of
the rings, sees the rings as in the picture. Paul is behind the rings. What does
he see?
(A)
(B)
(C)
(D)
(E)
13
Grade – 5 & 6
MATH KANGAROO WORK BOOK
74. In the following addition, some of the digits have been replaced by stars.
12
13
14
−−− −−−−
309
What is the sum of the missing digits?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 10
75. What is the difference between the smallest 5-digit number and the largest 4digit number?
(A) 1
(B) 10
(C) 1111
(D) 9000
(E) 9900
76. A square of perimeter 48 cm is cut into 2 pieces to make a rectangle (see
picture).
(A) 24 cm
What is the perimeter of the rectangle?
(B) 30 cm
(C) 48 cm
(D) 60 cm
(E) 72 cm
77. Katrin has 38 matches. She builds a triangle and a square, using all the
matches. Each side of the triangle consists of 6 matches. How many matches
are in each side of the square?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
78. The pearl necklace in the picture contains dark grey pearls and shiny white
pearls.
Arno wants to have 5 of the dark grey pearls. He can only take pearls from
either end of the necklace, and so he has to take some of the white pearls also.
What is the smallest number of white pearls Arno has to take?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
79. Harry participated in a broom flight contest which consisted of 5 laps. The times
when Harry passed the starting point are shown in the picture. Which lap took
the shortest time?
(A) the first
(B) the second
(C) the third
(D) the fourth
(E) the fifth
14
Grade – 5 & 6
MATH KANGAROO WORK BOOK
80. Ben’s digital watch is not working properly. The three horizontal lines in the
rightmost digit on the watch are not displayed. Ben is looking at his watch and
the time has just changed from the one shown on the left to the one shown on
the right. What time is it now?
(A) 12:40
(B) 12:42
(C) 12:44
(D) 12:47
(C)
(D)
(E) 12:49
81. Which figure has one half shaded?
(A)
(B)
(E)
82. My umbrella has KANGAROO written on top. It is shown in the picture. Which
of the following pictures does not show my umbrella?
(A)
(B)
(C)
(D)
(E)
83. Sam painted the 9 squares with the colours black, white and grey as shown. At
least how many squares does he need to repaint so that no two squares with a
common side have the same colour?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
84. There are 10 ducks. 5 of these ducks lay an egg every day. The other 5 lay an
egg every second day. How many eggs do the 10 ducks lay in a period of 10
days?
(A) 75
(B) 60
(C) 50
(D) 25
(E) 10
15
Grade – 5 & 6
MATH KANGAROO WORK BOOK
85. The figure shows a board where each small square has an area of 4 cm2. What
GVVF is the length of the thick black line?
(A) 16 cm
(B) 18 cm
(C) 20 cm
(D) 21 cm
(E) 23 cm
(C)
(D)
(E)
(C) 4 kg
(D) 5 kg
(E) 6 kg
86. Which of the following fractions is smaller than 2?
(A)
(B)
87.
How much does Dita weigh?
(A) 2 kg
(B) 3 kg
88. Peter looks through a magnifying glass at different parts of a drawing on a wall.
Which is the picture that he cannot see?
(A)
(B)
(C)
(D)
(E)
89. Each plant in John's garden has either 5 leaves, or 2 leaves and 1 flower. In
total, the plants have 6 flowers and 32 leaves. How many plants are there?
(A) 10
(B) 12
(C) 13
(D) 15
(E) 16
16
Grade – 5 & 6
MATH KANGAROO WORK BOOK
90. Alva has 4 paper strips of the same length. She glues 2 of them together with a
10 cm overlap, and gets a strip 50 cm long. With the other two paper strips, she
wants to make a strip 56 cm long. How long should the overlap be?
(A) 4 cm
(B) 6 cm
(C) 8 cm
(D) 10 cm
(E) 12 cm
91. Which of the following traffic signs has the largest number of lines symmetry?
(A)
(B)
(C)
(D)
(E)
92. Milk cuts a pizza into quarters. Then he cuts every quarter into thirds. What part
of the whole pizza is one piece?
(A) a third
(B) a quarter
(C) a seventh (D) an eighth
(E) a twelfth
93. A thread of length 10 cm is folded into equal parts as shown in the figure. The
thread is cut at the two marked places. What are the lengths of the three parts?
(A) 2 cm, 3cm, 5cm
(C) 1cm, 4 cm, 5cm
(E) 3 cm, 3 cm, 4 cm
(B) 2 cm, 2 cm, 6cm
(D) 1 cm, 3 cm, 6 cm
94. On Lisa’s refrigerator 8 strong magnets hold some postcards. What is the
largest number of magnets that she could remove so that no postcard falls to
the ground?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
17
Grade – 5 & 6
MATH KANGAROO WORK BOOK
95. Cathy draws a square with side length 10 cm. She joins the midpoints of the
sides to make a smaller square. What is the area of the smaller square?
10 cm
(A) 10 cm2
(B) 20 cm2
(C) 25 cm2
(D) 40 cm2
(E) 50 cm2
96. Alice’s mother wants to see a knife on the right side of each plate and a fork on
the left side. How many interchanges of a fork does Alice need to make in order
to please her mother?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
97. A centipede has 25 pairs of shoes. It needs one shoe for each of its 100 feet.
How many more shoes does the centipede need to buy?
(A) 15
(B) 20
(C) 35
(D) 50
(E) 75
98. Tom and john build rectangular boxes using the same number of identical
cubes. Tom’s box looks like this:
The first level of john’s box looks like this:
How many levels will john’s box have?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
99. On the left side of the room, Bea and Pia are sleeping with their heads on their
pillows facing each other. On the right side of the room. Mary and Karen are
sleeping with their heads heads on their pillows with their backs to each other.
How many girls are sleeping with their right ear on their pillow?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
18
Grade – 5 & 6
MATH KANGAROO WORK BOOK
100. The piece of paper shown is folded along the dotted lines to make an open box.
The box is put on a table with top open. Which face is at the bottom of the
box?
(A) A
(B) B
(C) C
(D) D
(E) E
101. 2002 is a number that stays the same when read backwards as when read
forwards. Which of the following numbers does not have this property?
(A) 1991
(B) 2323
(C) 2112
(D) 2222
(E) 191
102. Far away we see the skyline of a castle.
Which of the pieces cannot belong to the skyline?
(A)
(B)
(C)
(D)
(E)
103. The kangaroo's dad and mom have 3 little kangaroo girls. Each girl has two
kangaroo brothers. How many members are there in the kangaroo family?
(A) 11
(B) 9
(C) 8
(D) 7
(E) 5
104. What numbers should be in the boxes instead of the?-signs?
(A) 2 and 14
(E) 4 and 30
(B) 2 and 30
(C) 3 and 221 (D) 4 and 14
105. On the next day after my birthday this year, it would be correct to say "The day
after tomorrow is a Thursday." On which day is my birthday?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
(E) Friday
19
Grade – 5 & 6
MATH KANGAROO WORK BOOK
106. On which of the following necklaces are the dark hearts two thirds of all hearts?
(A)
(B)
(C)
(D)
(E)
107. How many angles with different degree measures can be seen in the picture?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 11
108. The area of a rectangle equals 1. What is the area of the triangle, which is cut
off from the rectangle by the line connecting the midpoints of the two adjacent
sides?
(A) 1/3
(B) 1/4
(C) 2/5
(D) 3/8
(E) 1/8
109. Which of the following is the greatest number?
(A) 2 + 0 + 0 + 3
(B) 2 x 0 x 0 x 3
(D) 20 x 0 x 3
(E) (2 x 0) + (0 x 3)
(C) (2 +0) x (0 + 3)
110. Sophie draws kangaroos: a blue one, then a green, then a red, then a black, a
blue, a green, a red, a black, and so on…What colour is the 29th kangaroo?
(A) blue
(B) green
(C) red
(D) black
(E) it’s impossible to know
111. How many integers can one find in the interval from 2.09 to 15.3?
(A) 13
(B) 14
(C) 11
(D) 12
(E) infinitely many
112. Which is the smallest positive integer divisible by 2, 3, and 4?
(A) 1
(B) 6
(C) 12
(D) 24
(E) 36
113. The sum of the numbers in each ring should be 55. What is the value of A?
(A) 9
(B) 10
(C) 13
(D) 16
(E) 17
20
Grade – 5 & 6
MATH KANGAROO WORK BOOK
114. Tom has 9 bills of 100 euro, 9 bills of 10 euro, and 10 coins of 1 euro. How
many euro does he have in total?
(A) 1000
(B) 991
(C) 9910
(D) 9901
(E) 99010
115. Betty likes calculating the sum of the digits that she sees on her digital clock (for
instance, if the clock shows 21:17, then Betty gets 11). What is the biggest sum
she can get if the clock is a 24-hour clock?
(A) 24
(B) 36
(C) 19
(D) 25
(E) Another answer
116. In the picture, AC=10m, BD=15m, AD=22m. Find BC.
(A) 1m;
(B) 2m;
117. How much is 1000 – 100 + 10 - 1?
(A) 111
(B) 900
(C) 3m;
(D) 4m;
(E) 5m;
(C) 909
(D) 990
(E) 999
118. Caroline wants to write the numbers 1, 2, 3, 4 in the square
4 × 4 in such a way that every row and every column has
each number. You see how she started. What number must
be put in the place of ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) Impossible to determine
119. The product (10 × 100) × (20 × 80) is equal to
(A) 20,000 × 80,000
(B) 2000 × 8000
(C) 2000 × 80,000
(D) 20,000 × 8000
120. How many hours is 360,000 seconds?
(A) 3
(B) 6
(C) 8.5
(E) More than 90
121. If 20042003 is divided by 2004, the remainder is
(A) 0
(B) 1
(C) 2
(E) 2000 × 800
(D) 10
(D) 3
(E) 2003
122. Which of the rectangles A to E can be covered by the pattern on
the right-hand side in such a way that the result is a totally black
rectangle?
(A)
(B)
(D)
(E)
(C)
21
Grade – 5 & 6
MATH KANGAROO WORK BOOK
123. Which of the following is not a factor of 2004?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
124. The three members of a rabbit family have altogether eaten 73 carrots. The
father has eaten five carrots more than the mother. The son Bunny has eaten
12 carrots. How many carrots has the mother eaten?
(A) 27
(B) 28
(C) 31
(D) 33
(E) 56
125. Nine bus stops are equally spaced along a bus route. The distance from the
first stop to the third stop is 600 m. How many meters is it from the first to the
last?
(A) 1800
(B) 2100
(C) 2400
(D) 2700
(E) 3000
126. The sum of the digits of a ten-digit number is equal to 9. What is the product of
the digits of this number?
(A) 0
(B) 1
(C) 45
(D) 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2
(E) Depends of the given number
127. Carrie has started to draw a cat.
She finishes her drawing. Which of
the figures below can be her drawing?
(A)
(B)
(C)
(D)
(E)
128. The Mayan people wrote numbers with dots and bars. A dot is written for 1 and
a bar for 5. How did they write 17?
(A)
(B)
(C)
(D)
(E)
129. A digital clock shows the time 20:19. What will the clock show the next time it
uses the same digits?
(A)
(B)
(C)
(D)
(E)
22
Grade – 5 & 6
MATH KANGAROO WORK BOOK
130. There are 14 girls and 12 boys in a kindergarten. If half of the children go for a
walk, at least how many of them are girls?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
131. The sum of the dots on opposite faces of an ordinary dice is equal to 7. Which
of the following shows the ordinary one?
(A)
(B)
(C)
(D)
(E)
132. Which of the following geometric figures is not in this design?
(A)
Triangle
(B)
(C)
Hexagon
(D)
(E)
Dodecagon
133. Laura wants to colour a 2× 2 square
possibilities are there?
(A) 5
(B) 6
Square
Octagon
of this figure
(C) 7
(D) 8
. How many
(E) 9
134. The 6 smallest odd natural numbers are written on the faces of a dice. Toni
throws it three times and adds the results. Which of the following numbers
cannot be the sum?
(A) 21
(B) 3
(C) 20
(D) 19
(E) 29
135. The sum of the ages of a group of kangaroos is 36 years. In two years time the
sum of their ages will be 60 years. How many kangaroos are in that group?
(A) 10
(B) 12
(C) 15
(D) 20
(E) 24
23
Grade – 5 & 6
MATH KANGAROO WORK BOOK
136. Michael paints the following buildings. Which one needs the most paint?
(A)
(B)
(D)
(E)
(C)
137. Susanna’s cat Tigger is 6 years old. Her sister has two cats- Oscar and Max.
Max is one year younger than Oscar and Oscar is one year older than Tigger.
How old are the three cats in total?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
138. Rubi and Yann become a couple at Rubi’s sweet 16 birthday party. How old will
Rubi be when she can say for the first time: “I am with Yann for more than half
of my life”?
(A) 20
(B) 24
(C) 30
(D) 32
(E) 36
139. Grand mother has a basket with apples. All her grandchildren come to visit her
and they share the apples. All children get the same number of apples, and
they get more than one each. How many apples could it have been in the
basket?
(A) 17
(B) 29
(C) 39
(D) 43
(E) 53
140. Which of the geometric figures is lacking in this design?
(A)
(B)
(C)
(D)
(E)
141. Aziz likes to encode different numbers using Russian postal code template and
simplest mathematical operations. For example, he can write 2 like this
He decided to encode the year of first Kangaroo contest. He wrote following
expressions
24
Grade – 5 & 6
MATH KANGAROO WORK BOOK
Identify the year when Kangaroo contest was launched.
(A) 1981
(B) 1987
(C) 1990
(D) 1991
(E) 1994
142. What is the smallest positive value that can be obtained if the signs +, – and ×
are placed in some order between the digits of the number 2019? (each sign is
used exactly once.)
(A) 12
(B) 11
(C) 10
(D) 9
(E) 8
143. Five boys belongs to the chess club: Luke, Michael, Andrew, Pete and Tom.
No two of them are the same age, all the while, and Michael is older than Pete,
Tom is older than Luke, Pete isn’t the youngest, Luke is younger than Andrew.
Which boy is the youngest?
(A) Luke
(B) Michael
(C) Andrew
(D) Tom
(E) Cannot be determined with the information given.
144. Oswald counted how many Mondays, Tuesdays etc. are in each month. He said
this about one of the months’: “This month has the same number of each dayin-a-week.”
Which month could he be talking about?
(A) January
(B) February
(C) March
(D) April
(E) May
145. On the 2nd floor of a castle in Castleville is a corridor with five rooms:
gentleman’s room, playroom, library and ladies room. We know that library
neighbours the playroom, but not the ladies room, dinning room neighbours
both the gentleman’s room and ladies room, ladies room isn’t at the end of the
corridor. Which room is in the centre of the corridor?
(A) library
(C) gentleman’s room
(B) ladies room
(D) dining room
(E) Playroom
146. Milly thought to herself: “the day yesterday and the day after tomorrow are both
work days.” Which day of the week could it be today?
(A) Sunday
(D) Thursday
(B) Monday
(E) Friday
(C) Tuesday
147. There were 160 Kangaroos in a Kangaroo camp. One day three fifth of them
competed in a bag jump and the other learned how to cook the chef’s specialty.
How many Kangaroos were cooking?
(A) 32
(B) 64
(C) 96
(D) 100
(E) 128
25
Grade – 5 & 6
MATH KANGAROO WORK BOOK
148. A jumping pit was built on the school yard, which has a rectangular footprint
with dimensions of 6m and 2m. 30cm high layer of sand was poured in. How
many cubic meters of sand is in the pit?
(A) 2.4 m3
(B) 3.6 m3
(C) 12.3 m3
(D) 24 m3
(E) 36 m3
149. Three race horse were resting in a stable when a couple of cats sneaked in,
and by a chance there was also a sparrow conference happening there at the
same time. A breeder counted 24 animal heads and 64 animal legs in the
stable. How many cats sneaked into the stable?
(A) 13
(B) 8
(C) 7
(D) 6
(E) 5
150. We have to put in the white cells of the board cards so that in each of two row
and in each of two columns (each one with five white cells), a properly written
operation appears. There are already six cards placed. Which of the ten cards
at the right of figure (the three missing equal sign, two sum sign, two product
sign and three cards with a number) will be placed in the cell indicated with the
question marks?
(A) 4
(B) 9
(C) 16
(E) It is impossible to get what is requested.
(D) Any of the three numbers.
151. You can see a numerical puzzle. You have to deduce how it is built. Which
piece should be placed at the center of the figure?
(A)
(B)
(C)
(D)
(E)
26
Grade – 5 & 6
MATH KANGAROO WORK BOOK
152. In an orchard the trees are in a square grid. On the boundary there are 24
trees. The total number of trees is:
(A) 16
(B) 25
(C) 36
(D) 49
(E) 64
153. Edda the turtle has many eggs in her nest at a sandy beach. One day, Jack
lizard found Edda’s nest and ate 20 eggs. Each day after that, he ate 5 eggs
less than in his previous visit, until the nest was emptied. How many eggs did
Edda have in her nest?
(A) 35
(B) 50
(C) 15
(D) 65
(E) 20
154. The 20 houses on my street are numbered as in the pictured below. In front of
each house numbered with an odd number there is a house numbered with an
even number.
One day, the house with number 8 was demolished and the other houses on
that side of street were renumbered with consecutive even numbers.
What is the current number of the house situated in front of the house with
number 15?
(A) 18
(B) 16
(C) 14
(D) 12
(E) 10
155. In a flower shop there are many bouquets of red roses at the price of 2 and 5
dollars, and only one at the price of 3 dollar. John had 14 dollars and spent all
of them to buy 4 bouquets of red roses. How many bouquets of 2 dollars did he
buy?
(A) none
(B) 1
(C) 2
(D) 3
(E) 4
156. Between John and his older brother Paul there an age different of 8 years.
Knowing that Paul is 11 years older than Mary and John is 3 years younger
than Tom, find out age different between Tom and Mary.
(A) One year
(B) 6 years
(C) 17years
(E) Tom and Mary are the same age
(D) 4 years
27
Grade – 5 & 6
MATH KANGAROO WORK BOOK
157. How many different ropes can you see in the next picture?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
(C) 2 x 3
(D) 2 x 2
(E) 3 x 3
158. A x A = 2 x 2 x 3 x 3. What is A?
(A) 2
(B) 3
159. When you multiply by 5 and then by 7, you multiply by :
(A) 12
(B) 35
(E) it depends on the initial factor
(C) 57
(D) another number
(C) 409
(D) 419
160. 20 x 19 + 20 + 19 =
(A) 389
161.
(B) 399
(E) 429
On each edge of a regular hexagon of area 1 an equilateral triangle is
drawn. The result is the “star” shown in the picture. What is the area of this star
(grey + white)?
(A) 1
1
2
(B) 1
2
3
(C) 3
(D) 2
(E) 1 +
3
162. There are 12boys and 14 girls in a kindergarten. If half of them caught a cold, at
least how many of them would be girls?
(A) 3
(B) 4
(C) 1
(D) 5
(E) 2
163. Tina’s family consist of her mother, her father and her brother in addition to Tina
herself. Tina added the age of everyone in the family and the sum was 88. How
many years does it take until the sum of their ages is 100?
(A) 3 Years
(B) 4 Years
(C) 6 Years
(D) 10 years (E) 12 years
164. All the notes on the image are square and equal in size. The notes have side
length 2.
What is the area of all the notes together?
(A) 9
(B) 18
(C) 24
(D) 36
(E) 72
28
Grade – 5 & 6
MATH KANGAROO WORK BOOK
165. Which calculation has smallest result?
(A) 2 . 3 + 4 . 5
(D) 2 + 3 + 4 + 5
(B) 2 . (3 + 4) . 5
(E) 2 . (3 + 4 + 5)
(C) (2 + 3) . (4 + 5)
166. A model train needs exactly 1 minutes and 11 seconds for each round on the
course. How long does it need for six round?
(A) 6 minutes 56 seconds
(C) 7 minutes 16 seconds
(E) 7 minutes 36 seconds
(B) 7 minutes 6 seconds
(D) 7 minutes 26 seconds
167. A die is labelled with the 6 smallest odd natural numbers. Toni throws it three
times and adds the results. Which of the following numbers cannot be the sum?
(A) 21
(B) 3
(C) 20
(D) 19
(E) 29
168. Mary wrote all possible even numbers with 4 different digits taken from the
number 2019. How many numbers did Mary write?
(A) 2
(B) 4
(C) 6
(D) 10
(E) 14
169. How many edges does the two three dimensional cubes
connected a shown have?
(A) 12
(D) 32
(B)18
(E) 36
(C) 24
170. The sum of the digits of a 3- digit number is 15. And the digit in the unit’s place
is 2 greater than the hundreds digit and 4 greater than the tens digit. What
number has this property?
(A) 726
(B) 735
(C) 426
(D) 537
(E) 357
171. There’s a cake on the table. Anton takes a quarter of the cake for himself and
his friends. Brigitte then takes a third of the rest. Finally, Claudia takes half of
the rest. What proportion of the cake is left after that?
(A) nothing at all (B)
1
12
(C) 1
(D) 1
4
6
(E) 1
3
172. In Which cloud are only numbers divisible by 3?
(A)
(B)
(C)
(D)
(E)
29
Grade – 5 & 6
MATH KANGAROO WORK BOOK
173. The Sum of the ages of group of Kangaroo’s is 36 years. In two years time the
sum of their ages will be 60 years. How many are the Kangaroo’s in that group?
(A) 10
(B) 12
(C) 15
(D) 20
(E) 24
174. John has a partial copy of the schedule of his English classes: Tuesday : 16:51
; Thursday: 18:01 ; Friday : 18:36 If the schedule was done according to a
pattern, at what time will he have classes on Monday?
(A)16:06
(B) 16:16
(C)14:41
(D) 17:26
(E) 17:30
175. Carlos, Mario, Antonio, Pilar and Pedro are in a queue. The two women occupy
the second and third place. Between Antonio and pilar are Carlos and Pedro.
Carlos is between Pedro and Pilar. Who is in third place?
(A) Carlos
(B) Mario
(C) Alba
(D) Antonio
(E) Pilar
176. Four 1 x 1 squares are removed from a 5 x 5 grid as shown. Determine the
Total number of 2 x 2 squares on the grid.
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
177. When you throw three coins, regarding of the order, you can get the following
Result: face face face, face face tails, face tails tails, tails tails tails. How many
times, as a minimum, should you toss the coins to get one of the result again?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
178. The biggest possible number of consecutive composite numbers smaller than
101 is :
(A) 4
179.
(B) 5
(C) 6
(D) 7
(E) 8
(B) -1
(C) 0
(D)1
(E) 39
20  19  20  19

19  20  19  20
(A) -39
180. The given rectangle is divided into 4 smaller rectangles and the
perimeters of 3 of them are 11 cm, 16 cm and 19 cm in some
order. The perimeter of the fourth one is not the biggest nor the
smallest. Find the perimeter of the given rectangle.
(A) 27 cm
(B) 30 cm
(C) 32 cm
(D) 32 cm
(E) 35 cm
30
Grade – 5 & 6
MATH KANGAROO WORK BOOK
181. Mary wants to cover a rectangle of dimensions 2019 x 1 using tiles of
dimension 673 x 1. What is the minimal number of tiles that Mary needs?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
182. Lola the Kangaroo jumps backward each time she jumps three times forward. If
Lola wants to move 10 meters forward, how many jumps does she have to
make?
(A) 10
(B) 12
(C) 16
(D) 18
(E) 22
183. Jana has two vases square base. The first vase has a base side length of 5 cm
and a height of 40 cm. A maximum of 1 liter of water flows into it. The second
vase has a twice longer side of the base, but half the height. What maximum
water is flowing into it?
(A) half a liter
(B) 1 liter
(E) other quantities
(C) 2 liters
(D) 4 liters
184. Pedro has three rectangular blades of length a and width b. With these three
palates it forms a letter C. If the perimeter of the figure is 20 centimeters then
the length of the palate
(A) 4
(B) 3
(C) 2
(D) 1
(E) Impossible to determine
185. The value of expression 1 – (2 – (3 – (4 – 5))) is equal to
(A) 0
(B) -1
(C) -3
(D) 7
(E) 8
186. Three hedgehogs have 1000 needles. Then the number of needles of some
Two of them is not less than….
(A) 600
(B) 666
(C) 667
(D) 670
(E) 700
187. Bill and his father have birthday today. The father is exactly 5 times older than
his son. Few years ago he was 7 times older than his son. How many times will
the father be older than his son if the same number of years will pass?
(A) 6
(B) 4,5
(C) 4
(D) 3,5
(E) 3
188. Two friends seeing each other always the same days of the week: every
Saturday and every Monday. If it is known that it is not a leap year at most how
many times will they see each other in that year?
(A) 106
(B) 105
(C) 104
(D) 103
(E) 102
31
Grade – 5 & 6
MATH KANGAROO WORK BOOK
189. Both x and y are positive integers and x3  y 2 . If y <100, how many y satisfy the
equation above?
(A) 4
190.
(B) 3
(C) 2
(D) 1
(E) 0
1
1
1
1


 .......... 

1.2 2.3 3.4
2017.2018
(A) 2017/2018 (B) 2018/2017
(E) 1/2019
(C) 1/2017
(D) 1/2018
191. The sum of the divisors of 42 is
(A) 84
(B) 96
(C) 94
(D) 79
(E) 78
192. Once Tom whitewashed the fence. First, he made the fourth part of the job.
When he whitewashed one more fenceboard, it appeared that the one third part
of the job was done. How many fenceboards does the fence contain?
(A) 8;
(B) 10;
(C) 12;
(D) 7;
(E) 14;
193. Erik has 6 bricks:
Which of the boxes is possible to make with his 6 bricks?
(A)
(B)
(C)
(D)
(E)
194. A measuring tape is wound around a cylinder.
What is the measure at the question mark?
(A) 53
(B) 60
(C) 69
(D) 77
(E) 81
,
195. Which piece is not part of the puzzle?
32
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A)
(B)
(C)
(D)
(E)
196.
A number is created by starting at the cross, following the line and writing down
the digits along the line while passing.
For example the red line
shown represents the number 42685. Which of the following lines represents
the greatest number?
(A)
(B)
(C)
(D)
(E)
197. In this product, A is a digit. What is the value of A?
(A) 4
(B) 6
(C) 3
(D) 5
(E) 1
198. The trapezoid in the figure was built with equal equilateral triangles, each of
area 4. What is the area of the shaded surface?
(A) 26
(B) 104
(C) 84
(D) 90
(E) 120
33
Grade – 5 & 6
MATH KANGAROO WORK BOOK
199. Every day, baby Louise feels either ill or healthy. When she feels ill, she fills 7
diapers a day. When she feels healthy, she fills 4 diapers a day. This week
Lousise' parents refreshed 37 diapers. How many healthy days did Louise have
this week?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
200. A student added the two figure numbers on the left of the board and found 89.
How much will he find if he adds the four figure numbers on the right of the
board?
(A) 8989
(B) 8998
(E) None of the previous
(C) 9089
(D) 9889
201. Mary had a piece of paper. She folded it in half, the two pieces exactly
matching. Then she folded it again in half. She got the shape
.
Which of the shapes P, Q, R on the right could be the original piece of paper?
(A) only P
(B) only Q
(E) any of P, Q, R
(C) only R
(D) only P or Q
202. Which of the following fractions has a different value from the others?
30  70
60  70
3  700
60  70
60  70
(A)
(B)
(C)
(D)
(E)
40  50
40 100
400  5
8  500
8  50
203. The numbers from 1 to 10 were arranged in some order to make another
number. Example of such number can be this: 11,083,942,567, which is a
number made out of: 1, 10, 8, 3, 9, 4, 2, 5, 6, and 7. The numbers 1 to 10,000
were arranged in some order as well. What is the maximum number of at most
15 digits that could be 1s?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
34
Grade – 5 & 6
MATH KANGAROO WORK BOOK
204. 4x + 7 = 2x + 17, solve for x.
(A) 10
(B) 8
(C) 6
205. Calculate the square root of the number 9 + 16.
(A) 1
(B) 2
(C) 3
(D) 9
(E) 5
(D) 4
(E) 5
206. The number 5021972970 is written on a sheet, Julian wants to cut the sheet
twice, get three numbers and add them. What is the smallest sum that he can
have?
(A) 3244
(B) 3444
(C) 5172
(D) 5217
(E) 5444
207. A is a product of all integers less or equal 100 dividing by 5. How may zeros
has A in its end?
(A) 16
(B) 18
(C) 20
(D) 23
(E) 24
208. Given two positive integers with two digits AB and CD, with sum AB + CD = 86
and difference AB - CD = 62. Determine the value of the sum A + B + C + D
(A) 14
(B) 24
(C) 18
(D) 22
(E) 28
209. The Kangaroo contest is being held this year on March 18 (the third Thursday
of March). The competition schedule for the following years has been drawn up.
Which row of the table contains the error?
(A) 2021 18 March
(B) 2022 17 March
(C) 2023 16 March
(D) 2024 14 March
(E) 2025 20 March.
210. Each of the four boys A, B, C, and D either always tells the truth (truthful) or
always lies (liar). Here is a recording of the conversation between them. A says
to B: You are a liar. D says to A: You yourself are a liar. C says to D: They both,
A and B. lie. C again says to D: You are a liar yourself. Which of these boys is
truthful?
(A) B and D
(B) B and C
(C) C and D
(D) D and A (E) Nobody
211. The rectangle is divided into five squares (see figure). The side length of the
small square is 2. Find the area of the rectangle.
(A) 36
(B) 42
(C) 48
(D) 64
(E) cannot be found
212. One side of the square was increased by 4, and the other was decreased by 3.
The area of the resulting rectangle turned out to be 8 more than the area of the
original square. What will be the area of a rectangle if one side of the square is
increased by 5, and the other is reduced by 4?
(A) +8
(B) +20
(C) –6
(D) –12
(E) Does not changed
35
Grade – 5 & 6
MATH KANGAROO WORK BOOK
213. The number 210 is written twice in the next square.
How many times is the number 2021 written in the following square?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
214. Five athletes start the race at the same time. The winner finished the race in 10
seconds and any other athlete finishes the race in a time twice as long as his
immediate predecessor. How long did the race last?
(A) 3 min and 40s
(B) 2 min and 20s
(C) 3 min
(D) 2 min and 40s
(E) 5 min and 20s
215. Some nodes of a grid are numbered as in the next image. Mary has drawn a
straight line between each consecutive pair of even numbers and between the
largest and the smallest even number. Which of the following shapes could be
her drawing?
(A)
(B)
(C)
(D)
(E)
36
Grade – 5 & 6
MATH KANGAROO WORK BOOK
216. The pieces on the board move only in the directions indicated by the black
arrows. Which of these pieces can leave the board through the gate G?
(A) A
(B) B
(C) C
(D) D
(E) E
217. Which of the figures below has this shape in it?
(A)
(B)
(C)
(D)
(E)
218. 6 matches were played in a foosball tournament. Each match lasted 30 minutes
and there was a ten minute break between each match. How long did the
tournament last from the beginning of the first match until the end of the last
match?
(A) 4 h
(B) 3 h 50 min
(C) 3 h 40 min
(D) 3 h 30 min
(E) 3 h 20 min
219. They sell apples in bags weighing 2 kg in a shop. The price of 1 kg of apples is
3 euros 60 cents. Approximately how many cents does one apple cost if there
are 10 apples in the bag?
(A) 36
(B) 72
(C) 112
(D) 360
(E) 720
220. Camille has only three types of coins in her wallet: 50 cent, 1 euro and 2 euro.
All but eight coins are 2 euros, all but seven coins are 1 euro, all but nine coins
are 50 cents. How many coins does Camille have in her wallet?
(A) 12
(B) 16
(C) 22
(D) 24
(E) 48
37
Grade – 5 & 6
MATH KANGAROO WORK BOOK
221. In picture 1, the cuboid is built only from the pieces in picture 2. Two storeys are
white, two are orange. How many orange and white pieces fell off of the block if
the formation in picture 3 was formed?
(A) 7 orange, 8 white
(C) 7 orange, 6 white
(E) 6 orange, 6 white
(B) 8 orange, 7 white
(D) 6 orange, 8 white
222. From the same place in the city there are two circuit bike paths. Their total
length is 45 km 400 m. The Meadow route is 6 km 200 m shorter than Lake
route. John cycled the Meadow route twice and the Lake route once in one day.
How many meters did he cycle?
(A) 25 700 m
(B) 45 400 m
(C) 51 400 m (D) 65 000 m
(E) 90 800 m
223. Walking by the forest, Irina found the following piece
.
Then she arrived at a temple and saw the following symbol over the entrance:
How many such pieces Irina saw at the symbol?
(A) 12
(B) 17
(C) 18
(D) 20
(E) 24
2
224. Six rhombus, each of area 5 cm form a star. The tips of the star are joined to
draw an hexagon, as shown. What is the area of the hexagon?
(A) 36 cm2
Grade – 5 & 6
(B) 40 cm2
(C) 45 cm2
(D) 48 cm2
(E) 60 cm2
38
MATH KANGAROO WORK BOOK
225. Albert has a lot of marbles white and black. He wants to put 5 of them in a row.
He wants that each black marble has only white marbles as neighbors and that
the maximum number of white marbles next to each other is 3. In how many
ways can he do this?
(A) 1
(B) 2
(C) 3
(D) 4
(E) more than 4
226.
In the picture you can see the necklace of Sophie. On the table are lying some
necklaces.
Which one is the necklace of Sophie?
(A) A
(B) B
(C) C
(D) D
(E) E
227. This is a roadplan of Kangcity. Ann, living at A, wants to drive to John, living at
J. She wants to bring some cakes, so she has to go to the baker at B first. How
many km is a shortest possible route long?
(A) 8
(B) 12
(C) 13
(D) 19
(E) 25
39
Grade – 5 & 6
MATH KANGAROO WORK BOOK
228. In a flower-shop a bunch of tulips costs EUR 1,69. This week the shop has a
special offer: 3 bunches of tulips cost only EUR 5. How many eurocent
reduction do you get during this action?
(A) 0,03
(B) 0,07
(C) 3
(D) 7
(E) 10
229. When the kangaroo Roo ate a third part of all the berries on the bush and a
third of one berry, there was only one berry left on the bush. How many berries
were on the bush?
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
230. A carrot and a potato weigh 160 g. A carrot and an onion weigh 100 g. A potato
and an onion weigh 120 g. What is the weight of a carrot?
(A) 50
(B) 70
(C) 90
(D) 30
(E) 40
231. By pouring the same amount of water into two bottles of the same diameter but
different height, one of them is filled to half its height and the other is filled to a
third of its height. How much taller is one bottle relative to the other?
(A) 10%
(B) 25%
(C) 50%
(D) 75%
(E) 100%
232. Alan has five brothers. Every one of the brothers have exactly two sisters. How
many siblings are there?
(A) 7
(B) 8
(C) 10
(D) 11
(E) 12
233. Carin is going to paint the walls in her room green. The green paint is too dark
so she mixes it with white paint. She tries different mixtures. Which of the
following mixtures will have the darkest colour green?
(A) 1 part green + 3 parts white
(B) 2 parts green + 6 parts white
(C) 3 parts green+ 9 parts white
(D) 4 part green + 12 parts white
(E) They will all be equally dark
234. The jigsaw puzzle in the figure will be shaped like a rectangle when finished.
Which of these could NOT be the total number of pieces in the puzzle?
(A) 62
(B) 63
(C) 64
(D) 65
(E) 66
40
Grade – 5 & 6
MATH KANGAROO WORK BOOK
235. A square floor is tiled with large square tiles of the same size. All 9 tiles along
the two diagonals are removed in order to substitute them with new coloured
tiles. How many tiles are not along the diagonals?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
236. When you put the five puzzle pieces correctly together they form a rectangle
with a calculation. What is the result of this calculation?
(A) 37
(B) 55
(C) 127
(D) 145
(E) 244
237. The 24 students of a class want to play tag. There should be 5 times as many
runners as catchers. How many catchers are needed?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
238. If we calculate in this way: 3 * 1 = 4, 3 * 2 = 17, 4 * 2 = 32 what is equal 5 * 2?
(A) 42
(B) 57
(C) 61
(D) 62
(E) 63
239. Calculate x + y + z knowing that xy = 56, xz = 140 and yz = 40.
(A) 28
(B) 30
(C) 32
(D) 33
(E) 35
240. David draws kangaroos: a red one, then a black, then a blue, then a green, then
a yellow, a red, a black, a blue, a green, a yellow, and so on...What colour is the
27th kangaroo?
(A) green
(B) yellow
(C) red
(D) black
(E) it's impossible to know
241. How many integers can one find in the interval from 1.03 to 12.6?
(A) 10
(B) 11
(C) 12
(D) 13
(E) in
242. If 20202021 is divided by 2020, the remainder is:
(A) 0
(B) 1
(C) 2
(E) 2021
(D) 2020
243. On a rectangular strip of paper, Eve wrote a number and cut the strip into 4
parts | see drawing.
What number did Eve write?
(A) 4571
(B) 4175
Grade – 5 & 6
(C) 5471
(D) 5174
(E) 5714
41
MATH KANGAROO WORK BOOK
244. How many triangles with area 1 cm2 and vertices at the given points can be
built?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
245. In how many places in the picture are two children holding each other with their
left hands?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
246. How many of all 4-digit numbers created of digits of the number 2021 is
divisible by 4?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
247. Anna, Bill, Cecilia and Dan took turns to write consecutive multiples of 3. So
Ann wrote 3, Bill wrote 9 etc. Who wrote 43046721?
(A) Ann
(B) Bill
(C) Cecilia
(E) the given number is not a multiple of 3
(D) Dan
42
Grade – 5 & 6
MATH KANGAROO WORK BOOK
248. What is the value of A?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 9
249. Two friends celebrate their birthday the same day, and it happens that one
turns 66 and the other 77 years old this year. In how many years from now will
they celebrate their birthday with both ages being again numbers with two equal
digits?
(A) 9
(B) 10
(C) 11
(D) 12
(E) It will never happen again.
250. We have a triangle made with ten tiles. If we look closely, we can see 13
equilateral triangles of different sizes. Some examples can be seen in the
image. If we remove some tiles, we will stop seeing some of these triangles.
What is the minimum number of tiles that must be removed so that none of
them can be seen?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
251. Clara wants to draw polygons on a 3  3 grid so that the vertices are on the plot
points. He starts trying and first draws a polygon with 3 sides, then one with 4,
and so on. What will be the maximum amount of sides she can get?
(A) 5 sides
(B) 6 sides
(C) 7 sides
(D) 8 sides
(E) 9 sides
43
Grade – 5 & 6
MATH KANGAROO WORK BOOK
252. How many triangles can you see in the figure that have all three sides already
drawn?
(A) 16
(B) 20
(C) 22
(D) 28
(E) 32
253. A rectangle has area of 63 cm2. What is the area of the largest square that can
be cut of the rectangle?
(A) 25 cm2
(B) 36 cm2
(C) 49 cm2
(D) 64 cm2
(E) 81 cm2
254. Minky and Momo clean their house on Saturday. Minky's room is 45(square
meter) and it took about 30 minutes to clean. Momo's room is 60(square meter)
and it took 40 minutes to clean. Then how long will it take to clean a 180(square
meter) living room together?
(A) 50 minutes
(B) 55 minutes
(C) 60 minutes
(D) 65 minutes
(E) 70 minutes
255. What number goes in the question mark?
(A) 28
(B) 33
(C) 35
(D) 36
(E) 42
256. Hannah mows the lawn in the garden. In an hour, she mowed the lawn by half
of its width and one third of the length. Following an hour, she did the same
thing of the remaining area. After two hours of work, she found out that only 236
m2 remained to finish the whole garden. What is the area of Hannah's garden?
(A) 284 m2
(B) 324 m2
(C) 368 m2
(D) 384 m2
(E) 402 m2
257. Sally made a small square hole in the large square. Subtracting the area of the
small square from the large square was 108 cm2. What is the length of one side
of the small square?
(A) 5 cm
(B) 6 cm
(C) 6.5 cm
(D) 7 cm
(E) 7.5 cm
44
Grade – 5 & 6
MATH KANGAROO WORK BOOK
258. A dog Fluffy's age is 1/4 of a tuttle Shelly. A parrot Harley's age is 2/5 of Shelly.
What fraction is Flully's age of Harley?
(A) 1/3
(B) 3/5
(C) 4/7
(D) 3/8
(E) 5/8
259. 21 children participate in the math lesson. Children draw line segments of the
different lengths between 1 cm and 5 cm. If all the segments are joined together
one by one, the total length of all the lines cannot be equal to ...
(A) 20 cm
(B) 83 cm
(C) 60 cm
(D) 104 cm
(E) 99 cm
260. When John folds a sheet of paper once, he gets one line that separates the
sheet into 2 regions. When he folds another sheet twice, he may get 3 regions
or 4 regions, as shown in the pictures. At most, how many regions can he get if
he folds another sheet three times?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
261. Half of the children in the class attend a music club, half of them are girls (it
means that 7 girls attend a music club). Half of the children in the same class
attend a science club. Half of the children in the same class attend a sports
club. How many children attend this class?
(A) 14
(B) 21
(C) 28
(D) 35
(E) 42
262. If F = 6, K = 11 and S = 19, calculate K (S + F) :
(A) 180
(B) 200
(C) 250
(D) 275
(E) 300
263. Goat Gertruda is on a leash, which is fixed in one point between two fences
(see the picture).
What is the area she can reach?
(A)
(B)
45
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(C)
(D)
(E)
264. Which one is the last digit of the product
1 5  9  13  17  21… 2021 ?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
265. Three friends went on a hiking trip and each of them took the same amount of
water with themselves. During the trip, Regina drank half of what Jonas has
drunk and Monika has drunk twice as much as Jonas has drunk. Taken
together, three friends have drunk
water has Regina drunk?
1
1
(A)
(B)
8
7
266. Adele put square tiles
of the water they had. How much of her
(C)
1
6
(D)
1
4
(E)
1
3
in a pattern of white and black squares. She made
a patterns with two squares (a white one and a black one) from 7 tiles as shown
in the picture:
What is the biggest number of squares Adele can make from 12 tiles?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
267. A perfect number is a positive integer that is equal to the sum of its positive
divisors, excluding the number itself. Which of the followings is a perfect
number?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
46
Grade – 5 & 6
MATH KANGAROO WORK BOOK
268. If the following four circles have shared members two by two, which circle would
be the fourth one?
(A)
(B)
(D)
(E)
(C)
269. Planets are spheres that are made of multiple layers, material and thickness of
which are different. A group of the residents of a magical planet have been able
to make a machine which helps them pass through all the layers and get to the
other side. But they have to wear special clothes for each layer. The thickness
of each layer is given below. The speed of the machine is fixed throughout the
trip. In what layer can the travelers move for the longest time without changing
clothes?
(A) A
(B) B
(C) C
(D) D
(E) E
47
Grade – 5 & 6
MATH KANGAROO WORK BOOK
270. There is a square with line segments drawn inside it. The line segments are
drawn either from the vertices or the midpoints of other line segments. We want
1
to color of the large square. Which one is our coloring?
8
(A)
(B)
(C)
(D)
(E)
48
Grade – 5 & 6
MATH KANGAROO WORK BOOK
1.
The five cards with the numbers from 1 to 5 lie in a
horizontal row (see the figure). Per move, any two
cards may be interchanged. Find the smallest
number of the moves required to arrange all cards in
increasing order?
(A) 1
(B) 2
(C) 3
(D) 4
2.
How many hours are there in half of a third of a quarter of a day?
(A)
(B)
(C) 1
(D) 2
3.
Raza needs 40 minutes to walk from home to the sea by foot and to return
home on an elephant. When he rides both ways on an elephant, the journey
take 32 minutes. How long would the journey last, if he would walk both
directions?
(A) 36 minutes
(B) 42 minutes
(C) 46 minutes (D) 48 minutes
4.
If the sum of five consecutive positive integers is 2005, then the largest of these
numbers is
(A) 401
(B) 403
(C) 405
(D) 2001
5.
How many different factors (including 1 and 100) does 100 have?
(A) 6
(B) 7
(C) 8
(D) 9
6.
If you count the number of all possible triangles and the number of
all possible squares in the picture how many more triangles
than squares do you find?
(A) the same quantity
(B) 1
(C) 2
(D) 3
7.
Which of equalities means that m makes 30 % from k?
(A) 10m – 3k = 0 (B) 3m – 10k = 0 (C) 7m – 10k = 0
(D) 7m – 3k = 0
49
Grade – 5 & 6
MATH KANGAROO WORK BOOK
8.
If you fold up the net on the right, which of these cubes can you make?
(A)
9.
(B)
(C)
(D)
We need 9 kg of ink to paint the whole cube. How
much ink do you need to paint the surface of figure
near the cube (see figure)?
(A) 4
(B) 5
(C) 6
(D) 9
10. What is the difference between the sum of the first 100 strictly positive even
numbers and the sum of the first 100 positive odd numbers?
(A) 20
(B) 50
(C) 100
(D) 200
11. A paper in the shape of a regular hexagon, as the one shown, is
folded in such a way that the three marked corners touch each
other at the centre of the hexagon. What is the obtained figure?
(A) six corner star
(C) square
(B) hexagon
(D) triangle
12. The diameter AB of the circle is 10 cm (as shown in
figure). What is the perimeter of the figure which is
marked with dark line, if the rectangles in the figure are
coincident?
(A) 16 cm
(B) 20 cm
(C) 25 cm
(D) 30 cm
50
Grade – 5 & 6
MATH KANGAROO WORK BOOK
13. Which path is the shortest?
(A)
(B)
(C)
(D)
14. Ali is building squares with matches adding small squares that it already has
built according to the schema of the figure. How many matches does he have to
add to the 5th square to build the 6th square?
1
(A) 12
ST
2
(B) 18
3RD
ND
(C) 20
(D) 24
15. The first three letters of the word
KANGAROO are put in equal squares
with length of side 2 (as shown in figure).
Find a false statement.
(A) perimeter of K is more than perimeter of A by 1
(B) perimeter of N is more than perimeter of A by 1
(C) perimeters of A and N are equal
(D) perimeters of K and N are equal
16. Find a truly end of the sentence: If I look on your reflection
then
(A) your reflection looks on me
(B) my reflection looks on you
(C) my reflection looks on your reflection
(D)your reflection looks on mine reflection
17. In a square grid Hina colours the small squares that lie on the two diagonals.
What is the size of the grid if Hina altogether colours 9 small squares?
(A) 3 ×3
(B) 4 × 4
(C) 5 ×5
(D) 8 ×8
51
Grade – 5 & 6
MATH KANGAROO WORK BOOK
18. In three adjacent faces of a cube, diagonals are drawn as
shown in the figure. Which of the following net is that of the
given cube?
(A)
(B)
(C)
(D)
19. There were 60 birds at three trees. In some moment 6 birds flew away from the
first tree, 8 birds flew away from the second tree, and 4 birds flew away from
the third tree. Then there were the same number of birds at each of the three
trees. How many birds were there at the second tree at the beginning?
(A) 24
(B) 22
(C) 21
(D) 20
20. Two 9 cm × 9 cm squares overlap to form a 9 cm ×13 cm rectangle as shown.
Find the area of the region in which the two squares overlap.
(A) 36cm2
(B) 45cm2
(C)54 cm2
(D) 63cm2
21. Imran let a pigeon out at 7.30 a.m., to deliver a message to Saad. The pigeon
delivered the envelope to Saad at 9.10 a.m. A pigeon flies 4 km in 10 minutes.
What was the distance between Saad and Imran?
(A) 14 km
(B) 20 km
(C) 40 km
(D) 56 km
22. A parallelogram is divided in two parts 1 and 2, as
shown in the figure. What sentence is surely true?
(A) 2 has a bigger perimeter than 1
(B) 2 has a smaller perimeter than 1
(C) 2 has a smaller area than 1
(D) 1 and 2 have the same perimeter
23. The squares are formed by intersecting the segment
of 24 cm by the broken
line
...
(see the Fig.). Find the length of
...
.
(A) 72 cm
(B) 96 cm
(C) 56 cm
(D) 106 cm
52
Grade – 5 & 6
MATH KANGAROO WORK BOOK
24. The 2007th letter in the sequence KANGAROOKANGAROOKANG. . . is
(A) O
(B) A
(C) N
(D) R
25. With what number of identical matches it is impossible to form a triangle? (The
matches should not be broken!)
(A) 7
(B) 6
(C) 5
(D) 4
26. There are 5 boxes and each box contains some cards labeled A, B, O, R, V as
shown. Peter wants to remove cards from each box in such a way that at the
end each box contains only one card, and different boxes contain cards with
different letters. What card remains in box 5?
B
A
V
R
V
1
(A) A
B
R
A
2
(B) V
B
A
B
V
O
3
(C) O
4
V
5
(D) R
27. The triangle and the square have the same perimeter.
What is the perimeter of the whole figure (a pentagon)?
(A) 12 cm
(B) 24 cm
(C) 28 cm
(D) 32 cm
28. A circular table is surrounded by 60 chairs. people are sitting at this table in
such a way that each of them is a neighbour of exactly one person. The largest
possible value for is
(A) 40
(B) 30
(C) 20
(D) 10
29. By shooting two arrows at the shown aiming board on the
wall, how many different scores can we obtain? (Missing
the board is possible.)
(A) 4
(B) 6
(C) 8
(D) 9
2
6
3
30. Rabia has some CDs on a table. She put them into three cases. She put seven
CDs into each, but there were still two more CDs, which did not fit into those
cases, so she left them on the table. How many CDs does Rabia have?
(A) 23
(B) 21
(C) 20
(D) 19
53
Grade – 5 & 6
MATH KANGAROO WORK BOOK
31. Which of the “buildings” (A),..., (E) – each consisting of exactly 5 cubes – can
you not obtain from the building on the right hand side if you are
allowed only to move exactly one cube?
(A)
(B)
(C)
(D)
32. Points A, B, C and D are marked on the straight line in some order. It is known
that AB = 13, BC = 11, CD = 14 and DA = 12. What is the distance between the
farthest two points?
(A) 14
(B) 38
(C) 50
(D) 25
33. What is the perimeter of the figure below (whose angles are
all right angles)?
(A) 3×5 + 8×2
(B) 6×5 + 4×2
(C) 6×5 + 6×2
(D) 6×5 + 8×2
34. Which of the following expressions has a different value?
(A) 20 ÷ 10 × 20 ×10;
(B) 20 × 10 × 20 ÷ 10;
(C) 20 × 10 + 10 × 20;
(D) 20 ÷ 10 × 20 +10.
35. If the figure
(A)
is rotated half turn (180°) around , the result is
(B)
(C)
(D)
36. Bilal has selected a number, has divided it by 7, then added 7 and finally
multiplied the sum by 7. That way he comes up with the number 777. Which
number was it he selected?
(A) 111
(B) 722
(C) 567
(D) 728
37. The numbers 1, 4, 7, 10 and 13 have to be written in the
picture so that the sum of three numbers in a row equal to
the sum of three numbers in a column. What is the biggest
possible sum?
(A) 20
(B) 21
(C) 22
(D) 24
54
Grade – 5 & 6
MATH KANGAROO WORK BOOK
38. Using next picture we can observe that 1+3+5+7 = 4 x 4. What
is the value of 1 + 3 + 5 + 7 + … + 17 + 19 + 21?
(A) 10 x 10
(B) 11 x 11
(C) 12 x 12
(D) 13 x 13
39. Esha has drawn a flower with 5 petals. She wants to
colour the flower, but she has only 2 different
colours– red and yellow. How many different flowers
can Esha get if she has to colour each petal using
one of these 2 colours?
(A) 7
(B) 8
(C) 9
(D) 10
40. What fraction of the square is shaded?
(A)
(B)
(C)
(D)
41. Andrew wrote the letters of the word KANGAROO in cells. He can write the first
letter in any cell he wants. He writes every subsequent letter in a cell that has at
least one point in common with the cell in which the previous letter was written.
Which of the tables can Andrew not create in this way?
(A)
(B)
(C)
(D)
(E)
42. All 4-digit integers with the same digits as the number 2011 are listed in
increasing order (so each number in the list has two 1s, one 0 and one 2). What
is the difference between the two numbers appearing on either side of 2011 in
this list?
(A) 890
(B) 891
(C) 900
(D) 909
(E) 990
43. Four of the numbers on the left are moved into the cells on the right so that
the addition is correct. Which number remains on the left?
(A) 17
(B) 30
(C) 49
(D) 96
(E) 167
55
Grade – 5 & 6
MATH KANGAROO WORK BOOK
44. Nina used 36 identical cubes to build a fence of cubes around a square region.
Part of her fence is shown in the picture. How many more cubes will Nina need
in order to fill the region inside her fence?
(A) 36
(B) 49
(C) 64
(D) 81
(E) 100
45. Some square floors have been covered with white and grey tiles. Floors using 4
and 9 grey tiles are shown in the picture. Each floor has a grey tile in every
corner and all the tiles around a grey tile are white. How many white tiles are
needed altogether for a floor using 25 grey tiles?
(A) 25
(B) 39
(C)45
(D)56
(E) 72
46. Paul wanted to multiply an integer by 301, but he forgot the zero and multiplied
by 31 instead. The result he got was 372. (He did manage to multiply by 31
correctly!) What result was he supposed to get?
(A) 3010
(B) 3612
(C) 3702
(D) 3720
(E) 30 720
47. In three games FC Barcelona scored three goals and let one goal in. In these
three games, the club won one game, drew one game and lost one game. What
was the score in the game FC Barcelona won?
(A) 2-0
(B) 3-0
(C) 1-0
(D) 4-1
(E) 0-1
48. We are given three points on a sheet of paper. The points are the vertices of a
triangle. We want to draw another point so that the four points are the vertices
of a parallelogram. How many possibilities are there for the fourth point?
(A) 1
(B) 2
(C) 3
(D) 4
(E) It depends on the initial triangle
49. The picture shows eight marked points connected by lines. One of the numbers
1, 2, 3 or 4 is to be written at each of the marked points so that the two numbers
at the ends of every line are different. Three numbers have already been
written. How many times does 4 appear in the completed picture?
56
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
50. Using only pieces like the one in the picture, Daniel wants to make a complete
square without gaps or overlaps. What is the smallest number of pieces he can
use?
(A) 8
(B) 10
(C) 12
(D) 16
(E) 20
51. Which three of the numbered puzzle pieces should you add to the picture to
complete the square?
(A) 1, 3, 4
(B) 1, 3, 6
(C) 2, 3, 5
(D) 2, 3, 6
(E) 2, 5, 6
52. Lisa has 8 dice with the letters A, B, C and D, the same letter on all sides of
each die. She builds a block with them. Two adjacent dice always have different
letters. What letter is on the die that cannot be seen on the picture?
(A) A
(B) B
(E) Impossible to say
(C) C
(D) D
57
Grade – 5 & 6
MATH KANGAROO WORK BOOK
53. There are five cities in Wonderland. Each pair of cities is connected by one
road, either visible or invisible. On the map of Wonderland, there are only seven
visible roads, as shown. Alice has magical glasses: when she looks at the map
through these glasses she only sees the roads that are otherwise invisible. How
many invisible roads can she see?
(A) 9
(B) 8
(C) 7
(D) 3
(E) 2
54. The positive integers have been coloured red, blue or green: 1 is red, 2 is blue,
3 is green, 4 is red, 5 is blue, 6 is green, and so on. Renate calculates the sum
of a red number and a blue number. What colour can the resulting number be?
(A) Impossible to say
(B) red or blue
(C) only green
(D) Only red
(E) Only blue
55. The perimeter of the figure below, built up of identical squares, is equal to 42
cm. What is the area of the figure?
(A) 8 cm2
(E) 128 cm2
(B) 9 cm2
(C) 24 cm2
(D) 72 cm2
56. Look at the pictures. Both shapes are formed from the same five pieces. The
rectangle measures 5 cm × 10 cm, and the other parts are quarters of two
different circles. The difference between the perimeter lengths of the two
shapes is
(A) 2.5 cm
(B) 5 cm
(C) 10 cm
(D) 20 cm
(E) 30 cm
58
Grade – 5 & 6
MATH KANGAROO WORK BOOK
57. Place the numbers from 1 to 7 in the circles, so that the sum of the numbers on
each of the indicated lines of three circles is the same. What is the number at
the top of the triangle?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
58. A rubber ball falls vertically through a height of 10 m from the roof of a house.
After each impact on the ground it bounces back up to
of the previous height.
How many times will the ball appear in front of a rectangular window whose
bottom edge has a height of 5 m and whose top edge has a height of 6 m?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
59. There are 4 gearwheels on fixed axles next to each other, as shown. The first
one has 30 gears, the second one 15, the third one 60 and the last one 10. How
many revolutions does the last gearwheel make, when the first one turns
through one revolution?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 9
60. A regular octagon is folded in half exactly three times until a triangle is obtained,
as shown. Then the apex is cut off at right angles, as shown in the picture. If the
paper is unfolded what will it look like?
(A)
(B)
(C)
(D)
(E)
59
Grade – 5 & 6
MATH KANGAROO WORK BOOK
61. Which of the following pieces covers the largest number of dots in the table?
(A)
(B)
(C)
(D)
(E)
62. Mary shades various shapes on square sheets of paper, as shown. How many
of these shapes have the same perimeter as the sheet of paper itself?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
63. Ann rides her bicycle throughout the afternoon with constant speed. She sees
her watch at the beginning and at the end with the following result:
Which picture shows the position of the minutes hand when Ann finishes one
third of the ride?
(A)
(B)
(C)
(D)
(E)
64. Matthew is catching fish. If he had caught three times as many as he actually
did, he would have 12 more. How many fish did he catch?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
65. John has made a building of cubes. In the picture you see this building from
above. In each cell you see the number of cubes in that particular tower. When
you look from the front, what do you see?
60
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A)
(B)
(C)
(D)
(E)
66. In an election each of the five candidates got a different number of votes. The
candidates received 36 votes in total. The winner got 12 votes. The candidate in
last place got 4 votes. How many votes did the candidate in second place get?
(A) 8
(B) 8 or 9
(C) 9
(D) 9 or 10
(E) 10
67. From a wooden cube with side 3cm we cut out at the corner a little cube with
side 1cm (see picture). What is the number of faces of the solid after cutting out
such a small cube at each corner of the big cube?
(A) 16
(B) 20
(C) 24
(D) 30
(E) 36
68. Find the number of pairs of two-digit natural numbers whose difference is equal
to 50.
(A) 40
(B) 30
(C) 50
(D) 60
(E) 10
69. The final of the local hockey championship was a match full of goals. There
were 6 goals in the first half and the guest team was leading after the first half.
After the home team scored 3 goals in the second half, they won the game.
How many goals did the home team score altogether?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
61
Grade – 5 & 6
MATH KANGAROO WORK BOOK
70. In the squares of the 4 × 4 board numbers are written such that the numbers in
adjacent squares differ by 1. Numbers 3 and 9 appear in the table. Number 3 is
in the top left corner as shown. How many different numbers appear in the
table?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
71. Which tile must be added to the picture so that the light grey area is as large as
the dark grey area?
(A)
(B)
(E) It is impossible.
(C)
(D)
72. Henry and John started walking from the same point. Henry went 1 km north, 2
km west, 4 km south and finally 1 km west. John went, 1 km cast, 4 km south
and 4 km west. Which of the following must be the final part of his walk in order
to reach the same point as Henry?
(A) He has already reached the same point.
(B) 1 km north.
(C) 1 km north-west.
(D) More than 1 km north-west.
(E) 1 km west.
73. At the summer camp, 7 pupils eat ice cream every day, 9 pupils eat ice cream
every second day and the rest of the pupils don’t eat ice cream at all.
Yesterday, 13 pupils had ice cream. How many pupils will eat ice cream today?
(A) 7
(B) 8
(C) 9
(D) 10
(E) it cannot be determined
74. Kangaroos A, B, C, D and E are sitting in that order, clockwise, around a
circular table. Exactly when the bell rings, each kangaroo but one exchanges its
position with a neighbour. The resulting positions, clockwise and starting with A,
are A, E, B, D, C. Which kangaroo did not move?
(A) A
(B) B
(C) C
(D) D
(E) E
62
Grade – 5 & 6
MATH KANGAROO WORK BOOK
75. A square can be formed using four of these five pieces. Which one will not be
used?
(A) A
(B) B
(C) C
(D) D
(E) E
76. A natural number has three digits. When we multiply the digits we get 135.
What result do we get if we add the digits?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
77. In a restaurant there are 16 tables, each having either 3, 4 or 6 chairs.
Together, the tables having 3 or 4 chairs can accommodate 36 people.
Knowing that the restaurant can accommodate 72 people, how many tables are
there with 3 chairs?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
78. The points A, B, C, D, E, F are on a straight line in that order. We know that AF
= 35, AC = 12, BD = 11, CE = 12 and DF = 16. What is the distance BE?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
79. Parisa set her stones in groups on the desk. After she arranged the stones in
groups of 3, she found that there were 2 stones left. Then she arranged the
stones in groups of 5, and again there were 2 stones left. At least how many
more stones does she need so that there won’t be any left when she arranges
them in groups of 3 and in groups of 5?
(A) 3
(B) 1
(C) 4
(D) 10
(E) 13
80. The faces of a cube are numbered 1, 2, 3, 4, 5, and 6. The faces 1 and 6 have
a common edge. The same is true for faces 1 and 5, faces 1 and 2, faces 6 and
5, faces 6 and 4, and faces 6 and 2. Which number is on the face opposite the
one with number 4?
(A) 1
(B) 2
(C) 3
(D) 5
(E) It cannot be determined
81. Tom used 6 squares with side 1 to form the shape in the picture. What is the
perimeter of the shape?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
63
Grade – 5 & 6
MATH KANGAROO WORK BOOK
82. Every day Mary writes down the date and calculates the sum of the digits
written. For example, on March 19 she writes 19.03 and calculates 1 + 9 + 0 + 3
= 13. What is the largest sum that she calculates during a year?
(A) 7
(B) 13
(C) 14
(D) 16
(E) 20
83. The rectangle ABCD in the picture consists of 4 equal rectangles. If BC has
length 1 cm, what is the length of AB?
(A) 4 cm
(B) 3 cm
(C) 2 cm
(D) 1 cm
(E) 0.5 cm
84. Which of these five nets cannot be the net of a pyramid?
(A)
(B)
(C)
(D)
(E)
85. On Jump Street, there are 9 houses in a row. At least one person lives in each
house. Any two neighbouring houses together are inhabited by at most six
people. What is the largest number of people that could be living on Jump
Street?
(A) 23
(B) 25
(C) 27
(D) 29
(E) 31
86. Lucy and her mother were both born in January. Today, March 19 2015, Lucy
adds the year of her birth, the year of her mother's birth, her age, and her
mother's age. What result does she get?
(A) 4028
(B) 4029
(C) 4030
(D) 4031
(E) 4032
87. The area of a rectangle is 12 cm2. The lengths of its sides are natural numbers.
Then, the perimeter of this rectangle could be:
(A) 20 cm
(B) 26 cm
(C) 28 cm
(D) 32 cm
(E) 48 cm
88. Each of the 9 segments in the figure is to be coloured either blue, green or red.
The sides of every triangle are to have different colours. Three of the segments
have already been coloured, as shown. What colour can the segment marked
with x have?
(A) Only blue
(B) only green
(C) only red
(D) Either blue, green or red
(E) such a colouring is not possible
64
Grade – 5 & 6
MATH KANGAROO WORK BOOK
89. In a bag there are 3 green apples, 5 yellow apples, 7 green pears and 2 yellow
pears. Simon randomly takes fruits out of the bag one by one. How many fruits
must he take out in order to be sure that he has at least one apple and one pear
of the same colour?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
90. A new chess piece ''kangaroo'' has been introduced. In each move, it jumps
either 3 squares vertically and 1 horizontally, or 3 squares horizontally and 1
vertically, as shown in the picture. What is the minimum number of moves the
kangaroo needs in order to go from its current position to the square marked
with A?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
91. Which of the following figures cannot be formed by gluing these two identical
squares of paper together?
(A)
(B)
(C)
(D)
(E)
92. Mary, Ann, and Nata work in a kindergarten. Each day from Monday to Friday
exactly two of them come to work. Mary works 3 days per week and Ann works
4 days per week. How many days per week does Nata work?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
93. Five squirrels A, B, C, D and E are sitting on the line. They pick 6 nuts marked
by crosses. At one moment the squirrels running to the nearest nut at the same
speed. As soon as a squirrel picks a nut it starts running to the next closest nut.
Which squirrel will get two nuts?
(A) A
(B) B
(C) C
(D) D
(E) E
65
Grade – 5 & 6
MATH KANGAROO WORK BOOK
94. There are 30 students in a class. They sit by pairs so that each boy is sitting
with a girl, and exactly half of the girls are sitting with a boy. How many boys
are there in the class?
(A) 25
(B) 20
(C) 15
(D) 10
(E) 5
95.
The are 2581953764 is written on a strip of paper. John cuts the strip 2 times
and gets number. Then he adds these 3 number. Which is the smallest possible
sum he can get?
(A) 2675
(B) 2975
(C) 2978
(D) 4217
(E) 4298
96. Bart is getting his hair cut. When he looks in the mirror the clock like this:
What would he have seen if he had looked in the mirror ten minutes earlier?
(A)
(B)
(D)
(E)
(C)
97. Grandmother bought enough catfood for her four cats to last for 12 days. On
her way home she brought back two stray cats. If she gives each cat the same
amour of food every day. How many days will the catfood last?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
98. Each letter in BENJAMIN represents one of the digits 1, 2, 3, 4, 5, 6 or 7.
Different letters represent different digits. The number BENJAMIN is odd and
divisible by 3. Which digit corresponds to N?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
99. Tim, Tom and Jim are triplets, while their brother Carl is 3 years younger. Which
of the following numbers could be the sum of the ages of the four brothers?
(A) 53
(B) 54
(C) 56
(D) 59
(E) 60
66
Grade – 5 & 6
MATH KANGAROO WORK BOOK
100. The perimeter of the rectangle ABCD is 30 cm. Three other rectangles are
placed so that their centres are at the points A, B and D (see the figure). The
sum of their perimeters is 20 cm. what is the total length of the thick line?
(A) 50 cm
(B) 45 cm
(E) Impossible to determine
(C) 40 cm
(D) 35 cm
101. What is the difference between the biggest and the smallest three-digit each
formed by different digits?
(A) 899
(B) 885
(C) 800
(D) 100
(E) Other
102. Figures I, II, III and IV are squares. The circumference of square I is 16m and
the circumference of square II is 24m.Find the circumference of square IV.
(A) 56m
(B) 60m
(C) 64m
(D) 72m
(E) 80m
103. Julien, Manon, Nicolas and Fabienne each have a different pet: a cat, a dog, a
parrot and a goldfish. Manon has a furry animal, Fabienne owns a four-legged
creature, Nicolas has a bird and Manon doesn’t like cats. Which statement is
not true?
(A) Fabienne has a dog
(B) Nicolas has a parrot
(C) Julien has a goldfish
(D) Fabienne has a cat
(E) Manon has a dog
104. Christian added 3g. of salt to 17g. of water. What is the percentage of salt in the
solution obtained?
(A) 20%
(B) 17%
(C) 16%
(D) 15%
(E) 6%
105. Six kids ate 20 cookies altogether. Andrew ate one cookie, Betty ate two
cookies, Carl ate three cookies. Daniella ate more cookies than any of the other
kids. What is the smallest possible number of cookies that Daniella ate?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
67
Grade – 5 & 6
MATH KANGAROO WORK BOOK
106. A computer virus is eating disk space. During the first day it eats 1/2 of the disk.
During the second day, it eats 1/3 of the remaining disk space. The third day it
eats 1/4 of what still remains and the fourth day it eats 1/5 of what is left. What
fraction of the original disk space remains intact?
(A) 1/5
(B) 1/6
(C) 1/10
(D) 1/12
(E) 1/24
107. In Mesopotamia in 2500 B.C.,
This sign was used to represent 1,
This – to represent 10 and
This - to represent 60. Thus, 22 would be written like this:
How would 124
have been written?
(A)
(B)
(C)
(D)
(E)
108. 28 children took part in a math league competition. The number of children who
finished behind Raul was twice as large as the number of children who were
more successful than him. In which place did Raul finish?
(A) Sixteenth
(B) Seventeenth (C) Eighth
(D) Ninth
(E) Tenth
109. How long (in cm) is the segment denoted by x?
(A) 9 cm
(B) 2 cm
(C) 7 cm
(D) 11 cm
(E) 10 cm
110. Which two of these figures can one use to cover exactly the empty area?
(A) 1+3
(B) 2+4
(C) 2+3
(D) 1+4
(E) 3+4
68
Grade – 5 & 6
MATH KANGAROO WORK BOOK
111. The picture shows Dave the clown dancing at the top of two balls and
one cubic box. The radius of the lower ball is 6 dm, the radius of the
upper ball is three times less. The side of the cubic box is 4 dm longer
than the radius of the upper ball. How high above the ground is Dave
standing?
(A) 14 dm
(E) 28 dm
(B) 20 dm
(C) 22 dm
(D) 24 dm
112. The figure, shown in the picture, consists of 7 squares. Square A is the biggest
one; square B – the smallest one. How many squares B can square A be
divided into?
(A) 16
(B) 25
(E) it is impossible to decide
113.
(C) 36
(D) 49
(C) 3
(D)
=?
(A) 2003
(B)
(E) 6009
114. Benito has 20 small balls of different colours: yellow, green, blue and black. 17
of the balls are not green, 5 are black, 12 are not yellow. How many blue balls
does Benito have?
(A) 3
(B) 4
(C) 5
(D) 8
(E) 15
115. There are 17 trees along the road from Basil’s home to a pool. Basil marked
some trees with a red strip as follows. On his way to his swimming lesson he
has marked the first tree, and then every second tree, and on his way back,
again, he has marked the first tree, and then every third tree. How many trees
have no mark after that?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
116. The picture on the right has been drawn on paper and cut out to make a house.
Which of the houses did it become?
69
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A)
(B)
(C)
(D)
(E)
117. You have two identical pieces that you can turn around
but not upside down. Which picture can you not make
with these two pieces?
(A)
(B)
(C)
(D)
(E)
118. Harry folds a sheet of paper five times. Then he makes a hole in the folded
paper, after which he unfolds it. How many holes has the unfolded paper?
(A) 6
(B) 10
(C) 16
(D) 20
(E) 32
119. Different figures represent different digits. Find the digit corresponding to the
square.
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
70
Grade – 5 & 6
MATH KANGAROO WORK BOOK
120. The weight of 3 apples and 2 oranges is 255 g. The weight of 2 apples and 3
oranges is 285 g. Each apple has the same weight, and each orange has the
same weight. What is the weight in grams of 1 apple and 1 orange together?
(A) 110
(B) 108
(C) 105
(D) 104
(E) 102
121. The best mathematician in the 7th grade was asked to guess the positive
integer about which his friends made the following statements:
Thomas: “This number is 9.”
Ronald: “This number is prime.”
Andrew: “This number is even.”
Michael: “This number is 15.”
Ronald and Thomas together made one true statement, as well as Andrew and
Michael. This number is:
(A) 1
(B) 2
(C) 3
(D) 9
(E) 15
122. What is the smallest number of little squares that need to be painted to get at
least one axis of symmetry in the picture?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
123. We have cut off one corner of a cube. Which of the developments
below is the development of the remaining part?
(A)
(D)
(B)
(C)
(E)
124. Snail quadruplets have gone hiking on a path paved with identical rectangular
tiles. The shape and length of each snail’s trip is shown below. How many
decimeters has the snail Tin hiked?
(A) 27
(B) 30
(C) 35
(D) 36
(E) 40
71
Grade – 5 & 6
MATH KANGAROO WORK BOOK
125. Turtle Island has an unusual weather system: on Mondays and Wednesdays it’s
always rainy, on Saturdays it’s foggy, and the other days are sunny. A group of
tourists would like to go on a 44-day-long holiday to the island. Which day of the
week should be the first day of their holiday in order to enjoy the most sunny
days?
(A) Monday
(B) Wednesday (C) Thursday (D) Friday
(E) Tuesday
126. The sum of two positive integers is equal to 77. If the first number is multiplied
by 8 and the second by 6, the two products are equal. The larger of these
numbers is
(A) 23
(B) 33
(C) 43
(D) 44
(E) 54
127. On each of three pieces of paper a three digit number is written. Two of the
digits are covered. The sum of the three numbers is 826. What is the sum of the
two covered digits?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
128. Riri the frog usually eats 5 spiders a day. When Riri is very hungry, she eats 10
spiders a day. She ate 60 spiders in 9 days. How many days was she very
hungry?
(A) 1
(B) 2
(C) 3
(D) 6
(E) 9
129. Pia plays with a yardstick consisting of 10 sticks (see picture). Which of the
following figures cannot be formed with this yardstick?
(A)
(B)
(C)
(D)
(E)
72
Grade – 5 & 6
MATH KANGAROO WORK BOOK
130. Five equal squares are divided into smaller squares. Which square has the
largest black area?
(A)
(B)
(D)
(E)
(C)
131. A big triangle is divided into equilateral triangles as in the figure. The side of the
small gray triangle is 1 m. What is the perimeter of the big triangle?
(A) 15 m
(B) 17 m
(C) 18 m
(D) 20 m
(E) 21 m
132. In the garden of a witch there are 30 animals: dogs, cats and mice. The witch
turns 6 dogs into cats. Then she turns 5 cats into mice. Now her garden has the
same number of dogs, cats and mice. How many cats were there at the
beginning?
(A) 4
(B) 5
(C) 9
(D) 10
(E) 11
133. With blocks of dimension 1cm × 1cm × 2cm, you can build towers as shown in
the picture. How high is a tower that is built in the same way with 28 blocks?
(A) 9cm
(B) 11cm
(C) 12cm
(D) 14cm
(E) 17cm
134. Bridget folded a square sheet of paper twice, and then cut it twice as shown
in the figure. How many pieces of paper will she get?
73
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) 6
(B) 8
(C) 9
(D) 12
(E) 16
135. Alex, Bob and Carl go for a walk every day. If Alex doesn't wear a hat, then Bob
wears a hat. If Bob doesn't wear a hat, then Carl wears a hat. Today Bob is not
wearing a hat. Who is wearing a hat?
(A) Both Alex and Carl
(B) Only Alex
(C) Only Carl
(D) Neither Alex, nor Carl
(E) It is not possible to determine.
136. Each of the following pictures shows the net of a cube. Only one of the resulting
cubes has a closed line on it. Which one?
(A)
(B)
(C)
(D)
(E)
137. For how many positive integers does n satisfy that the sum 2n  6 n  3n is even?
(A) for n multiple of 12
(B) For n multiple of 18
(C) for no value n
(D) for n multiple of 6
(E) for n higher of 9
138. How many times one have to break chocolate 4x6 along one of the lines to
Get maximum number or rectangular pieces of chocolate?
(A) 12
(B) 18
(C) 20
(D) 23
(E) 24
74
Grade – 5 & 6
MATH KANGAROO WORK BOOK
139. Five Kangaroo went ice skating and made their initials into the ice with their
skating tracks.
Who had to turn the largest number of degrees in total while making their letter?
(Both sharp turns and arcs count as turning .)
(A) Bella
(B) George
(C) Risto
(D) Sven
(E) Wayne
140. Seven strips are weaved together as shown, but a coin covers some of it.
What is it possible to see when you turn the weave over?
(A)
(B)
(C)
(D)
(E)
141. A plummer has 10 pipes of lengths 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10
How few pipes is it possible for the plummer to bring to her job in order to be
able to make a pipe of any of the lengths 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, and 15 by combining some of these?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
75
Grade – 5 & 6
MATH KANGAROO WORK BOOK
142. For the allergy, the doctor prescribed Filip 28 tablets. Filip tool 3 tablets daily in
two batches, 1 and ½ every 12 hours. Filip started taking the pills on Thursday
evening. When did he finish his medication?
(A) Friday morning
(B) Friday evening
(C) Saturday morning
(D) Sunday morning
(E) Sunday evening
143. The first digit of the smallest number, which is divisible by all numbers from 1 to
10, is ………
(A) 1
(B) 2
(C) 3
(D) 5
(E) 8
144. The sum of the digits of a three digit number is 26. What is their product?
(A) 12
(B) 26
(C) 81
(D) 648
(E) 729
145. There is a tradition in a school that whenever some children sit around a table
in the school canteen each girl sits between a boy and a girl while each boy sits
either between two boys or between two girls. Four children sit around a table.
How many of them are girls?
(A) 1
(B) 2
(C) 3
(D) none
(E) impossible to know
146. A felt pen costs 4 kr more than a pencil. Kurt bought 3 felt pens and 5 pencils
and paid 60 kr. Lisa bought 1 felt pen and 1 pencil. How much did she pay?
(A) 6 kr
(B) 10 kr
(C) 12 kr
(D) 15 kr
(E) 16 kr
147. In the park there are 20 animals, dogs, cows, cats, and Kangaroos. We know
that 4 are dogs, 14 are NOT cows and 13 are NOT cats. How many are the
Kangaroos in the park?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 7
148. A tank is served by ten water supplies. One of them can make the tank full in
one day; each of two of the remaining one can make the tank full in two days;
each of three of the remaining ones can make the tank full in three days; each
of the remaining four can make the thank full in four days. If all the supplies
work simultaneously, how many hours are needed to make the Tank full?
(A) 14
(B) 12
(C) 10
(D) 8
(E) 6
76
Grade – 5 & 6
MATH KANGAROO WORK BOOK
149. The electric clock shows hours and minutes. The digits are constructed
From some of seven elements as follows:
Goes correct, but some two elements (the same in all digits) burned out and
stopped working.
The clock shows:
What will they show after 3 hours and 45 minutes?
(A)
(B)
(C)
(D)
(E)
150. 3% of 1000 is :
(A) 0, 3
(B) 3
(C) 30
(D) 300
(E) 3000
151. Bicycle for sale: 200 euros instead of 250. What is the discount percentage?
(A) 20%
(B) 25%
(C) 50%
(D) 10%
(E) 5%
152. Is John goes to school by bus and returns by walking he needs 3 hours. If he
goes by bus both ways he needs 1 hour. How long does it take him if he walk
both ways to school and back?
(A) 3, 5 hours
(B) 4 hours
(C) 4, 5hours
(D) 5 hours
(E) 5,5 hours
153. Six friends are travelling on a ski trip in a train with six- person compartment
(pic.) Tom is sitting opposition of Lucy. Oliver is sitting in the direction of travel,
but not next to the window. Sophie and Clair are sitting next to each other,
David is sitting next to the door. Who is sitting is chair 6?
77
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) David
(C) Lucy or Tom
(E) Oliver or Lucy
(B) Oliver
(D) Sophie or Claire
154. Lea has two flowerpots with violets, one rose, one forget-me-not and one orchid
in her room. She always waters the violets first. How many ways are there in
which she can water the plants in her room?
(A) 24
(B) 12
(C) 10
(D) 8
(E) 6
155. Three sisters were born on the 1st of September, each in a different year. Kate
is 10 years older than Lydia and Annie is 10 times older than Lydia. Their
combined age is 34 years. How old is the oldest one?
(A) 12
(B) 13
(C) 18
(D) 20
(E) 22
156. After the first kilometer in a race Petra was next to last. She then managed to
overtake seven runners. She slowed down a little bit, so two runners overtook
her. She gave it her all and she overtake eight runners. In the last section of the
race, four runners were able to overtake her. She finished ninth. How many
runners ran in the race?
(A) 15
(B) 18
(C) 19
(D) 20
(E) 21
157. Mike got a 75-piece puzzles. He laid down all the edge pieced and found out
that the puzzles are rectangular with a width of 5 pieces. (part of the rectangle
is on the picture). How many pieces does he still have to lay down in order to fill
out the entire picture?
(A) 18
(B) 35
(C) 36
(D) 39
(E) 58
158. A group of friends were at a garden party. A third of men and half of the women
came in flip flops. When everyone jumped into the pool, there were 12 pieces
(not pairs) of men’s and 18 pieces of women’s flip flop. How many people were
at the party?
(A) 15
(B) 18
(C) 24
(D) 30
(E) 36
78
Grade – 5 & 6
MATH KANGAROO WORK BOOK
159. Ellie is going to a three day long ski trip. She wants to buy a gingerbread cookie
for each day she will be there. There are three types of her favorite gingerbread
cookie, but she cannot decide whether she should buy a different one for each
day, or all of the same one or….. How many options to buy three does she
have?
(A) 4
(B) 6
(C) 9
(D) 10
(E) 27
160. The mayor ordered to paint 2019 houses so that at least 1000 houses were red
and at least 1000 houses were green. What is the maximum number of different
colors can be use?
(A) 2
(B) 3
(C) 19
(D) 20
(E) 21
161. Flower shop brought 60 red roses and 60 white roses. Each 3 red roses cost 2
euros, and every 2 white – 3 euros. The seller created 5 flower bouquets and
wanted to sell them for 5 euros per bouquet. Will the received revenue differ
from the planned and how much?
(A) does not differ
(B) larger by 10 euros
(C) less by 120 euros
(D) larger by 12 euros
(E) less by 12 euros
162. I bought some cookies. If I had bought 20 less, I would have paid a fifth of what
I paid. How many cookies did I buy?
(A) 24
(B) 30
(C) 25
(D) 32
(E) 35
163. Jutta throws five regular dice. The total number of dots is at least fifteen. Three
dice are as shown.
Which of these cannot be on the remaining two dice?
(A) Two sixes
(B) A two and a six
(C) 25 two fives
(D) A three and a four
(E) Two fours
164. The following square is used for encoding by replacement each letter with the
letter that corresponds by a rotation of quarter –turn around the center of the
square. For example, letter G would be replaced by letter V.
79
Grade – 5 & 6
MATH KANGAROO WORK BOOK
How many consonants does the original string contain if, after encoding, The
string becomes CEROCTX
(A) 5
(B) 1
(C) 2
(D) 3
(E) 4
165. A full glass of water weighs 400 gram. An empty glass of water weighs 100
grams.
(A) 200
(B) 225
(C) 275
(D) 325
(E) 350
166. We have 16 equilateral triangles with 1 cm sides. We wish to build a shape by
placing the triangles next to each other so that they touch each other at least
one entire side. One such is shown.
We wish build the shape with the smallest possible perimeter. What is that
perimeter?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
167. Which of the following buildings needs more paint to be painted?
(A)
(B)
(C)
(D)
(E)
80
Grade – 5 & 6
MATH KANGAROO WORK BOOK
168. Every of the four friends is a serious person (always tells the truth) or a joker
(always lies). One day friends made the following statements. Andy: “benny is
joker”. Benny: “Charlie is joker”. Dannie: “Andy is joker.” How many jokers are
there among these four friends?
(A) 1
(B) 2
(C) 3
(D) 4
(E) impossible to determine
169. The number 1728 is the cube of 12. What is the smallest positive natural
number that multiplied by 1728 gives us a perfect square?
(A) 2
(B) 3
(C) 6
(D) 12
(E) 18
170. A team must win 60% of the matches that must be played if they want to qualify
for a second phase. Of the 8 games that he has played he has won 4. How
many match must he win, at least, of the 12 who are missing to play, so that he
can qualify for the second phase?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
171. Three lions live in a cave. Every third time the biggest lion roars the middle lion
answer with two roars. Every fifth time the middle lion roars the smallest lion
answer with three roars. One day every lion roared exactly 32 times. How many
of these roars were not answers to other roars?
(A) 48
(B) 54
(C) 56
(D) 58
(E) 68
172. Let ABC be a 3- digit number. What is the smallest possible positive value of
ABC - CBA ?
(A) 1
(B) 9
(C) 90
(D) 99
(E) 101
173. Bridget folded a square sheet of paper twice, and then cut it twice as shown in
the figure. How many pieces of paper of paper will she get if she deployed all
the pieces?
(A) 6
(B) 8
(C) 9
(D) 12
(E) 16
174. A block of wood as seen in the diagram on the right was split in two pieces. One
of the pieces is shown next to it. Which of the following are the two pieces?
81
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A)
(B)
(C)
(D)
(E)
175. How many colors are needed at least to paint the sides of a cube in such a
Way that adjacent sides are in the same color?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
176. If you take the letter L and turn it upside down or invert it laterally, you get four
symbols:
How many symbols do you get this way from the letters A, B and R together?
(A) 12
(B) 10
(C) 9
(D) 8
(E) 7
177. The positive integers a , b , c satisfy the relations a  b  c , a . b  a , a  a  a  c
.Then a  b  c equals.
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
178. When Alan left his home, the clock on the wall looked as in Fig.1 and when he
came back clock looked as in Fig.2. Meantime, the two clock hands overlapped
three times, showing 12:00. How many hours was Alan gone?
(A) 38h
(B) 26h
(C) 36h
(D) 24h
(E) 14h
179. Alibaba and 40 thieves equally divided 42 identical bags of gold coins. Each of
them got one full bag and 2 coins. How many coins did a bag contain?
(A) 42
(B) 81
(C) 82
(D) 84
(E) 41
82
Grade – 5 & 6
MATH KANGAROO WORK BOOK
180. Riri the frog usually eats 5 spiders a day. When Riri is very hungry, she eats 10
spiders a day. How many times was she very hungry, if she ate 60 spiders in 9
days?
(A) 1 days
(B) 2 days
(C) 3 days
(D) 4 days
(E) 5 days
181. A bale of hay can be eaten by a horse in 2 days, by a cow in 3 days and by
sheep in 6 days. How many days a farmer can feed all those animals with 2
bales of hay?
(A) 1 day
(B) 2 days
(C) 3 days
(D) 4 days
(E) 5 days
182. Two identical business cards of rectangular shape will be cut from the cardboard shown in the picture. Their width and length are 5 cm and 10 cm,
respectively. John cuts off the two business cards by using a minimum number
of cuts. The remaining part of the cardboard is
15 cm
5 cm
10 cm
5 cm
10 cm
(A) a rectangle
(C) three squares
(E) a square and a rectangle
(B) two squares
(D) a square
183. Stephen is the middle boy in a family with five children: 3 boys and 2 girls.
Stephen notes that the sum of the ages of any two boys is equal to the age of
one of the other family’s children. Knowing that the girls are 5 and 7 years old,
what is the age of Stephen?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
184. 100 000 seconds is about :
(A) 10 years
(B) 1 years
(C) 1 month
(D) 1 day
(E) 1 hour
185. In pascals triangle starts with a 1 in the top. Each line (except the first one)
starts and ends with a 1. Each number between the 1’s is the sum of the two
numbers directly above it. The picture shows six lines of pascals triangle. After
the dotted line we make new lines by putting the difference of two neighboring
numbers below it. In the picture the first of those lines is shown. Suppose we’ll
do the same thing starting after nine lines of pascals triangle. After some time
we’ll end with a line with just one number. What is this number?
83
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) -9
(B) 0
(C) 1
(D) 5
(E) 9
186.
In a rectangular lattice of 10 x 3 cm a ball is shot from the left bottom with an
angle of 45 . Each time it hits the border of the lattice it is reflected, see the
picture. In the same says a ball is shot in a 30 x 5 cm lattice. What distance will
the ball have travelled when it hits the right hand site of this lattice?
(A) 3 18  2
(B) 925
(C) 35
(D) 30 2
(E) 150.
187. The figure shows a 8 x 4 rectangular lattice with a diagonal. This diagonal
intersects 8 cells. How many calls will a diagonal in a rectangular 10 x 3 lattice
intersect?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
188. ABC is a rectangular triangle. AB = 60, BC = 80 and AC = 100. BD is
perpendicular to AC. How long is AD?
(A) 30
(B) 36
(C) 42
(D) 48
(E) 54
189. In the picture we can see the building glued of two identical dice. On each face
of a die one of numbers 1, 2, 3, 4, 5, and 6 is written, on different faces different
numbers. One pair of the opposite faces has a property that the sum of
numbers is equal to 5. The sum numbers on the glued faces of dice is equal to
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
84
Grade – 5 & 6
MATH KANGAROO WORK BOOK
190. Linas builds a cube of dimension 4 x 4 x 4 using 32 white and 32 black unit
cubes. He would like the surface of the so obtained cube to contain as many
white walls of unit cubes as possible. What part of the entire surface of the cube
will be white with this setting?
(A)
1
4
(B)
1
2
(C)
2
3
(D)
3
4
(E) D
191. On a rectangular paper card one has drawn a line parallel to the long side and a
line parallel to the short side. Four rectangles have been formed in this way.
What is the sum of the circumferences of these rectangles in relation to the
circumference of the card?
(A) It is 4 times bigger
(B) It is 3 times bigger
(C) It is 2 times bigger
(D) It is the same
(E) It can not be determined without knowing the dimension of the card.
192. The cube shown in the figure has a positive integer written on each face.
The product of numbers on the opposite faces is the same for each pair of such
walls. The numbers on the walls do not have to be different. What is the
smallest possible sum of all numbers written on the cube?
(A) 37
(B) 44
(C) 36
(D) 60
(E) 41
193. A floorer wants to cover the floor of a 3 x 3 m2 room with 30 x 30 cm2 tiles
(image A). Four adjacent tiles result in image B. After the flooring, how many
complete octagrams (eight-angled stars) can be seen on the floor?
(A) 81
(B) 100
(C) 125
(D) 181
(E) 200
194. Ayla, like all Qashqai girls, spends her free time weaving a type of traditional
carpet, called ‘gabbeh carpets’. Last summer, she wove the ‘gabbeh carpet’
below. She used 1 kilogram of blue and 2.1 kilograms of black yarn to weave
this gabbeh carpet. Can you determine how many kilograms of green yarn did
Ayla use for this ‘gabbeh carpet’?
85
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) 200 gr
(E) Not specified
(B) 400 gr
(C) 500 gr
(D) 800 gr
195. War broke out and Gholi Khan, the commander of an eight-man battalion,
betrayed his country and escaped with his men. After a few months, the king’s
men arrested Gholi Khan and his men in a remote village, but they had no idea
which one of those men were Gholi Khan . The king knew that Gholi Khan was
the youngest of those men, so he had them form a line and asked them to
count the number of men in front of them that are younger than them. The
answers are as follows:
Which man is Gholi Khan? Which of these men has the median age? In other
words, which one is fifth youngest/ oldest man? (Note: they can only see those
that are standing in front of them.)
(A) 1st man
(B) 6th man
(C) 9th man
(D) 2nd man (E) 8th man
196. Each group in the group stage of a World Cup has four teams. Each team plays
once with each of the other three teams. The winning team earns 3points and
the losing team doesn’t earn any points. In case of a draw, each team earn 1
point. At the end of the group stage, how many possible numbers can be the
total points of the four teams?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
197. Which of the following drawings is the development of the pyramid shown on
the right?
86
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A)
(B)
(C)
(D)
(E)
198. A family has as children 2 girls and one boy. Their names are Ka, La and Ma is
some order. Their mother said
- Only one of Ka or La is a girl,
- Only one is the boy?
(A) Ka
(B) La
(E) We cannot be sure
(C) Ma
(D) One of La or Ma
199. The sum of the number in each row and in each column of the table on the right
is 50. Some of the number are written with invisible ink and others cannot be
seen because some blue ink fell on them. What is the number in the square
with the question mark?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
87
Grade – 5 & 6
MATH KANGAROO WORK BOOK
200. IN the garden of which there are 30 animals in all, dogs, cats and mice. The
witch changed 6 dogs and turned them into cats. Then she changed 5 cats and
turned them into mice. Now her garden has the same number of dogs, cats and
mice. How many where the cats at the beginning?
(A) 4
(B) 5
(C) 9
(D) 10
(E) 11
201. Some numbers can be written as a sum of three consecutive whole numbers
such as 42 = 13 + 14 + 15. Which of the numbers below can be written as a
sum of three consecutive whole numbers?
(A) 22
(B) 29
(C) 32
(D) 36
(E) 11
202. Three brother went fishing and brought 50 fishes back home. The oldest
brother, Andy, Carried 10 more fishes than Billy. Billy carried twice as many
fishes as the youngest brother, Cato. How many fishes did Cato carry?
(A) 5
(B) 8
(C) 10
(D) 12
(E) 20
203. Maria will do a job and gets two different salary options.
Options A: 100 euro per day Option B: 50 euro first day, then 60 euro, then 70
euro and so on. The salary increases 10 euro every day.
How many days must Maria work at least in order to make more money on
option 2?
(A) 9 days
(B) 10 days
(C) 11 days
(D) 12 days
(E) 13 days
204. A large square is divided into smaller squares.
What total part of the large square is colored grey?
(A) 1
(B) 1
(C) 1
(D) 1
6
5
4
3
(E) 1
2
88
Grade – 5 & 6
MATH KANGAROO WORK BOOK
205. In an ice cream parlor, the different flavours are arranged in rectangular
containers of two different sizes, as shown. The number of flavours differs,
depending on how many containers of each size are used. What is the largest
number of flavours that could be offered?
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
206. With blocks of dimension 1cm x 1cm x 2cm, you can build towers in the way as
you can see in the picture. How high is a tower that is built in the same way with
28 blocks?
(A) 9cm
(B) 11cm
(C) 12
(D) 14
(E) 17
207. Peter’s friends are going to the movies and for ice-cream afterwards. Peter has
already seen the movie and wants to pick them up when the movie is finished.
He lives 12 minutes away from the cinema. The film starts at 17:30 and lasts 97
minutes. When does he need to leave home?
(A) 18:18
(B) 18:48
(C) 18:55
(D) 19:07
(E) 19:19
208. Nauru, Vatican, Monaco, and Kiribati play the world cup of non-FIFA members.
Each team plays against each tea, exactly once, A victory bring 5 points, a tie 2
points and a loss zero points. Which Total is not possible for any team at the
end of the tournament?
(A) 12
(B) 10
(C) 9
(D) 8
(E) 6
209. Emily took selfies with her 8 cousins. Each of the 8 cousins is on two or three
pictures and on each picture there are exactly 5 cousins. How many selfies did
Emily take?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
210. The rightmost digit of 2019  9201 is:
(A) 0
(B) 1
(C) 3
(D) 8
(E) other
211. At 23:35 the minutes hand started to move backward, while the hour one
continued its usual movement. How many times will the hands meet during the
next 24 hours?
(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
89
Grade – 5 & 6
MATH KANGAROO WORK BOOK
212. Masha made five pies with cabbage, several with mushrooms, and several with
meat as many as with cabbage and with mushrooms together. How many pies
could she make altogether?
(A) 10
(B) 11
(C) 13
(D) 14
(E) 15
213. On the island of nobles and liars 25 people are standing in a queue. Everyone,
except the first person in the queue, said, that the person before him in the
queue is a liar. The first man in the queue said, that all people, standing after
him are liars. How many liar are there in the queue? (Nobles always speak the
truth, and liars always tell lies.
(A) 0
(B) 12
(C) 13
(D) 24
(E) impossible to determine
214. Little hares grew carrots in the garden. The number of carrots is two- digit
number. The carrots can be divided among 2, 3, 5 little hares, but cannot be
divided among 4 hares. How many carrots grew in the garden?
(A) 60
(B) 40
(C) 30
(D) 15
(E) 13
215. Each square of the table 10 x 19 contains either 1 or 0. All sums of the number
both in lines and columns have been calculated. What greatest number of
different sums can we get?
(A) 9
(B) 10
(C) 15
(D) 19
(E) 29
358. On the coordinate plane, point A= (7, 3) and point B have created a parallel line
to the horizontal axis. Which can be point B?
(A) (4,5)
(B) (3,7)
(C) (5,7)
(D) (5,3)
(E) (4,5)
217. In a pet shop the owner discovered that for each five hatched female goldfish
there are seven male goldfish that hatch. If 156 goldfish did hatch last week,
how many of them were male?
(A) 22
(B) 91
(C) 65
(D) 31
(E) 28
218. Lena is at a market stall where they sell lovely fruit. She wants to buy 3 kilo of
apples and 4 kilo of pear and gives the salesman 26 EUR, which is the exact
amount All of a sudden she changes her mind and declares “I’d rather have 4
kilo of apples and 3 kilo of pears”. The salesman replies “In that case you’ll get
90 cents back “. What can you deduce about the price of apples and pears?
(A) apples and pears cost the same per kilogram
(B) apples are 90 cents more expensive per kilogram than pears
(C) apple are 90 cents cheaper per kilogram than pears
(D) apples are 30 cents more expensive per kilogram than pears
(E) apples are 30 cents cheaper per kilogram than pears
90
Grade – 5 & 6
MATH KANGAROO WORK BOOK
219. It takes 50 seconds for the merry- go- round to make a full round. At the
beginning, the horse is at the front; after 10 second, the dolphin is at the front,
etcetera. What animal is at the front after 3 minutes?
(A)
(B)
(C)
(D)
(E)
220. A 3 x 3 x 3 cube was built with 1 x 1 x 1 cubes. Then, in each of the three
directions, a hole was drilled from front to back, from left to right and from top to
bottom, removing always the central 1 x 1 x 1 cubes (see picture). How many
1 x 1 x 1 cubes are left?
(A) 15
(B) 18
(C) 20
(D) 21
(E) 22
221. In the numbering of the pages of the book that Joseph is reading, 0 was used
five times and 8 was used six times. What is the maximum number of pages of
the book? (The book does not have any blank page)
(A) 57
(B) 58
(C) 59
(D) 60
(E) 61
222. What is the last digit (units digit) of the number 20192019 ?
(A) 1
(B) 2
(C) 6
(D) 7
(E) 9
223. Alex drew all possible rectangles of area 2019 where the measure of the sides
are positive integers. How many rectangles did he drew?
(A) 1
(B) 2
(C) 679
(D) 1000
(E) 2019
224. One panel is composed of 9 circles. When Lucy touches one circle, this circle
and the other that are tangent to it change from white to black or black to white,
as shown in the picture.
91
Grade – 5 & 6
MATH KANGAROO WORK BOOK
How many circles will Lucy need to touches to change all circles to black?
(A) 2
(B) 3
(C) 4
(D) 5
(E) more than 5
225. Gabriela feeds the birds of a park every day. Each day the amount of acorn
eaten by the birds doubles with respect to the previous day. If a bird ate two
grains of acorn on Monday, how many grains of corn would that bird have eaten
in total from Monday to Friday?
(A) 20
(B) 32
(C) 48
(D) 60
(E) 62
226. A 3 x 2 rectangle can be covered by 2 x 1 rectangles in 3 different ways as
shown below.
In how many different ways the figure
(A) 1
(B) 2
(C) 3
(D) 4
(E) Not possible
227. Jean wants to calculate 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 =, but he forget to
press two + signs while doing the calculation. Which one of the following could
be the answer?
(A) 120
(B) 153
(C) 183
(D) 235
(E) 280
228. Each Mars-man has 3 fingers in his right-hand and 7 in his left- hand. Each
Jupiter-man has 7 fingers in his right-hand and 3 in his left-hand. Each Saturnman has 4 fingers in his right-hand and 8 in his left-hand Each Uranus-man has
8 fingers in his right-hand and 4 in his left-hand. To an interplanetary meeting a
typical man from each of the following five planets was nominated, from: Earth,
Mars, Jupiter, Saturn and Uranus. Only 4 men came. They had together as
many right- hand-fingers as left-hand-fingers. Which planet was not
represented?
92
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) Earth
(B) Mars
(C) Jupiter
(D) Saturn
(E) Uranus
229. Sven has 20 plums, eight yellow and twelve blue. How many blue plums will he
remove if he wants the probability of puling a blue plum without looking is the
same as pulling a yellow plum?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
230. Determine v
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
231. The price of the button badge is USD 7 while the price of the coaster is USD 9.
Andy left with USD 4 is he spends all his money to buy the button badges but
he needs USD 2 more is he wants to buy the coaster as much as the button
badges. How much money
That Andy has?
(A) USD 18
(B) USD 21
(C) USD 25
(D) USD 27
(E) USD 30
232. How many of these pictures can be seen, if you rotate the picture on the right
on the plane?
93
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
233. What is the value of the expression
(1  0)3 :1  (1  1)3 : 4  (1  2)3 : 9  (1  3)3 :16  ...  (1  99)3 :10000  ?
(A) 0
(B) 5
(C) 50
(D) 505
(E) 5050
234. Using small cubes with a side length of 1cm we will create bigger cubes by
wrapping smaller ones. The first cube is the single one with a side length of
1cm. Another cube is thus obtained by wrapping the first cube using 26 small
cubes. Which minimum number of small cubes must be used to create another
bigger cube?
(A) 26
(B) 37
(C) 63
(D) 98
(E) 125
235. Nina writes 3 whole and positive numbers on a blackboard and writes the value
of the sum 20. Marta arrives and replaced one of these numbers with another
and notes that the sum increases by 10. The highest value that Marta could
have replace is
(A) 11
(B) 13
(C) 17
(D) 20
(E) impossible to determine
236. Mario goes up and down a hill in 3 hours. He climbs the hill at 4 kilometers per
hour and he descends at 12 kilometers per hour. The total distance traveled by
Mario is
(A) 12
(B) 6
(C) 24
(D) 16
(E) impossible to determine
237. A water tank has dimensions 3m  10m  12m. Inside it there are three solid towers
each of base 1m  1m and heights 1m, 2 m and 3 m, respectively. How many cubic
meters of water can we pour into the tank?
(A) 300m3
Grade – 5 & 6
(B) 320m3
(C) 346m3
(D) 354m3
(E) 360m3
94
MATH KANGAROO WORK BOOK
238. Carmen has 5 paper which are precisely cut in shape of digits:
She stacked 3 of then onto single pile, trying to cover much of one :
Which papers were stacked?
(A)
(B)
(C)
(D)
(E)
239. The surface of a transparent glass cube consists of two equal triangles. Ben
colored some triangles in black so that if you look at the cube from the side of
any face, you will see a black square. Which of the following nets can be a net
of this cube?
(A)
(B)
(C)
(D)
(E)
240. The sums of points on the opposite faces of the correct dice are equal.
Which of the following dice can be correct one?
(A)
(B)
(C)
(D)
(E)
241. It’s 12:00 now . What time will be in 2019 minutes?
(A) 12:19
(B) 21:39
(C) 19:29
(D) 09:49
(E) other answer
95
Grade – 5 & 6
MATH KANGAROO WORK BOOK
242. The number 20 is in a set with more 19 numbers. We know that the average of
these 20 numbers is 20. If we take out the number 20 from the set, what is the
average of the number left?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
243. Three Kangaroos Alex, Bob and Carl go walk every day. If Alex doesn’t wear a
hat, then Bob wears a hat. If Bob doesn’t wear a hat, then Carl wears a hat.
Today Bob doesn’t wear a hat. Who from other two Kangaroos certainly wears
a hat?
(A) Both Alex and Carl wear hats.
(B) Only Alex
(C) Only Carl wears a hat.
(D) Neither Alex, nor Carl wears a hat.
(E) Only Carl certainly wears a hat.
244. Rosa wants to start at the arrow, follow the red line, and get out at the other
arrow.
Which piece is not possible to put in the middle to obtain that?
(A)
(B)
(C)
(D)
(E)
245. Two trolls are always lying. They look at a digital clock and say:
The clock is showing one of the following. Which?
(A) 7:30
(B) 8:30
(C) 12:30
(D) 13:30
(E) 0:00
246. There are 20 apples and 20 pears in the box. Carl arbitrarily took 20 fruits from
this box, and Luca took other 20 fruits. Only one of the following sentences is
surely true. Which one?
(A) Carl got at least one pear.
96
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(B) Carl got as many apples as pears.
(C) Carl got as many apples as Luca got apples
(D) Carl got as many pears as Luca got apples.
(E) Carl got as many pears as Luca got pears.
247. Five of the Avengers came to a meeting. Thor was neither first nor last. Captain
America came earlier than Iron Man and Falcon. Iron Man arrived not after
Falcon. Black Widow came together with Falcon, but Falcon politely let her in
front of him. Which superhero was the third?
(A) Captain America
(B) Iron Man
(C) Black Widow
(D) Falcon
(E) Thor
248. Today (Kangaroo Day) is Thursday. Which day will it be in 2021 days?
(A) Tuesday
(B) Wednesday (C) Thursday (D) Friday
(E) Saturday
249. An ice hockey game consists of three thirds. The result was 2 : 0 after the first
third, 3 : 1 after the second third, and 4 : 3 after the last third (at the end of the
match). In how many different orders could the two teams have scored?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 12
250. What is the smallest positive integer divisible by 45 such that each of its digits is
0 or 6?
(A) 6000
(B) 6060
(C) 6600
(D) 6660
(E) other
251. Ali builds a figure with a pencil and many round tokens. She has white and gray
tokens. First, she drew 4 concentric circles. Then, she glued the tokens
following the pattern shown in the picture. If Ali wants to add 3 concentric circles
following the same pattern, how many gray tokens will she use in the whole
figure?
(A) 37
(B) 16
(C) 54
(D) 92
(E) 38
252. Karla writes the expression that represents the product of all the prime numbers
that are factors of 504. What is the correct expression?
(A) 8  3  7
97
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(B) 2  9  7
(C) 2  3  7
(D) A and C are correct
(E) All the options are correct
253. In a ball pool there are 10 yellow balls, 40 blue balls and 60 red balls. Each
time, a patient toddler blindly takes 3 balls from the bath. When all three are the
same color, he throws the balls out of the pool. If they are not all the same
color, he throws the balls back into the pool. He repeats that until only two balls
remain in the pool. Which balls are left?
(A) two yellow balls
(B) two blue balls
(C) two red balls
(D) a blue and a red ball
(E) a yellow and a blue ball
254. Between X and Y runs a single train track. Trains leaving X reach Y in 180
minutes. Trains leaving Y reach X in 60 minutes. Trains run at constant speed.
If we want that every 4 hours a train leaves X and Y at the same time and that
these trains don't crash, where do we have to replace the single track
with a double track
?
(A)
(B)
(C)
(D)
(E)
255. A builder has a brick whose height is 4 cm. With several such bricks he built a
cube (all sides equal) as shown. What are the dimensions of the brick, in
centimetres?
(A) 4  6  12
(E) 4  12  16
(B) 4  6  16
(C) 4  8  12
(D) 4  8  16
98
Grade – 5 & 6
MATH KANGAROO WORK BOOK
256. The floor of a room has dimensions 5m  6m. A builder wants to cover it with
identical tiles. No overlaps or gaps are allowed. Which of the following types of
tiles cannot be used?
(A)
(B)
(D)
(C)
(E)
257. The teacher placed the numbers 1, 2, 3, 4 and 5 in the five boxes shown, once
each. When she added the numbers formed she found sum 555. In how many
ways could she do this?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
258. Professor Vesna gave the following assignment to the students in the math
class: students, you have nine balls that are exactly the same, in shape, color,
size and you have a scale for which you do not have weights to measure the
balls. One of the balls weighs less than the other eight. What is the smallest
number of measurements that student Aneta should discover?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
99
Grade – 5 & 6
MATH KANGAROO WORK BOOK
259. The code consists of 6 digits. It is known that the sum of the digits written in
even places is equal to the sum of the digits written in odd places. Which of the
following can be a code?
(A) 81**61
(B) 7*727*
(C) 4*4141
(D) 12*9*8
(E) none of the previous
260. At Ferney's farm, 9 rabbits eat carrots every day, 11 rabbits eat every other
day. The other rabbits do not eat carrots. Yesterday, 15 rabbits ate carrots. How
many rabbits will eat carrots today?
(A) 9
(B) 13
(C) 14
(D) 15
(E) not enough information
261. Mark has a bag full of marbles. He decides to divide the group of marbles into
two parts, not necessarily equal, and then wants to divide the larger group in
half. At that moment he discovers that all the groups were left with the same
amount of marbles. The total number of marbles that Mark initially had can be?
(A) 31
(B) 37
(C) 43
(D) 49
(E) 54
262. Task 21. Which figure continues the sequence?
(A)
(B)
(C)
(D)
(E)
263. In a computer game, a regular ball with the value of 3 points appears on the
screen every 2s and remains there. Knowing that the game starts with one
regular ball on the screen, find out after how many seconds the total score of
the balls on the screen will be of 60 points?
(A) 60s
(B) 40s
(C) 38s
(D) 30s
(E) 20s
264. Two regular dice are tossed three times. If none of the numbers shown on the
top faces of the dice are repeated, then the sum of all these numbers will be:
(A) 36
(B) 21
(C) 14
(D) 26
(E) 42
100
Grade – 5 & 6
MATH KANGAROO WORK BOOK
265. Sofie wants to write the word KENGU by using letters from the boxes. She can
only take one letter from each box.
What letter must Sofie take from box 4?
(A) K
(B) E
(C) N
(D) G
(E) U
266. Lucy is older than Rio, but younger than Dana. Theresa is younger than Susan,
but older than Rio. Which of the girls is the youngest?
(A) Dana
(B) Theresa
(C) Susan
(D) Rio
(E) cannot determine with certainty
267. Adam glued together a house made of several equally sized cubes. The house
has one door and two windows - on the front and on the side wall (picture 1).
When viewed from above, the house looks like in picture 2. How many cubes
did Adam need to build the walls of the house?
(A) 122
(B) 130
(C) 136
(D) 142
(E) 154
268. For all her savings, Lucy can buy either her favorite almond chocolate bar or
five Violet chewing gums. The chocolate is 90 cents more expensive than three
chewing gums. How much does Lucy's favorite chocolate bar cost?
(A) 1.20 EUR
(B) 1.40 EUR
(C) 1.50 EUR (D) 1.80 EUR
(E) 2.25 EUR
269. Today is Thursday. What day will it be in a 100 days' time?
(A) Wednesday (B) Thursday
(C) Friday
(D) Saturday
(E) Sunday
270. Two neighboring switches can not be off at the same time. In how many ways
can a panel with four switches be set?
(A) 4
(B) 5
(C) 7
(D) 8
(E) 9
101
Grade – 5 & 6
MATH KANGAROO WORK BOOK
271. Which of these expressions gives the greatest value?
5
3
3
5
(A) 3 
(B) 4 
(C) 5 
(D) 4 
4
5
4
3
(E) 3 
4
5
272. In each of the cells of an 88 table is a light bulb. We say two light bulbs are
adjacent if they share a common side or vertex. In the beginning some of the
light bulbs are on. Each minute, every light bulb that has at least three adjacent
light bulbs that are on, turns on. a) Find the smallest number of light bulbs that
should be on from the beginning such that after some minutes all the light bulbs
will be turned on.
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
273. Mia is doing a project in which she decides to add up the ages of all the
students in her primary school. She finds that, at the beginning of Term 3, their
ages add up to exactly 2021. Approximately how many students are there in
Mia's school?
(A) 50
(B) 100
(C) 250
(D) 500
(E) 1000
274. Five friends decide to play some tennis matches one day. In each match, one of
them plays against another one. At the end of the day, they notice that each
person has played exactly one match against every other person. How many
matches were played that day between the five friends?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
275. Madeleine has a lot of $5 notes, $10 notes and $20 notes. She would like to
buy a guitar worth $95. What is the smallest number of notes that she would
need to pay for the guitar, without requiring any change?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
276. A regular hexagon has area 12. An equilateral triangle has the same perimeter
as the hexagon. What is the area of this triangle?
(A) 6
(B) 8
(C) 9
(D) 10
(E) 12
277. In a school are 4 classes. In class one, two and three there are on average 22
pupils. In all 4 classes together there are on average 20 pupils. How many
pupils are there in class 4?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
278. Consider a row of 9 consecutive multiples of 5. Their average is 45. What is the
largest of these multiples?
(A) 9
(B) 45
(C) 55
(D) 65
(E) 70
102
Grade – 5 & 6
MATH KANGAROO WORK BOOK
279. A prisoner wants to escape. He has to pass 9 doors, each locked with a
different key. From the guard he stole the 9 keys he needs, but he has mixed
them up. On his way out he tries the keys until a key fits. He then opens the
door and runs further, leaving the right key behind. How many keys must he trie
at most before he's out of prison?
(A) 1
(B) 9
(C) 44
(D) 45
(E) 81
280. A student took a test consisting of 4 questions each graded from 0 to 10. On
Question Number 3 he got 6 points. His average on the test was 9. How many
points did he get on Question Number 2?
(A) 7
(B) 8
(C) 9
(D) 10
(E) we do not have enough information to know.
281. Max folds a cube-shaped gift-box out of paper. He labels each side with a
number. He ties a string around the box and places it on a table. The face of the
cube with the number 3 lies on the surface of the table. He then ties the bow
above the top face of the cube. What number is the underneath the bow?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
282. With 10 cannon balls we build a triangular pyramid, as shown. Each cannon ball
has one of the letters A, B, C, D and E on it. There are 2 cannon balls for each
letter. The picture shows three side views of the pyramid. What is the letter on
the cannon ball with the question mark?
(A) A
(B) B
(C) C
(D) D
(E) E
103
Grade – 5 & 6
MATH KANGAROO WORK BOOK
283. The diagram shows three hexagons with numbers at their vertices, but some
are invisible. The sum of the six numbers of each hexagon is 30. What is the
number on the vertex marked with a question mark?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
284. A 4 x 3 x 2 cube is made up by white, grey and black 1 x 1 x 1 cubes, as
shown. The figures on the right show the white and the black parts of the cube.
Which of the following is the grey part?
(A)
(B)
(C)
(D)
(E)
285. Place four of the numbers 112, 121, 231, 321, 322 in the grid shown, with the
numbers crisscrossing as in a crossword. Which is the number not used?
(A) 112
(B) 121
(C) 231
(D) 321
(E) 322
104
Grade – 5 & 6
MATH KANGAROO WORK BOOK
286. A rectangle is divided into smaller ones, some of whose dimensions are shown.
What is the area of the shaded rectangle?
(A) 36m2
(B) 36m2
(C) 44m2
(D) 45m2
(E) 48m2
287. Claude's house is on a hill, 200 meters above the town where the school is
located. To go from his house to the school, Claude has to go up in one section
of the route for 50 meters and in another one for 25 meters; the rest of the route
is down. Altogether, when Claude goes to school and comes back home, for
how many meters does Claude walk uphill?
(A) 250
(B) 275
(C) 300
(D) 350
(E) 400
288. Four soccer teams play a tournament: each team plays exactly one time versus
any other team. In each game the winner team gets 3 points and the loser 0
points, while 1 point is given to each team in case of tie. Among the following
scores, which one is not possible?
(A) Three teams get 4 points each and one team 3 points.
(B) The four teams get 4 points each.
(C) The four teams get 3 points each.
(D) The last team gets 2 points, the last but one 3 points.
(E) Two teams get 7 point each, the other two 2 points each.
289. A chocolate cake weighs 112 g. The cake consists of 4 larger pieces. Each
larger piece can be divided into 4 smaller pieces. How much does a smaller
piece weigh?
(A) 112 g
(B) 28 g
(C) 16 g
(D) 7 g
(E) 4 g
290. Mr. Gordian had six pieces of string which he tied together using 4 knots, as
shown. Later Mt Gordian dropped his construction of the floor. Which of the
following is Mr. Gordian's construction?
105
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A)
(B)
(D)
(E)
(C)
291. A tomato contains 96% water. Nils cuts it into two halves. How many
percentages of water do one half of the tomato contain?
(A) 38%
(B) 48%
(C) 50%
(D) 94%
(E) 96%
292. Carin is going to paint the walls in her room green. The green paint is too dark
so she mixes it with white paint. She tries different mixtures. Which of the
following mixtures will have the darkest colour green?
(A) 1 part green + 3 parts white
(B) 2 parts green + 2 parts white
(C) 2 parts green + 6 parts white
(D) 3 parts green + 4 part white
(E) 3 parts green + 2 parts white
293. How many triangles are there in the following picture?
(A) 16
(B) 17
(C) 20
(D) 22
(E) 24
294. The picture shows a multiplication of a three digit number times 23. The result is
a four digit number but some figures are invisible. What is the sum of the four
digits of the result?
(A) 19
(B) 22
(C) 23
(D) 25
(E) 28
106
Grade – 5 & 6
MATH KANGAROO WORK BOOK
295. In total, on which of the following activities does Nancy spend the most time per
week with?
(A) hip hop dancing half an hour every Tuesday
(B) watching her favorite TV series on Fridays for 50 minutes
(C) brushing her teeth for 3 minutes twice every day
(D) preparing breakfast on weekend days for 20 minutes
(E) learning vocabulary for 15 minutes four times a week
296. I just dropped a round plate. It broke into four of the following five pieces. Which
of the following pieces is not one of them?
(A)
(B)
(D)
(E)
(C)
297. Leyla wrote down 9 computations. She wants to put them in the squares such
that there are three different results in each row and in each column. She
already put in 4 computations. Which of the 5 remaining computations must go
in the middle?
(A) 5  2
(B) 36 : 3
(C) 10 + 8
(D) 3  4
(E) 7 + 5
298. Tommy attached a 0 at the end of one of the following five numbers. He then
added the five numbers and got the result 2021. To which number did he attach
a 0?
(A) 143
(B) 144
(C) 145
(D) 146
(E) 147
299. After Luca had a shower, he wants to put on underpants, pants, a shirt and a
sweater. In how many different orders can Luca get dressed?
(A) 2
(B) 4
(C) 6
(D) 12
(E) 24
300. My little brother closed his bike lock with digits from 0 to 9 and turned each digit
in the same direction equally far. Now it shows the combination as shown.
107
Grade – 5 & 6
MATH KANGAROO WORK BOOK
Which of the following cannot be the right code of my brother's lock?
(A)
(B)
(C)
(D)
(E)
301. The weight of 7 bananas and 3 pears is 750 g. The weight of 3 pears and 7
bananas is 780 g. Each banana has the same weight, and each pear has the
same weight. What is the weight in grams of 1 banana and 1 pear together?
(A) 150
(B) 153
(C) 155
(D) 157
(E) 159
302. Adam, Bob, Celine, Daniel and Ellie have got animals. Each of the children has
got one animal, which is a chamster or a cat or a dog. Ellie does not have a
chamster and her animal is of different species as Daniel's animal. Bob has got
an animal of the same species as Adam has. Adam does not have neither a cat
nor a dog. Daniel and Celine have got animals of different species as Adam has
and the Celine's animal is not a cat. The children have got together
(A) 2 chamsters, 2 cats and 1 dog. (B) 3 chamsters, 1 cat and 1 dog.
(C) 1 chamster, 2 cats and 2 dogs. (D) 1 chamster, 1 cat and 3 dogs.
(E) 2 chamsters, 1 cat and 2 dogs.
303. On one side of the street the houses are numbered with odd numbers: 1,3, 5, 7,
... Renata's house is number 19 and is the nineteenth one on this side of the
street, counting from the last one. What's the last house number on this side of
the street?
(A) 55
(B) 51
(C) 49
(D) 39
(E) 37
304. It's been almost 1000 seconds that Romeo has been waiting for Juliet to
answer his sms. Approximately how long has Romeo been waiting?
(A) 1/4 h
(B) 1 h
(C) 1 day
(D) 1 week
(E) 1 month
305. What digit in place of T would make this sum true?
(A) 1
(B) 5
(C) 6
(D) 7
(E) 9
108
Grade – 5 & 6
MATH KANGAROO WORK BOOK
306. If we cut the year 2021 in the middle to have two numbers, then the second
number (21) immediately follows the first (20). How many years after 2021 will
we have this happen again?
(A) 10
(B) 11
(C) 100
(D) 101
(E) 202
307. A garden has the shape of a rectangle of dimensions 5m x 8m. A mouse walks
from corner A to corner B along the path shown. Every part of the path is
parallel to one of the sides. What is the length of the path?
(A) 20 m
(B) 22 m
(C) 24 m
(D) 26 m
(E) 28 m
308. We write a long number writing 2021, and after, successively, the whole
numbers 2022, 2023, 2024,... that is 20212022202320242025... What figure is
in the 2021st place of this number?
(A) 2
(B) 3
(C) 0
(D) 1
(E) 5
309. 2021 is a number where the addition of the two last digits is 1 unit higher than
the addition of the two first digits (from left to right), and the addition of all four
digits is 5. How many times does this property happen (both conditions at the
same time) during the 21st century? (From 2001 to 2100)
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
310. You can observe that the first odd number is 1 = 111; the sum of the two
next odd numbers is 3 + 5 = 2  2  2; after we can see that 7 + 9 + 11 = 3  3
 3, and so we can successively obtain all the cubes of natural numbers as the
sum of consecutive odd numbers. What will be the first of six consecutive odd
numbers that add up to 6  6  6?
(A) 31
(B) 33
(C) 29
(D) 35
(E) 21
311. At the map of a town there three bus stations at points A, B, C. A round trip
from station A to the Zoo and Port and back to A is 10 km long. A round trip
from station B to the Park and Zoo and back to B is 12 km long. A round trip
from station C to the Port and Park and back to C is 10 km long. Also A round
trip from the Zoo to the Park and Port and back to the Zoo is 15 km long. How
long is the round trip from A to B and C and back to A?
109
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) 18 km
(B) 20 km
(C) 25 km
(D) 35 km
(E) 50 km
312. Andy travels with Benny and Chris. Andy has two loaves, Benny has three
loaves and Chris has no loaves. They eat all these 5 loaves together. For the
bread he ate, Chris pays 10 euros to the other two travelers and they will share
their money according to how much bread Chris ate from each one. In this
case, Andy will receive ...
(A) 2 euros
(B) 3 euros
(C) 4 euros
(D) 5 euros
(E) 8 euros
313. A given whole number consists of two non-zero digits. If we subtract from this
number the number made of the same digits but reversed, we get a positive
difference that has the last digit 5. What is that difference?
(A) 25
(B) 35
(C) 45
(D) 55
(E) 65
314. There are 30 children in the first grade each 6 or 7 years old. The sum of the
ages of the teacher and all the children is 230. What cannot be teacher's age?
(A) 30
(B) 25
(C) 40
(D) 55
(E) 35
315. Consider the following rectangle. What percentage of the rectangle is covered
by the black triangle?
(A) 33.33 %
(B) 40 %
(C) 50 %
(D) 60 %
(E) 66.67 %
316. If you order the numbers according to size, which one is in the middle?
20
2
20
0
(A)  1
(B) 20.21
(C) 20 
(D)
(E) 2 
2
1
21
21
110
Grade – 5 & 6
MATH KANGAROO WORK BOOK
317. Each shelf holds a total of 64 deciliters of apple juice. The bottles have three
different sizes: large, medium and small. How many deciliters of apple juice
does a medium bottle contain?
(A) 3
(B) 6
(C) 8
(D) 10
(E) 14
318. Ronja and Wanja play a game: Both have four tokens each, Ronja white ones
and Wanja dark ones. They put down the token in alternation and form two
piles, Ronja begins. Which one of the situations did not result from such a
game?
(A)
(B)
(D)
(E)
(C)
319. The figure shows a toy with 8 connected gears of the same size that can all turn
at the same time. Each gear is formed by 8 equally spaced teeth. In one of the
gears you can see a triangle and in another one a hexagon. In the gear in the
lower left corner there is a guide represented by a black circle. If the gear with
the black circle is taken to the position
how will the triangle and hexagon
be seen in the toy?
(A)
(B)
(C)
(D)
(E)
111
Grade – 5 & 6
MATH KANGAROO WORK BOOK
320. The teacher wants to place the numbers 1 to 10 in the circles, one number per
circle. He wants the sum of the numbers in any four circles that are in a straight
line (as for example the yellow ones) to be 23. What number must he place at
the question mark on the central circle?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
321. The math kangaroo makes 1,000 jumps in one day from morning to evening.
When we start to count it from the morning 19. 3. 2021, so how many jumps will
he make by the end of the school year (until the last June including)?
(A) 101,000
(B) 102,000
(C) 103,000
(D) 104,000
(E) 105,000
322. Postal cars drive 55,000 km a day by daily distribution of newspapers. On
average, their cars consume 6 liters of diesel per 100 km. How much EUR per
day will they pass at the price of 1.1 EUR for 1 liter of diesel?
(A) 3,300
(B) 3,330
(C) 3,333
(D) 3,600
(E) 3,630
323. What is the first digit of the smallest positive integer whose sum of digits is
equal to 2021?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
324. Tom has two special dice with the following numbers on them: (1; 3; 5; 7; 9; 11),
(2; 4; 6; 8; 10; 12) . He throws them together once and adds the numbers. How
many ways can he get a sum of 13?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
325. There is a group of pupils in the room. 1/3 of them wears a red shirt, 1/4 have a
green shirt and 1/6 have a yellow shirt. Which of these could NOT be the total
number of pupils in the room?
(A) 12
(B) 24
(C) 30
(D) 36
(E) 48
112
Grade – 5 & 6
MATH KANGAROO WORK BOOK
326. The positive integer n has four digits and 2 − 1 is the four digit number
obtained by reversing the order of the digits in n. Which one is the sum of the
digits of ?
(A) 18
(B) 22
(C) 24
(D) 28
(E) 32
327. In a chess tournament with only 4 players, every player plays with another one
exactly once. If a player wins, he collects 2 points; if he looses, he doesn't get
any points; in case of a draw he gets 1 point. All players collected at least 1
point and all of them have different scores. How many points did the last but
one ranked player collect?
(A) 1
(B) 2
(C) 3
(D) 4
(E) Its not possible to solve
328. Let ABC be three digit number with A is smaller than B and B is smaller than C.
How many ABC numbers are there satisfying the condition A + B + C = 13?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
329. A child which wants to learn the age of his grandfather’s age asked the
following a question: - Hey grandpa, how many years are you older than me?
And his grandfather answered: - well, I lived many years as you lived as
months. If their ages sum is 91 find the age of the grandson.
(A) 6
(B) 7
(C) 8
(D) 9
(E) 12
330. A three side of a six-sided special dice shown in the figure. The numbers on this
dice are given integer and different from each other. If the numbers on the
opposite sides of this dice are equal to each other then which one of the
followings can be the other picture of this dice?
(A)
(B)
(D)
(E)
(C)
331. The square is divided into six equal size white squares and two equal size black
squares, and another grey shape as shown in the figure. The sum of the areas
of the white squares is 24 cm2 and the circumference of the grey shape is 36
cm. Find the area of one black square.
113
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) 16 cm2
(B) 17 cm2
(C) 18 cm2
(D) 24 cm2
(E) 25 cm2
332. There were five white fences of the same fence pickets, but of different lengths.
Five boys started to paint fences grey on one side at the same moment, each
painting a different fence. Some time later, pictures of all the fences were taken
at the same time, as shown in the picture. Who finishes painting his fence first?
(A) Alex
(B) Bruno
(C) Carl
(D) Denis
(E) Evan
333. In how many different ways can you make a rectangle out of 100 identical
squares?
(A) 1
(B) 4
(C) 5
(D) 8
(E) 9
334. The distance from city A to city B by air is 30 km, from B to C is 80 km, from C
to D is 236 km, from D to E is 86 km, from D to A is 40 km. What is distance
from C to E?
(A) 70 km
(B) 110 km
(C) 150 km
(D) 322 km
(E) 472 km
335. Four points are on a line as shown in the figure. It is known that AC = 10 cm,
BD = 15 cm, AD = 22 cm. Find BC.
(A) 1 cm
(B) 2 cm
(C) 3 cm
(D) 4 cm
(E) 5 cm
336. How many different results can you get if you add some two different of the
numbers 1, 2, 3, ..., 10?
(A) 20
(B) 19
(C) 18
(D) 17
(E) 12
337. 2021 is a product of two consecutive primes. What is their sum?
(A) 78
(B) 84
(C) 88
(D) 90
(E) 100
338. If you get two containers without scale of volume 12L and 15L respectively.
Which of the following amount of water CANNOT be measured using these two
containers?
(A) 3L
(B) 27L
(C) 45L
(D) 60L
(E) 64L
114
Grade – 5 & 6
MATH KANGAROO WORK BOOK
339. Ms. Wong's class has more than 30 and less than 40 students. which of the
following ratios CANNOT be the number of boys to the number of girls in this
class?
(A) 2 : 3
(B) 3 : 4
(C) 3 : 6
(D) 4 : 7
(E) 3 : 7
340. Among the first 100 integers from 1 to 100, how many of them have the sum of
digits be a multiple of 5?
(A) 6
(B) 10
(C) 15
(D) 16
(E) 20
341. You have a supply of boxes of volumes 1; 3; 9; 27 and 81 cubic meters. Given
that the box must be filled completely, what is the least number of boxes that
will hold exactly 2020 cubic meters of sand?
(A) 24
(B) 25
(C) 26
(D) 28
(E) 30
342. 20 people have gathered in a room. At least one of them is a woman. Also, one
in every two randomly selected people is a man. How many men are there in
that room?
(A) 10
(B) 9
(C) 19
(D) 13
(E) Cannot be determined from the information given.
343. Niloufar, Fatemeh, Shima, and Neda are going on a trip together. They have
agreed to split the costs evenly. At the end of the trip, Niloufar has spent
1520000 Tomansand Fatemeh has spent 50000 Tomans. How much should
Fatemeh and Shima respectively payto Niloufar? (Toman is the currency in their
country.)
(A) 392500 and 342500
(B) 342500 and 392500
(C) 380000 and 330000
(D) 330000 and 380000
(E) 342500 and 330000
344. It takes 15 minutes to get to the bus stop from Sara's house. The first bus
arrives to the stop at 8:00 and returns to the same stop every 30 minutes. Sara
wakes up at 8:30. If it takes her 30 minutes to eat breakfast and 20 minutes to
get ready, which bus can she take?
(A) The fifth bus
(B) The second bus
(C) The third bus
(D) The fourth bus
(E) The fifth bus
345. The following digits are 0 to 9 which are used in some of the countries like Iran
for writing numbers.
Which one of the following 5-digit numbers, when mirrored, is still a number?
115
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A)
(B)
(C)
(D)
(E)
346. George has more money than Peter and more comfort than Sara. Peter has
more comfort than George and less money than Sara. Which statement is
certainly true?
(A) Sara has the least money.
(B) George has the least comfort.
(C) George has the most money.
(D) Peter has the most comfort.
(E) George has the least comfort.
347. Numbers 1 to 7 are put in the following squares in a way that the sum of the
numbers in the row and column are both equal to 17. What number should be
put in the square with *?
(A) 1
(B) 3
(C) 6
(D) 4
(E) 2
348. Maryam has a rectangular cube of cheese (see the picture).
She then cuts a layer of cheese with a thickness of 1 cm. She does this
precisely and with the intention of cutting the most amount of cheese with one
move. Which statement is true?
(A) The length of the cube has decreased.
(B) The width of the cube has decreased.
(C) The height of the cube has decreased.
(D) The length and height of the cube has decreased.
(E) The length and height of the cube has decreased.
116
Grade – 5 & 6
MATH KANGAROO WORK BOOK
349. A car arrives at the gas station with its last drops of gas and gets 45 liters of
gas. If the capacity of the gas tank is 60 liters and the indicator is precise, how
many degrees will it turn?
(A) 80 to 90
(E) 80 to 90
(B) 50 to 60
(C) 60 to 70
(D) 80 to 90
350. There are 5 cards, on back of which one of the numbers 7, 5, 3, 0, and 9 are
written. We don't know which card has which number. We turn all 5 cards
randomly. By putting them beside each other, which of the following numbers
would be impossible to get and certain to get accordingly?
(A) A 4-digit number and a 5-digit number.
(B) A number divisible by 5 and a 5-digit number.
(C) A number divisible by 5 and a number divisible by 9.
(D) A number divisible by 9 and a number divisible by 3.
(E) A 4-digit number and a 5-digit number.
351. Seven students got on a Ferris wheel on a class trip and each one sat alone in
a separate cabin. Two of them are twin brothers. Which statement is true?
(A) None of the students are in relation to the center of the wheel.
(B) Some of the students are symmetrical two by two in relation to the center of
the wheel.
(C) All of the students but one are symmetrical two by two in relation to the
center of the wheel.
(D) Only the twin brothers may be symmetrical in relation to the center of the
wheel.
(E) None of the students are in relation to the center of the wheel.
117
Grade – 5 & 6
MATH KANGAROO WORK BOOK
352. The following square is consisted of 7 shapes. They are known as the seven
pieces of Tangram.
We have made a rabbit with these seven pieces.
With at least how many right angle triangles with desired size would cover this
rabbit?
(A) 11
(B) 12
(C) 15
(D) 16
(E) 17
353. How many rectangles are there in the following shape?
(A) 14
(B) 15
(C) 17
(D) 19
(E) 21
354. Maryam has separated her books into three sizes of tall, medium, and short and
wants to arrange them in her shelf from left to right and tallest to shortest. In
each move, she can only change the position of two books by each other. What
is the minimum number of moves that are needed in order to arrange the book
shelf?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
118
Grade – 5 & 6
MATH KANGAROO WORK BOOK
355. Sina wants to take a picture of his friends who are standing as shown in the
image below, but he wants to arrange them in a way that his shortest friend is
on the left side and his tallest friend is on the right side. He moves from left to
right and switches the place of his friends only if the person on the right is
shorter than the one on the left. When he gets to the last person, he will begin
doing this again from the left. How many switches should he make?
(A) 13
(B) 10
(C) 11
(D) 12
(E) 13
356. 98% of Robin Hood's arrows hit the target. How many arrows does he have to
shoot so that exactly 10 of them do not hit the target?
(A) 200 arrows
(E) 1000 arrows
(B) 200 arrows
(C) 500 arrows
(D) 500 arrows
357. How many rectangles (that are not squares) are there without any marks on
them?
(A) 42
(B) 40
(C) 38
(D) 36
(E) 34
119
Grade – 5 & 6
MATH KANGAROO WORK BOOK
1.
Different figures represent the different digits. Find the digit corresponding to
the square.
(A) 9
(B) 8
(C) 7
(D) 6
2.
In a trunk there are 5 chests, in each chest there are 3 boxes, and in each box
there are 10 gold coins. The trunk, the chests, and the boxes are locked. How
many locks must be opened in order to get 50 coins?
(A) 5
(B) 7
(C) 8
(D) 9
3.
A caterpillar starts from his home and move directly on a ground, turning after
each hour at 90° to the left or to the right. In the first hour he moved 1 m, in the
second hour 2 m, and so on. At what minimum distance from his home the
caterpillar would be after six hours traveling?
(A) 0 m
(B) 1 m
(C) 1.5 m
(D) 2.5 m
4.
The sum of ten distinct positive numbers is 100. The largest of these numbers
can be:
(A) 10
(B) 13
(C) 55
(D) 60
5.
A rod of length 15 dm was divided into the greatest possible number of pieces
of different integer lengths in dm. The number of cuts is:
(A) 2
(B) 3
(C) 4
(D) 5
6.
A river goes through a city and there are two islands. There are also six bridges
as shown in the figure. How many paths there are going out of a shore of the
river (point A) and come back (to point B) after having spent one and only one
time for each bridge?
120
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) 0
7.
(B) 2
(C) 4
(D) 6
In which of triples the central number is strictly in the middle between two
others.
(A) , ,
(B) 12, 21, 32
(C) 3, 7, 13
(D) ,
,
8.
What is the smallest number of dots that need to be removed from
the pattern shown, so that no three of the remaining dots are at
the vertices of an equilateral triangle?
(A) 2
(B) 3
(C) 4
(D) 5
9.
Iqra is 10 years old. Her mother Asma is 4 times as old. How old will Asma be
when Iqra is twice as old as she is now?
(A) 40 years
(B) 70 years
(C) 60 years (D) 50 years
10. To the right side of a given 2-digit number we write the same number obtaining
4-digit number. How many times the 4-digit number is greater than the 2-digit
number?
(A) 100
(B) 101
(C) 10
(D) 11
11. Ahmed thought of an integer. Umar multiplied it either by 5 or by 6. Ali added to
the Umar’s result either 5 or 6. Tahir subtracted from Ali’s result either 5 or 6.
The obtained result was 73. What number did Ahmed think of?
(A) 10
(B) 11
(C) 12
(D) 14
12. The multiplication
uses each of the digits 1 to 9 exactly once. What is digit Y?
(A) 5
(B) 4
(C) 1
(D) 8
13. One of the cube faces is cut along its diagonals (see the fig.). Which of the
following nets are impossible?
1
(A) 1 and 3
(B) 1 and 5
(C) 3 and 4
(D) 3 and 5
121
Grade – 5 & 6
MATH KANGAROO WORK BOOK
14. Seven cards lie in a box. Numbers from 1 to 7 are written on these cards
(exactly one number on the card). Two persons take the cards as follows: The
first person takes, at random, 3 cards from the box and the second person
takes 2 cards (2 cards are left in the box). Then the first person tells the second
one: “I know that the sum of the numbers of your cards is even”. The sum of
card’s numbers of the first person is equal to
(A) 10
(B) 12
(C) 6
(D) 9
15. For each 2-digit number from 30 to 50, the digit of units was subtracted from the
digit of tens. What is the sum of all the results?
(A) 0
(B) 15
(C) – 5
(D) – 15
16. How many digits can be at most erased from the 1000-digit number 2008 2008
… 2008, such that the sum of the remaining digits is 2008?
(A) 260
(B) 510
(C) 746
(D) 1020
17. The picture shows a balanced mobile. We neglect weights of
horizontal bars and vertical strings. The total weight is 112
grams. What is the weight of the star?
(A) 7
(B) 12
(C) 16
(D) We can’t know.
18. A pizza-shop offers a basic version of pizza with mozzarella and tomatoes. One
or two toppings must be added: anchovies, artichokes, mushrooms, capers.
Moreover, for each pizza three different sizes are available: small, medium,
large. How many different types of pizza are available at all?
(A) 30
(B) 12
(C) 18
(D) 48
19. A jeweller makes chains by connecting identical grommets (picture 1).
Proportions of grommets are shown on picture 2. What is the length of a chain
which consists of 5 grommets?
(A) 20 mm
(B) 19 mm
(C) 17.5 mm
(D) 16 mm
122
Grade – 5 & 6
MATH KANGAROO WORK BOOK
20. Zoha has wound some rope around a piece of wood. She rotates the wood as
shown with the arrow. What is the correct back side of the piece of wood? Back
side:
Front side
(A)
(B)
(C)
(D)
21. There are 10 pupils in a dance class. Their teacher has 80 jelly beans. After she
gives the same number of jelly beans to each of the girls in the class, there are
3 jelly beans left over. How many boys are there in the class?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
22. A cat has 7 differently-coloured kittens: white; black; red; black & white; red &
white; black & red; and white, black & red. How many ways are there to put 4
kittens in a basket so that every pair in the basket has at least one colour in
common?
(A) 1
(B) 3
(C) 4
(D) 6
(E) 7
23. The picture shows four identical right-angled triangles inside a rectangle. What
is the total area of all four triangles?
(A) 46 cm2
(E) 64 cm2
(B) 52 cm2
(C) 54 cm2
(D) 56 cm2
24. Alex says Pelle is lying. Pelle says Mark is lying. Mark says Pelle is lying. Tony
says Alex is lying. How many of these four boys are lying?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
123
Grade – 5 & 6
MATH KANGAROO WORK BOOK
25. Lina has fixed two shapes on a 5 × 5 board, as shown in the
picture. Which of the following 5 shapes should she place on
the empty part of the board so that none of the remaining 4
shapes will fit in the empty space that is left? (The shapes
may be rotated or turned over, but can only be placed so
that they cover complete squares.)
(A)
(B)
(C)
(D)
(E)
26. The picture shows three identical dice stacked on top of each other. For each
die, the total number of pips on every pair of opposite faces is 7. The stack was
made so that the sum of the pips on every pair of faces that meet is 5. How
many pips are on the face marked X?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
27. I want to draw four circles on the blackboard so that every pair of circles has
exactly one common point. What is the greatest number of points that can
belong to more than one circle?
(A) 1
(B) 4
(C) 5
(D) 6
(E) 8
28. In a particular month there were 5 Saturdays and 5 Sundays, but only 4 Fridays
and 4 Mondays. In the next month there were
(A) 5 Wednesdays(B) 5 Thursdays (C) 5 Fridays (D) 5 Saturdays
(E) 5 Sundays
124
Grade – 5 & 6
MATH KANGAROO WORK BOOK
29. You are given four positive numbers a, b, c and d in ascending order of size.
You are asked to increase one of them by 1 in such a way that the product of
the four resulting numbers is as small as possible. Which number should you
increase?
(A) a
(B) b
(C) c
(D) d
(E) Either b or c
30. The digits of a positive five-digit number are 1, 2, 3, 4, 5 in some order. The first
digit of the number is divisible by 1, the first two digits (in order) form a number
divisible by 2, the first three digits (in order) form a number divisible by 3, the
first four digits (in order) form a number divisible by 4, and the whole number is
divisible by 5. How many such numbers are there?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 10
31. Winnie’s vinegar-wine-water marinade contains vinegar and wine in the ratio 1
to 2, and wine and water in the ratio 3 to 1. Which of the following statements is
true?
(A) There is more vinegar than wine.
(B) There is more wine than vinegar and water together.
(C) There is more vinegar than wine and water together.
(D) There is more water than vinegar and wine together.
(E) There is less vinegar than either water or wine.
32. Kangaroos Hip and Hop play jumping by hopping over a stone, then landing
across so that the stone is in the middle of the segment traveled during each
jump. Picture 1 shows how Hop jumped three times hopping over stones
marked 1, 2 and 3. Hip has the configuration of stones marked 1, 2 and 3 (to
jump over in this order), but starts in a different place as shown on Picture 2.
Which of the points A, B, C, D or E is his landing point?
(A) A
(B) B
(C) C
(D) D
(E) E
125
Grade – 5 & 6
MATH KANGAROO WORK BOOK
33. There were twelve children at a birthday party. Each child was either 6, 7, 8, 9
or 10 years old, with at least one child of each age. Four of them were 6 years
old. In the group the most common age was 8 years old. What was the average
age of the twelve children?
(A) 6
(B) 6.5
(C) 7
(D) 7.5
(E) 8
34. Rectangle ABCD is cut into four smaller rectangles, as shown in the figure. The
four smaller rectangles have the properties: (a) the perimeters of three of them
are 11, 16 and 19;(b) The perimeter of the fourth is neither the biggest nor the
smallest of the four. What is the Perimeter of the original rectangle ABCD?
(A) 28
(B) 30
(C) 32
(D) 38
(E) 40
35. Kanga wants to arrange the twelve numbers from 1 to 12 in a circle such that
any neighbouring numbers always differ by either 1 or 2. Which of the following
pairs of numbers have to be neighbours?
(A) 5 and 6
(B) 10 and 9
(C) 6 and 7
(D) 8 and 10
(E) 4 and 3
36. Peter wants to cut a rectangle of size 6 × 7 into squares with integer sides.
What is the minimal number of squares he can get?
(A) 4
(B) 5
(C) 7
(D) 9
(E) 42
37. Some cells of the square table of size 4 × 4 were colored red. The number of
red cells in each row was indicated at the end of it, and the number of red cells
in each column was indicated at the bottom of it. Then the red colour was
eliminated. Which of the following tables can be the result?
(A)
(B)
(C)
(D)
(E)
126
Grade – 5 & 6
MATH KANGAROO WORK BOOK
38. A square-shaped piece of paper has area 64 cm2. The square is folded twice as
shown in the picture. What is the sum of the areas of the shaded rectangles?
(A) 10 cm2
(B) 14 cm2
(C) 15 cm2
(D) 16 cm2
(E) 24 cm2
39. Abid’s house number has 3 digits. Removing the first digit of Abid’s house
number, you obtain the house number of Ben. Removing the first digit of Ben’s
house number, you get the house number of Chiara. Adding the house
numbers of Abid, Ben and Chiara gives 912. What is the second digit of Abid’s
house number?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 0
40. I give Ann and Bill two consecutive positive integers (for instance Ann 7 and Bill
6). They know their numbers are consecutive, they know their own number, but
they do not know the number I gave to the other one. Then I heard the following
discussion: Ann said to Bill: ”I don’t know your number”. Bill said to Ann: ”I don’t
know your number”. Then Ann said to Bill: ”Now I know your number! It is a
divisor of 20.”. What is Ann’s number?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
41. Aron, Bern and Carl always lie. Each of them owns one stone, either a red
stone or a green stone. Aron says: “My stone is the same color as Bern’s
stone”, Bern says: “My stone is the same color as Carl’s stone”. Carl says:
“Exactly two of us own red stones”. Which of the following statements is true?
(A) Aron’s stone is green.
(B) Bern’s stone is green.
(C) Carl’s stone is red.
(D) Aron’s stone and Carl’s stone have different colors
(E) None of the above is true.
42. 66 cats signed up for the contest MISS CAT 2013. After the first round 21 were
eliminated because they failed to catch mice. 27 cats out of those that remained
in the contest had stripes and 32 of them had one black ear. All striped cats
with one black ear got to the final. What is the minimum number of finalists?
(A) 5
(B) 7
(C) 13
(D) 14
(E) 27
43. There are four buttons in a row as shown below. Two of them show happy
faces, and two of them show sad faces. If we press on a face, its expression
turns to the opposite (e.g. a funny face turns into a sad face after the touch). In
addition to this, the adjacent buttons also change their expressions. What is the
least number of times you need to press the buttons in order to get all happy
faces?
127
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
44. 40 boys and 28 girls stand in a circle, hand in hand, all facing inwards. Exactly
18 boys give their right hand to a girl. How many boys give their left hand to a
girl?
(A) 18
(B) 9
(C) 28
(D) 14
(E) 20
45. A 2 × 2 × 2 cube is to be constructed using 4 white and 4 black unit cubes. How
many different cubes can be constructed in this way? (Two cubes are not
different if one can be obtained by rotating the other.)
(A) 16
(B) 9
(C) 8
(D) 7
(E) 6
46. How many 3-digits numbers possess the following property: after subtracting
297 from such a number, we get a 3-digit number consisting of the same digits
in the reverse order?
(A) 6
(B) 7
(C) 10
(D) 60
(E) 70
47. When Matthew and Marten found their old model railway, Matthew quickly
made a perfect circle from 8 identical track parts, Marten starts to make another
track with two of these pieces as shown in the picture. He wants to use as few
pieces as possible to make a closed track. How many pieces does his track
consist of?
(A) 11
(B) 12
(C) 14
(D) 15
(E) 16
48. There were 2013 inhabitants on an island. Some of them were knights and the
others were liars. The knights always tell the truth and the liars always lie.
Every day, one of the inhabitants said: ”After my departure the number of
knights on the island will equal the number of liars” and then left the island.
After 2013 days there was nobody on the island. How many liars were there
initially?
(A) 0
(B) 1006
(C) 1007
(D) 2013
(E) It is impossible to determine.
128
Grade – 5 & 6
MATH KANGAROO WORK BOOK
49. Starting with a list of three numbers, the ”changesum” procedure creates a new
list by replacing each number by the sum of the other two. For example, from
{3, 4, 6} ”changesum” gives {10, 9, 7} and a new ” changesum” leads to {16, 17,
19}. If we begin with the list {20, 1, 3}, what is the maximum difference between
two numbers of the list after 2013 consecutive ”changesums”?
(A) 1
(B) 2
(C) 17
(D) 19
(E) 2013
50. Alice forms 4 identical numbered cubes using the net shown. She then glues
them together to form a 2 × 2 × 1 block, as shown. Only faces with identical
numbers are glued together. Alice then finds the total of all the numbers on the
surface of the block. What is the largest total that Alice can get?
(A) 66
(B) 68
(C) 72
(D) 74
(E) 76
51. The 3 × 3 × 3 cube in the picture is made of 27 small cubes.
How many small cubes do you have to take away to see the following result
when looking from the right, from above, and from the front?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
52. There are 5 songs: song A lasts 3 min, song B 2 min 30 s, song C 2 min, song
D 1 min 30 s, and song E 4 min. These 5 songs are playing in the order A, B, C,
D, E in a loop without any breaks. Song C was playing when Andy left home.
He returned home exactly one hour later. Which song was playing when Andy
got home?
(A) A
(B) B
(C) C
(D) D
(E) E
129
Grade – 5 & 6
MATH KANGAROO WORK BOOK
53. Dan entered the numbers 1 to 9 in the cells of a 3x3 table. He began by placing
the numbers 1, 2, 3 and 4 as shown in the picture. It happened that for the
number 5, the sum of the numbers in the adjacent cells (having a common side)
is equal to 9. What is the sum of the numbers adjacent to the number 6?
(A) 14
(B) 15
(C) 17
(D) 28
(E) 29
54. Trees grow on only one side of Park Avenue. There are 60 trees in total. Every
second tree is a maple, and every third tree is either a linden or a maple. The
remaining trees are birches. How many birches are there?
(A) 10
(B) 15
(C) 20
(D) 24
(E) 30
55. A thin colourful ribbon is stuck on a transparent plastic cube (see
the picture). Which of the following pictures doesn’t show the
cube from any perspective?
(A)
(B)
(D)
(E)
(C)
56. The king and his messengers are travelling from the castle to the summer
palace at a speed of 5 km/h. Every hour, the king sends a messenger back to
the castle, who travels at a speed of 10 km/h. What is the time interval between
any two consecutive messengers arriving at the castle?
(A) 30 min
(B) 60 min
(C) 75 min
(D) 90 min
(E) 120 min
57. There were 3 one-digit numbers on the blackboard. Ali added them up, and got
15. Then he erased one of the numbers and wrote the number 3 in its place.
Then Reza multiplied the three numbers on the blackboard and got 36. What
are the possibilities for the number that Ali erased?
(A) Either 6 or 7 (B) Either 7 or 8 (C) Only 6
(D) Only 7
(E) Only 8
58. Rabbit Vasya loves cabbages and carrots. In a day, he eats either 9 carrots, or
2 cabbages, or 1 cabbage and 4 carrots. But some days he only eats grass.
Over the last 10 days, Vasya ate a total of 30 carrots and 9 cabbages. On how
many of these 10 days did he eat only grass?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
130
Grade – 5 & 6
MATH KANGAROO WORK BOOK
59. In Fabul and, every sunny day is immediately preceded by two consecutive
rainy days. Also, five days after any rainy day, it is another rainy day. It is sunny
today. For how many days at most can we predict the weather with certainty?
(A) 1 day
(B) 2 days
(C) 4 days
(D) We cannot predict even one day ahead
(E) We can predict the weather every day from here on
60. Granny has 10 grandchildren. Alice is the eldest. One day, Granny notices that
her grandchildren all have different ages. If the sum of her grandchildren’s ages
is 180, what is the youngest Alice could be?
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
61. In this sum, equal letters represent equal digits, and different letters represent
different digits. Which digit is represented by the letter X?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
62. Jane bought 3 toys. For the first toy she paid half of her money and EUR1
more. For the second toy she paid half of the remaining money and EUR2
more. Finally, for the third toy she paid half of the remaining money and EUR3
more, thus spending all of her money. How much money did she have initially?
(A) EUR36
(B) EUR45
(C) EUR34
(D) EUR65
(E) EUR100
63. Carla wants to fold a cube from a paper net. By mistake she drew 7 squares on
her sheet instead of 6 squares. Which square can she remove so that the figure
remains connected and Carla can fold a cube from it?
(A) Only 4
(B) only 7
(E) Only 3, 4 or 7
(C) only 3 or 4
(D) only 3 or 7
64. The number 100 is multiplied either by 2 or by 3, then the result is increased
either by 1 or by 2, and then the new result is divided either by 3 or by 4. The
final result is a natural number. What is this final result?
(A) 50
(B) 51
(C) 67
(D) 68
(E)There is more than one possible final result.
131
Grade – 5 & 6
MATH KANGAROO WORK BOOK
65. In a 4-digit number ABCD, the digits A, B, C and D are in increasing order from
left to right. What is the largest possible difference BD − AC of the 2-digit
numbers BD and AC?
(A) 86
(B) 61
(C) 56
(D) 50
(E) 16
66. Mary writes a number on each face of a cube. Then, for each vertex, she adds
the numbers on the three faces which share that vertex (for example, for vertex
B she adds the numbers on faces BCDA, BAEF and BFGC). The numbers
computed by Mary for vertices C, D and E are 14, 16 and 24, respectively.
What number does she compute for vertex F?
(A) 15
(B) 19
(C) 22
(D) 24
(E) 26
67. A train has 12 coaches. Each coach has the same number of compartments.
Mike is travelling in the third coach and in the 18th compartment from the
engine. Jane sat in the 7th coach in the 50th compartment from the engine. How
many compartments are there in each coach?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 12
68. In how many ways can you place the 3 kangaroos in 3 different cells so that no
2 kangaroos are neighbours?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
69. Four points lie on a line. The distances between them are, in increasing order:
2, 3, k, 11, 12, 14. What is k?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
70. Basil used small cubes with side 1 to construct a cube with side 4. After that,
he painted 3 faces of the big cube red and the other 3 faces blue. After he
finished, there was no small cube with 3 red faces. How many small cubes
have both red and blue faces?
(A) 0
(B) 8
(C) 12
(D) 24
(E) 32
132
Grade – 5 & 6
MATH KANGAROO WORK BOOK
71. Anna folds a round sheet of paper at the middle. Then she folds it once more
and then one last time.
In the end Anna cuts the folded paper along the marked line:
What is the shape of the middle part of the paper when unfolded?
(A)
(B)
(C)
(D)
(E)
72. Richard writes down all the numbers with the following properties: The first digit
is 1, each of the following digits is at least as big as the one before it, the sum
of the digits is 5. How many numbers does hewrits?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
73. What is the greatest number of shapes of the form
from a 5 5 square?
(A) 2
(B) 4
(C) 5
that can be cut out
(D) 6
(E) 7
74. Luigi started a small restaurant. His friend Giacomo gave him some square
tables and chairs. It he uses all the tables as single tables with 4 chairs each,
he would need 6 more chairs. If he uses all the tables as double tables with 6
chairs each, he would have 4 chairs left over. How many tables did Luigi get
from Giacomo?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
133
Grade – 5 & 6
MATH KANGAROO WORK BOOK
75. Clara wants to construct a big triangle using identical small triangular tiles. She
has already put some tiles together as shown in the picture. How many tiles
does she need to complete a triangle?
(A) 5
(B) 9
(C) 12
(D) 15
(E)
18
76. A big cube was built from 8 identical small cubes, some black ones and white
ones. Five faces of the big cube are:
What does the sixth face of the big cube look like?
(A)
(B)
(C)
(D)
(E)
77. Kirsten wrote number is 5 of the 10 circles as show in the figure. She wants to
write a number in each of the remaining 5 circles such that the sums of the 3
numbers along each side of the pentagon are equal. Which number will she
have to write in the circle marked by x?
(A) 7
78. The symbols
the 3-digit number
(B) 8
and
(C) 11
(D) 13
(E) 15
represent 3 different digits. If you add the digit of
the result is the 2-digit number
add the digits of the 2-digit number
Which digit does
represent?
(A) 4
(B) 5
if you
, you find the 1-digit number
(C) 6
(D) 8
.
(E) 9
134
Grade – 5 & 6
MATH KANGAROO WORK BOOK
79. A little Kangaroo is playing with his calculator. He starts with the number 12. He
multiplies or divides the number by 2 or 3 (if possible) 60 times in a row. Which
of the following results cannot be obtained?
(A) 12
(B) 18
(C) 36
(D) 72
(E) 108
80. Two 3-digit number have all their 6 digits distinct. The first digit of the second
number is twice the last digit of the first number. What is the smallest possible
sum of the such number?
(A) 552
(B) 546
(C) 301
(D) 535
(E) 537
81. Three plates, A, B, and C are arranged in increasing order of their weight.To
keep this order, plate D must be placed:
(A) Between A and B
(C) Before A
(E) D and C have the same weight
(B) between B and C
(D) After C
82. What is the maximum value of the sum of the digits of the sum of the digits of a
three-digit number?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 18
83. Five boys weighed themselves in pairs in all possible combinations. The
measured weights were 90kg, 92kg, 93kg, 94kg, 95kg, 96kg, 97kg, 98kg,
100kg and 101kg. The total weight of the five boys was:
(A) 225 kg
(B) 230 kg
(C) 239 kg
(D) 240 kg
(E) 250 kg
84. In a children's game you count from 1 to 100 and applaud every time that you
find either a multiple of 3 or a number ending with 3. How many times are you
supposed to applaud?
(A) 30
(B) 33
(C) 36
(D) 39
(E) 43
85. One cat and a half eat one mouse and a half in one hour and a half. How many
mice can 15 cats eat in 15 hours?
(A) 15
(B) 45
(C) 60
(D) 125
(E) 150
86. Magician Anthony has in his magic hat 14 grey, 8 white and 6 black mice. What
is the least number of mice he has to take out of his hat blindfolded to be
absolutely certain that he has got at least one mouse of each colour?
(A) 23
(B) 22
(C) 21
(D) 15
(E) 9
87. A circle, a square, and a triangle are drawn overlapping on the plane. What is
the maximum possible number of intersection points determined by these three
figures?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
135
Grade – 5 & 6
MATH KANGAROO WORK BOOK
88. In a basketball tournament 32 teams are competing. At each stage the teams
are divided into groups of 4. In each group every team plays once against every
other team. The best two teams are qualified for the next round. The other two
teams are eliminated. After the last stage the two remaining teams play one
final match to determine the winner. How many matches will be played in the
whole tournament?
(A) 49
(B) 89
(C) 91
(D) 97
(E) 181
89. Square ABCD is comprised of one inner square (white) and four coloured
congruent rectangles. Each coloured rectangle has a perimeter of 40 cm. What
is the area of square ABCD?
(A) 400 cm2
(E) 80 cm2
(B) 200 cm2
(C) 160 cm2
(D) 100 cm2
90. What date will it be exactly 2003 minutes after 20-03-2003 at 20:03
(A) 21-03-2003
(B) 22-03-2003
(C) 23-03-2003 (D) 21-04-200
(E) 22-04-2003
91. A barcode is formed by 17 black bars and white bars between them (the first
and the last bar is black). There are two types of black bars:
wide and narrow. The number of white bars is 3 more than the
number of wide black bars. The number of narrow black bars
is:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
92. A cylindrical glass that is 10cm high is partially filled with water. You see the
glass in two positions. What is the height of the water when the glass is
upright?
(A) 3cm
(B) 4cm
(C) 5cm
(D) 6cm
(E) 7cm
93. You have six sticks of lengths 1 cm, 2 cm, 3 cm, 2001 cm, 2002 cm and 2003
cm. You have to choose three of these sticks and form a triangle. How many
different choices of three sticks are there which work?
(A) 1
(B) 3
(C) 5
(D) 6
(E) More than 50
136
Grade – 5 & 6
MATH KANGAROO WORK BOOK
94. Use the diagram:
What is the length of the broken line from A to B?
(A) 10200 cm
(B) 2500 cm
(C) 909 cm (D) 10100 cm (E) 9900 cm
95. Here is one addition example: each shape replaces a digit, different shapes
replace different digits and same shapes replace the same digit. What is the
sum of the "square" and the "circle"?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 13
96. The figure on the drawing consists of five isosceles right
triangles of equal size. Find the area of the shaded
figure.
(A) 20 cm2
(B) 25 cm2
(C) 35 cm2
(D) 45 cm2
(E) cannot be determined
97. In the diagram drawn on the square grid, find the ratio of the
unshaded area to the shaded area.
(A)
(B)
(D)
(E)
(C)
98. Ella and Emma went mushrooming. They found 70 mushrooms. of the
mushrooms Ella found were boletuses, and
of the mushrooms Emma has
found were orange-caps. How many mushrooms did Ella find?
(A) 27
(B) 36
(C) 45
(D) 54
(E) 10
99. In the picture we have 11 fields. In the first field there is a 7, and in the ninth
field we have a 6. What positive integer has to be written in the second field for
the following condition to be valid: the sum of any three adjoining fields is equal
to 21?
(A) 7
(B) 8
(C) 6
(D) 10
(E) 21
137
Grade – 5 & 6
MATH KANGAROO WORK BOOK
100. This is a multiplication table. Which two letters represent the same number?
(A) L and M
(B) P and N
(C) R and S
(D) K and R (E) M and T
101. In a CD store two CD’s have the same price. The first CD becomes 5%
cheaper, and the other one increases 15% in price. Now the two prices differ
by 6 euros. What is the price in euros of the cheaper CD now?
(A) 1.50
(B) 6
(C) 28.50
(D) 30
(E) 34.50
102. You write a number in each square as shown in the square figure. Then, the
number cannot be:
(A) 128
(B) 256
(C) 81
(D) 121
(E) 400
103. Bill divided111 … 1by 3. The number of zeros in the quotient he obtained is
equal to
(A) 670
(B) 669
(C) 668
(D) 667
(E) 665
104. Imagine that you have 108 red balls and 180 green balls. You want to put all of
them in bags, and there must be the same number of balls in each bag, and all
the balls in each bag must be the same color. What is the minimum number of
bags you need?
(A) 288
(B) 36
(C) 18
(D) 8
(E) 1
105. In the Kangaroo summer camp a math competition was organized with 10
problems. Each correct answer was worth 5 points. For each incorrect answer 3
points were deducted. Everybody answered all the problems. Matt had 34
points, Zsolt had 10 points, and Ga´bor had 2 points. How many correct
answers did they have altogether?
(A) 17
(B) 18
(C) 15
(D) 13
(E) 21
138
Grade – 5 & 6
MATH KANGAROO WORK BOOK
106. A right triangle with legs of length 6 cm and 8 cm is cut out of a sheet of paper
and then folded along a straight line. What can the area be, in cm2, of the
resulting polygon?
(A) 9
(B) 12
(C) 18
(D) 24
(E) 30
107. The cube shown in the figure has a positive integer written on each face. The
products of the two numbers on opposite faces are the same. What is the
smallest possible sum of the six numbers on the cube?
(A) 36
(B) 37
(C) 41
(D) 44
(E) 60
108. Six identical gray beads and three identical white beads are arranged on
weighing scales as shown in the picture. What is the total weight of these nine
beads?
(A) 100 g
(B) 99 g
(C) 96 g
(D) 94 g
(E) 90 g
109. Robert made 5 statements (A) - (E), exactly one of which is false. Which one?
(A) My son Basil has 3 sisters.
(B) My daughter Ann has 2 brothers.
(C) My daughter Ann has 2 sisters.
(D) My son Basil has 2 brothers.
(E) I have 5 children.
110. Benjamin writes an integer in the first circle and then fills the other five circles
by following the instructions. How many of the six numbers in the circles are
divisible by 3?
(A) 1
(C) 2
(E) both 3 and 4 are possible
(B) both 1 and 2 are possible
(D) both 2 and 3 are possible
139
Grade – 5 & 6
MATH KANGAROO WORK BOOK
111. Five girlfriends sat in a cinema in a row of 5 seats, from 1 to 5. Anna went out
for popcorn, and after returning, found that Jeanne moved to two places to the
right, Katya - one place to the left, and Diana and Nastya switched places,
leaving Anna place number 3. Where was Anna before she got up?
(A) place number 1
(B) place number 2
(C) place number 3
(D) place number 4
(E) place number 5
112. Emily took selfies with her 8 cousins. Each of the 8 cousins is in two or three
pictures. In each picture there are exactly 5 cousins. How many selfies did
Emily take?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
113. Jette and Willi are throwing balls at two identical pyramids of 15 cans. Jette
knocks down 6 cans with a total of 25 points. Willi knocks down 4 cans. How
many points does Willi score?
(A) 22
(B) 23
(C) 25
(D) 26
(E) 28
114. Every digit on my digital clock is composed of at most 7 segments, as follows:
But, unfortunately, in every set of 7 segments the same 2 segments don't work.
At this moment my clock shows
What will it show after 3 hours and 45 minutes?
(A)
(B)
(C)
(D)
(E)
140
Grade – 5 & 6
MATH KANGAROO WORK BOOK
115. Linas builds a 4×4× 4 cube using 32 white and 32 black 1 ×1× 1 cubes. He
arranges the cubes so that as much of the surface of his large cube is white.
What fraction of the surface of his cube is white?
(A)
(B)
(C)
(D)
(E)
116. Zev has two machines: one exchanges 1 white token into 4 red tokens, while
the other exchanges 1 red token into 3 white ones. Zev has 4 white tokens.
After exactly 11 exchanges, he has 31 tokens. How many of those are red?
(A) 21
(B) 17
(C) 14
(D) 27
(E) 11
117. Alice, Jane and Dinah wanted to buy 12 cakes, Alice payed for 5 cakes, Jane
payed for 7 cakes and Dinah payed for her part of cakes 20 euros. How much
of that sum should be given to Jane ?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 16
118. After shooting several times on the target shown in the picture, the
Scored 100 points. How many shots did he produced?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
119. The cardboard is folded into a 2 x 1 x 1 box.
Which picture does Not show this box ?
(A)
(B)
(C)
(D)
(E)
141
Grade – 5 & 6
MATH KANGAROO WORK BOOK
120. When victor was 12 years old, his mother baked him a cake in the form of a
clock into several (more than one) Pieces, with the same sums of numbers on
the resulting pieces?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
121. In a theatre, rows are arranged in a specific way. There are three seats in the
first row and in each next row, there are two more seats than in the previous
one. There are 18 rows in the theatre. All ticket were sold for the movie. How
many people supposed to watch the movie?
(A) 280
(B) 320
(C) 360
(D) 400
(E) 440
122. Lotta mixed lemonade. When she tastes, she notices that it has become too
weak. According to the label it would be 1 part syrup to parts water, but Lotta
had 1 dl syrup and 2 liters of water. How many syrup does she have to add to
get it right?
(A) 1 dl
(B) 2 dl
(C) 3 dl
(D) 4 dl
(E) 5 dl
123. Four bird nest have 1, 4, 6 and 9 chicks, respectively. What is the least number
of chicks we need to move between the nests so in the end they all nests have
the same number of chicks?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
124. The date of today can be written as 21/03/2019 and number of the day is 21:
digits 0, 1 and 2 have been used twice. Which is the number if the last day
whose date was written using pairwise different digits?
(A) 30
(B) 25
(C) 29
(D) 28
(E) 31
125. Cathie wrote some numbers at the vertexes of the cube. Then she calculated
the sums of numbers on the left on the right and on the top faces. It got the
value 14, 22, and 18 respectively. What is the sum of the numbers on the lower
face?
(A) 16
(B) 18
(C) 20
(D) 22
(E) impossible to determine
142
Grade – 5 & 6
MATH KANGAROO WORK BOOK
126. Simon threw three dice. He wrote down the triplet of numbers that were shown
on the dice. After several throws he realized that the sum of every triplet is odd
and lower than 10 and that there are no other triplets with these characteristics
that he can still throw. How many legs does a hiparid have?
(A) 15
(B) 14
(C) 13
(D) 12
(E) 11
127. Hiparid is a made up animal that was the mascot of a children’s camp. At the
camp’s quiz the kids were asked this question: How many legs do six dogs, one
rooster and seven hiparids have together? Carl said 46, Mary 66, Nina 78 and
Owen 82. One child was right. How many legs does a hiparid have?
(A) 3
(B) 4
(C) 6
(D) 7
(E) 8
128. Two knights and several liars stood in a circle so that each of them could utter
the phrase “Both my neighbors are liars”. How many liars could there be?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 8
129. Five girlfriends sat in a cinema in a row of 5 seats, from 1 to 5. Anna went out
for popcorn, and after returning, found that Jeanne moved to two placed to the
right, Katya Where was Anna before she got up?
(A) place number 1
(B) place number 2
(C) place number 3
(D) place number 4
(E) place number 5
130. In the basket are single-colored balls of different colors. At least a third of the
balls are red, at least 30% of the balls are green, and not less than 4/11 of all
balls are blue. What is the minimum possible number of balls in the basket?
(A) 23
(B) 30
(C) 33
(D) 110
(E) 330
131. Zev has two machines: one can exchange a white token into 4 red tokens,
While the other can exchange a red token into 3 white ones. Zev has four white
tokens. After exactly 11 exchanges, he has 31 token. How many of those are
red?
(A) 21
(B) 17
(C) 14
(D) 27
(E) 11
132. There are 11 wagons in the train, 350 passengers are traveling in them. In any
three consecutive wagons there are 99 passengers. How many passengers are
in the sixth wagon?
(A) 32
(B) 33
(C) 39
(D) 46
(E) 53
133. Which of the following quadrilaterals, inscribed in the same grids, has the
bigger area?
(A
(B)
(C)
(D)
(E)
143
Grade – 5 & 6
MATH KANGAROO WORK BOOK
134. We have to fold a rectangular sheet, by doing two folds in half, always in
parallel to one side. In what of the following ways, the folded sheet will occupy
less surface:
(A) Always folds in parallel at the parallel at the initial long side.
(B) Always folds in parallel at the initial short side.
(C) Doing it alternately: once for the long and the other for the short.
(D) It will depend on the relative sizes of the sheet sides.
(E) The requested surface is the same we do as we do the tow folds.
135. The integers from 1 to 99 were written in increasing order without gaps and the
obtained sequences of digits was divided into triplets of digits:
(123) (456) (789) (101) (112)… (596) (979) (899).
Then all instances of the digit 4 were crossed out. How many of the triplets
remain intact?
(A) 43
(B) 46
(C) 47
(D) 48
(E) 51
136. Five friends met. Each of them gave each other 1 candy. Then they ate all the
candy received by friends. As a result, the friends total number of candies
decreased on a half. How many candies did friends have before the meeting?
(A) 20
(B) 24
(C) 30
(D) 40
(C)
(D)
(E) 60
137. Which is the missing triangle?
(A)
(B)
(E)
138. A cubic grid of points has 44 points on the edges
The number of points in the interior of the cube is:
(A) 27
(B) 64
(C) 81
(D) 125
(E) 216
144
Grade – 5 & 6
MATH KANGAROO WORK BOOK
139. A fishing contest lasted 3 hours and was attended by 20 fishermen. On
average, each competitor caught 1.5 fish per hour. Nine fishermen caught
exactly one fish each and the others caught at least one fish each but none of
them got the same number of fish. What is the maximum number of fish that the
winner of the contest could get?
(A) 18
(B)17
(C) 16
(D) 15
(E) 14
140. The box contains gray and white beads --- 160 pieces in total. Gabija
exchanged gray beads for white ones. For every 7 gray beads she gets 3 white.
How many times has she exchanged the beads if it is known that the
exchanges she has only white beads and there are 100 of them?
(A) 15
(B) 14
(E) This can not be determined.
(C) 12
(D) 10
141. Six identical gray beads and three identical white beads are arranged on
weighing scales and balances are in balance, see figure. The total weight of
these nine beads is equal
(A) 100 g
(B) 99 g
(C) 96 g
(D) 94 g
(E) 90 g
142. Agnes had a few sweets and Cathie had a few sweets. First Agnes gave Cathie
half of her sweets. Then Cathie gave Agnes half of all her sweets (including
initial and received from Agnes) As a result, the number of Agnes sweets
became 8 sweets more than Cathie. How many candies did Agnes have
initially?
(A) 8
(B) 12
(C) 16
(D) 24
(E) Impossible to determine
143. A rope with the length 40m is divided into two different lengths. The two length
are laid to form two different squares. The sum of the areas of the two squares
is 68 m2
How big is the difference between the areas of the two squares?
(A) 20m2
(B) 28m2
(C) 36m2
(D) 40m2
(E) 60m2
145
Grade – 5 & 6
MATH KANGAROO WORK BOOK
144. 5 boys and 6 girls are going to sell 100 newspapers. The boys get some
newspaper and share them equally among each other. Then the girls get the
rest of the newspapers and share then equally among each other. There are no
newspapers left over.
Which of these alternatives could be the number of newspapers each boy have
to sell?
(A) 5
(B) 6
(C) 8
(D) 10
(E) 12
145. Cory has 175 euro in banknotes. He has the most 20 euro banknotes and he
has as many 5 euro banknotes as 10 euro banknotes. Only one of the
banknotes is a 50 euro banknote.
How many banknotes does Cory have?
(A) 9
(B) 10
(C) 11
(D) 13
(E) 15
146. How many possibilities are there to cover the big 2 completely with the five
given tiles?
(A) 2
(B) 3
(C) 5
(D) 8
(E) 10
147. Matthew, Neve, Scott, Lacey, Claudia and Owen were at the bumper cars.
Owen broke one leg, so he watched the other and counted their collisions:
Matthew and Neve each bumped once. Scott, Lacey and Claudia each bumped
twice. The hardest bump was , as expected, between the twins Matthew and
Scott. No two children bumped into each other more than once. Which of the
following collisons did not happen for sure?
(A) Lacey- Claudia
(B) Lacey- Scott
(C) Neve-Scott
(D) Neve-Lacey
(E) Neve-Claudia
148. A gear is made by three gearwheels, A, B and C and each of them has a notch.
A has 16 teeth , B has 20 teeth and C has 30 teeth. B is directly connected with
both A and C , A is not directly connected with C. At this moment the gear starts
working. After how many revolutions of wheel B the three notches come back
the first time to the initial position?
(A) 12
(B) 96
(C) 240
(D) 9600
(E) It will never happen.
146
Grade – 5 & 6
MATH KANGAROO WORK BOOK
149. Using each of the digits of the number 2019 only once, Masha composed two
numbers with the largest possible product. What is this product?
(A) 918
(B) 1080
(C) 1820
(D) 1890
(E) 1980
150. Robert uttered 5 statements (A) – (E), Precisely one of which is false. Which
one?
(A) My son Basil has 3 sisters.
(B) My daughter Ann has 2 brothers.
(C) My daughter Ann has 2 sisters.
(D) My son Basil has 2 brothers
(E) I have 5 children.
151. In how many ways can the word KENGA be read in the figure on the right if
Neighboring letters of the word must lie in triangle that have a common side?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
152. After removing the first, a three-digit number became seven times less than it
was initially. What was the removed digit?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
153. The number 2019 contains four different digits and the last of them is more than
the quadruple of the first one. How many 4-digit numbers are there with this
property?
(A) 224
(B) 280
(C) 320
(D) 336
(E) 540
154. We say that a year is charming if from its digits we can compose two
consecutive 2-digit numbers. How many charming years are there in the XXI
century?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
155. Different natural numbers not greater than 2019 are written on the cards. For
any two cards, the number at one of them is divisible by the number at the
other. What greatest number of cards can be?
(A) 2
(B) 5
(C) 11
(D) 673
(E) 1009
147
Grade – 5 & 6
MATH KANGAROO WORK BOOK
156. 100 Participants had to solve 4 problems at the Math Olympiad. 90 people
solved the first problem, 80 people solved the second problem, 70 people
solved the third problem, and 60 people solved the fourth, none managed to
solve all 4 problems. Only those who succeeded with the third and the fourth
problems were announced the winners. How many winners were there?
(A) 10
(B) 15
(C) 20
(D) 30
(E) 35
157. Like a kind of code, each letter stands for a digit, the same letter means the
same digit. Now replace the letters with numbers so that the calculation is
correct!
Which digit stands for the letter C?
(A) 3
(B) 8
(C) 4
(D) 9
(E) 0
158. Maja and Ana have a square playing board with dimensions 4 x 4 has blue
diamonds – sapphires and Ana has red diamonds – rubies. They play the
following game: They put diamonds on empty field (in every field of the board,
only one diamond can be put in) and Maja can put a sapphire in any field so
that the distance between the middle points of two fields with sapphires can not
be √5, and Ana puts ruby in any empty field. Maja starts the game playing first.
How many sapphires can Maja put on the playing board at most?
(A) 2
(B) 3
(C) 4
(D) 5
159. Sam wants to cover a square of area 20192using tiles of dimension
673 x 1. What is the minimal number of tiles that Mary needs?
(A) 673
(B) 2019
(C) 4038
(D) 6057
(E) 7
(E) 8076
160. In the wholesale trade, each product is listed without VAT. (VAT amount is
21%, VAT to be added at checked at checkout) The customer bought goods
worth a total of 1000 EUR. (amount before discount) AT the checkout, today’s
discount will be applied. Then thanks to the golden loyalty card will be added
VAT. How much will the customer pay for the purchase?
(A) ca. 835
(B) ca. 860
(C) ca. 900
(D) ca. 935 (E) ca.1000
148
Grade – 5 & 6
MATH KANGAROO WORK BOOK
161. Helen walks 400 meters at the same time that Marcos walks 420 meters. If on a
walk of 400 meters Marcos is placed 2 meters behind to give Helen an
advantage. When they reach the goal, the difference is
(A) One meter to win Hellen
(B) A meter losing Hellen
(C) They arrive Equal
(D) Two meters in favor of marco
(E) Two meters in favor of Helen
162. 8 Kangaroos stand in a line as shown in the figure. Some two neighboring
Kangaroos, which look at each other, turn to half a turn. Then, the same is done
by the other two neighboring kangaroo that look at each other, etc. The process
ends when no two neighboring kangaroos look at each other. Which two
kangaroos will make the last turn?
(A) 2 and 3
(B) 3 and 4
(E) it depends on the order of turns
(C) 4 and 5
(D) 5 and 6
163. A number a is x% larger than 10 and 10% smaller than x. Determine the value
of x.
(A) 10
(B) 12.5
(C) 15
(D) 17.5
(E) 20
164. A train goes from Valleyville up to Mountainville and back down. The distance
between the two towns is 120 km. The speed of the train when going up is 40
km/h and the speed when going down is 60 km/h.
What is the average speed of the return trip?
(A) 46 km/h
(B) 48 km/h
(C) 50 km/h
(D) 52 km/h
(E) 54 km/h
165. The picture shows three gears with a black gear tooth.
Where are the black gear teeth placed when the small gear has turned a full
turn clockwise?
149
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A)
(B)
(C)
(D)
(E)
166. 201 balls are arranged in a row and are numbered from 1 to 201. Each ball is
colored either green or red. Among any ten consecutive balls there are exactly
five green balls. The ball nr. 1 is green. How many red balls are there in the
row?
(A) 99
(B) 100
(C) 101
(D) 199
(E) 200
167. Nine numbers are written on the blackboard: 11, 12, 13, 14, 15, 16, 17, 18 and
19. Andrew chooses arbitrarily two numbers from those written on the
blackboard, erases both chosen numbers and instead he writes only one
number: their product. He repeats this procedure until only one number remains
on the blackboard. What is the last digit of the last remained number?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
168. How many paths lead from 1 to 10, if we always step on a larger number, and
we can only step on an adjacent cell?
(A) 33
(B) 37
(C) 39
(D) 41
(E) 43
169. We calculate the product of digits in each of the 90 two-digit positive integers.
What is the sum of the 90 products?
(A) 1225
(B) 2025
(C) 2125
(D) 2215
(E) 2225
170. In which range is the product of all the even numbers between −100 and 100?
(A) Less than -500
(B) Between -500 and -100
(C) Between -100 and 100
(D) Between 100 and 500
(E) Greater than 500
150
Grade – 5 & 6
MATH KANGAROO WORK BOOK
171. Three rectangles of the same height are positioned as shown. The numbers
within the rectangles indicate their areas in cm2. If AB = 6 cm, how long is CD?
(A) 7 cm
(B) 7.5 cm
(C) 8 cm
(D) 8.2 cm
(E) 8.5 cm
172. A pirate has 4 chests full of gold coins. Each chest has the same amount of
coins. He knows that the four chests together contain a total of less than 270
coins but any three chests contain a total of more than 200 coins. How many
coins does each chest contain?
(A) 65 coins each
(C) 68 coins each
(E) none of the previous
(B) 66 coins each
(D) 69 coins each
173. Several pages were missing in the book. Page 231 is the first missing page and
the last missing pages number is composed of the same digits written in
different order. How many pages were missing in the book?
(A) 68
(B) 71
(C) 74
(D) 82
(E) 91
174. Two boys are playing the following game. They put into the box one after the
other balls-one or three. The winner is the one, that fills the box with required
number of balls. For which of the required number of balls the second player
will be able always to win?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
151
Grade – 5 & 6
MATH KANGAROO WORK BOOK
175. Three sisters have different ages, with average of ages 10 years, but when they
get together in pairs the averages are 11 and 12 years. How old is the oldest
one?
(A) 12
(B) 14
(C) 16
(D) 11
(E) 15
176. From the center of the circle spent 9 radii. What is the largest number of obtuse
angles formed by a pair of these radii that can happen?
(A) 8
(B) 18
(C) 21
(D) 27
(E) 36
177. 12 people for a training game of volleyball are divided into two teams of 6
people. What is the smallest number of games you need to play so that each
person plays in the same team with each of the others.
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
178. Monica has eight red, five green, seven blue and six brown-coloured pens in
the drawer. At least how many pens must she remove from the drawer
blindfolded to ensure that she takes out are at least two red-coloured pens?
(A) 19
(B) 20
(C) 23
(D) 24
(E) 25
179. The shoe-dealer bought 100 pairs of sneakers for EUR 20 each. He sold
75pairs for EUR 25 each. He sold all the remaining pairs for the same
discounted price. Evenso, he earned a fifth more money for all of the sneakers
than he had paid. How much did the sneakers cost when discounted?
(A) 16 EUR
(B) 20 EUR
(C) 21 EUR
(D) 24 EUR (E) 25 EUR
180. A magician gave his assistant the task of preparing a bag with 100 balls. The
balls come in eight different colours. There should be at least two balls of each
colour in the bag, and the number of balls of each colour must be different. The
assistant decided that the fewest balls will be brown and the most will be of his
favorite colour turquoise. At most how many torquoise balls could he could put
in the bag?
(A) 16
(B) 65
(C) 73
(D) 80
(E) 86
181. There were a total of 72 kangaroos in two enclosures. The breeder wanted
equal numbers of them in each enclosure. He moved 5 kangaroos from the first
enclosure to the second, but it was still not enough. Therefore, he moved
another quarter of the kangaroos from the first to the second enclosure. Only
then were there equally many kangaroos in both. How many kangaroos were in
the first enclosure at the beginning?
(A) 48
(B) 50
(C) 53
(D) 54
(E) 59
152
Grade – 5 & 6
MATH KANGAROO WORK BOOK
182. How many squares still need to be marked in the square shape in the picture so
that the marked shape has four axes of symmetry?
(A) 1
(B) 9
(C) 12
(D) 13
(E) 21
183. Some dogs, cats and mice live on an island. At midnight exactly half of all dogs,
half of all cats and half of all mice are transformed in the following way. Each
dog turns into 3 cats, each cat turns into 5 mice and each mouse turns into 7
dogs. The numbers of dogs, cats and mice are equal after midnight. Which of
the following can be the initial total number of animals?
(A) 100
(B) 102
(C) 104
(D) 106
(E) 108
184. Given a sequence of numbers 100, 105, 110, 115,...,195, 200. How many of the
numbers in the sequence are divisible by 6?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 10
185. In a bag there are 15 balls. The balls are in four different colors, and no colors
have the same number of balls. How many balls of one color is the most the
bag can contain?
(A) 4
(B) 6
(C) 9
(D) 11
(E) 12
186. How many possibilities are there for the smallest side of a rectangle that can be
formed with 5 tokens measuring 2 cm  1 cm if all tokens should be used?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
187. Two robots start from the bottom left-hand corner of a square grid. The first
robot follows a zig-zag path which systematically goes through every point on
the grid in the pattern shown below, travelling at a speed of 1 unit of the grid
each second. The second robot leaves 20 seconds after the first and travels in
a straight line along an edge of the grid. Where will they meet?
(A) A
(B) B
(C) C
(D) D
(E) E
153
Grade – 5 & 6
MATH KANGAROO WORK BOOK
188. Ann, Bob, Carina, Dan and Ed are sitting at a round table. Ann is not next to
Bob, Dan is next to Ed and Bob is not next to Dan. Who are next to Carina?
(A) Ann and Bob
(B) Bob and Dan
(C) Dan and Ed
(D) Ed and Ann
(E) it is not possible to guess
1
1
are kangaroo,
6
7
are horses and the rest are various other animals. What is the sum of the digits
of the number of animals in the park?
(A) 7
(B) 8
(C) 9
(D) 10
(E) there is no way of knowing exactly
189. At a park there are between 100 and 150 animals. Of these
190. Barnabe transforms the numbers from 1 to 100 by the rule: each number is
replaced by the number obtained by adding the original number with the sum of
its digits. Among the newly obtained numbers, how many are even?
(A) 49
(B) 50
(C) 51
(D) 45
(E) 55
191. Sam has a number made up of a row of magic cards. Each card has only one
digit. In each play Sam chooses a card, other than the extreme on the right and
such that its digit and the digit of the card to the right are less than 9. When
touching the chosen card both its digit and the digit on the card to the right of it
increases by 1, if the chosen card is the one on the far right nothing changes.
Sam makes 6 card touches on the number 2021. Which of the following
numbers cannot Sam get?
(A) 2087
(B) 2186
(C) 3176
(D) 3275
(E) 3280
192. A rabbit and a turtle are going to run 100 meters in a straight line. Both start at
the same time but when the rabbit reaches the goal, he returns immediately and
runs into the turtle halfway and immediately returns to the goal, and waits there
for half an hour until his friend arrives. What is the difference between the time it
takes for the rabbit to complete the 100 meter course and the time it takes for
the turtle to complete the same course?
(A) 60
(B) 90
(C) 45
(D) 30
(E) 70
193. If you multiply all even numbers from 2 to 20, what will be the last two digits of
the product?
(A) 00
(B) 10
(C) 20
(D) 40
(E) 50
194. A green ball rolls on a table with edges and in the direction as the arrows show.
Which hole will the ball fall into if it continues to roll in the same way?
154
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) A
(B) B
(E) None of these four holes
(C) C
(D) D
195. Four friends use the same number. Ana adds 2 to the number, then divides by
2. Ben subtracts 2 from the number, then divides by 2. Carla divides the
number by 2, then subtracts by 2. Daniel subtracts the number by 2, then
subtracts again by 2. Who will get the smallest result?
(A) Ana
(B) Ben
(C) Carla
(D) Daniel
(E) It depends on the number
196. A chocolate bar consists of many equal square pieces. Trudy breaks off one
row with 4 pieces. Then, Loris breaks off two rows with 6 pieces altogether.
How many pieces of chocolate are left?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 12
197. Maurice asked the canteen chef for the recipe of his pancakes.
How many pancakes can Maurice prepare at most with the supplies in his
kitchen: 6 eggs, 400g our, 500ml milk and 200g butter?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 15
198. Jack and Cames have a total of 35 cents. After Jack spends 3 cents and
Cames 10 cents, their money is equalized. According to this, how many cents
does Jack have in the beginning?
(A) 21
(B) 13
(C) 14
(D) 7
(E) 25
199. The student will get a pen from stationery. If he buys 8 of the same items, he
will pay 52 dollars. This student How many dollars will he pay if he buys 12
items?
(A) 73
(B) 78
(C) 80
(D) 83
(E) 85
155
Grade – 5 & 6
MATH KANGAROO WORK BOOK
200. Three pirates were asked how many coins and how many diamonds their friend
had. Each of the three answered the truth about one of the questions but lied
about the other. Their answers are written on the piece of paper pictured. What
is the total amount of coins and diamonds their friend has?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
201. We have a cube and its side is 7cm long. On its 6 faces, we draw the diagonals
in red. Then, we cut the cube into small cubes the side of which are 1cm long.
How many small cubes will have at least a red line drawn on it?
(A) 54
(B) 62
(C) 70
(D) 78
(E) 86
202. Bernard has a table of the following shape
.
He also has a 2 x 2 template made of squares he can place on top of the figure
such that the squares are well aligned and all four squares from the template
completely cover four squares
. Once he places the template over the
figure, he increases each number written in the squares by 1. He started with a
figure with zero in each square and he placed his template several times as per
indications. Unfortunately, some numbers are no longer visible
.
156
Grade – 5 & 6
MATH KANGAROO WORK BOOK
What number should be in the square marked by *?
(A) 5
(B) 4
(C) 10
(D) 6
(E) 13
203. We have a drawing program, but it works very partially: you can only use the
SQ command, that draw one square, of course of any size and anywhere on
the screen. What is the minimum number of SQ commands needed to draw a
4  4 grid?
(A) 12
(B) 5
(C) 6
(D) 8
(E) 16
204. If g is the area of the grey zone and w is the area of the white star, what is the
w
value of
g
(A)
3
5
(B)
4
5
(C) 1
(D)
5
4
(E)
5
3
205. 4 people Ann, Bob,Carla and Diana must cross a tunnel where only 2 people
can cross at the same time and it's dark inside. When crossing the tunnel they
must, necessarily, handle a lantern but they have only one. It takes Ann 10
minutes to cross the tunnel alone, and Bob, Carla and Diana need 5, 2 and 1
minutes respectively to cross the tunnel alone. When 2 people cross together,
they do it at the speed of the slowest of them. What is the minimum time they
need to cross all four?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
206. Aura and Blai play ping pong at two different clubs. One day Aura tells Blai:
"Today all 8 members of our club have played three games each without
repeating an opponent." Blai tells Aura: "The same thing happened to my club,
where we are 9. Everyone has played three games without repeating a rival".
Which of the following is true?
157
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A) Aura is lying and Blai may be telling the truth
(B) Aura may be telling the truth and Blai is lying
(C) Both may be telling the truth
(D) They are both lying
(E) It is not possible to know who is telling the truth and who is lying
207. The Natural Number String is the in finite string 0123456789101112131415...
made by joining together all the natural numbers. Numbers which appear earlier
than expected, such as "12" which is between "0" and "3" as well as its natural
place between "11" and "13" are called Early Bird numbers. What is the
smallest 3-digit Early- Bird number?
(A) 123
(B) 101
(C) 012
(D) 100
(E) 111
208. Joy forms distinct 2-digit even numbers using only the digits 1, 2, 3, and 4, with
each digit used at most once in each number formed. What is the sum of all
possible numbers she formed?
(A) 60
(B) 158
(C) 108
(D) 24
(E) 330
209. The volume of a cuboid whose lengths of all edges are integers is 2021. How
many different cuboids have this property?
(A) 0
(B) 1
(C) 2
(D) 3
(E) more than 3
210. The lengths of the edges of a cuboid are positive integers. If the areas of the
two sides of that cuboid are 5 cm2 and 7 cm2, then the area of that cuboid is
equal to:
(A) 12 cm2
(B) 13 cm2
(C) 24 cm2
(D) 26 cm2
(E) 35 cm2
211. An electric scooter costs 400 EUR. Within the seasonal sales discount for all
scooters was 20 %. There was another 15 % discount on the Kangaroo brand
from the discounted price. Yet another extra discount of 10 % of the price after
all previous discounts was given to the last exposed piece of the Kangaroo
scooter. How much did this last Kangaroo scooter cost? An electric scooter
costs 400 EUR. Within the seasonal sales discount for all scooters was 20 %.
There was another 15 % discount on the Kangaroo brand from the discounted
price. Yet another extra discount of 10 % of the price after all previous
discounts was given to the last exposed piece of the Kangaroo scooter. How
much did this last Kangaroo scooter cost?
(A) to 220
(B) 220 - 230
(C) 230 - 240 (D) 240 - 250
(E) more than 250
212. How many natural numbers n are there such that 2n < 200 < 5n?
(A) 54
(B) 55
(C) 56
(D) 58
(E) 59
158
Grade – 5 & 6
MATH KANGAROO WORK BOOK
213. ( − 1) + ( − 2) + ( − 3) + ⋯ + ( − 20) = 1 + 2 + 3 + ⋯ + 20, ℎ
=?
(A) 20
(B) 21
(C) 40
(D) 190
(E) 380
214. Each rectangular card was divided into four equal cells and the shapes
were drawn into each cell so that each cell had a different shape in it. Two
cards were placed side by side only if the same shapes appeared in the
corresponding cells on their common side. Nine cards were used to form a
rectangle as shown in the figure. Which of the following cards was definitely not
used to form this rectangle?
(A)
(B)
(C)
(D)
(E)
215. An apple and an orange weight together as much as pear and peach. An apple
with pear weights less than an orange with peach, and a pear with an orange
weighs less than an apple with a peach. Which of the fruits is the heaviest?
(A) apple
(B) peach
(C) orange
(D) pear
(E) impossible to determine
216. It takes 5 minutes for the ball to oat on the river from bridge A to bridge B. Peter
sails from B to A in the same time. How long does Peter sail from A to B?
(A) 1 min 20 s
(B) 1 min 40 s
(C) 2 min 30 s (D) 3 min 20 s (E) 5 min
217. Elena cut a square 55 into corners consisting of three cells and rectangles
consisting of two cells. What is the smallest number of parts she could get?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
218. 10 athletes participated in competition and everyone took a different place from
1 to 10. The next day, each of them was asked what place he took, and each,
of course, called a number from 1 to 10. The sum of their answers was 36.
What is the smallest number of athletes lied?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 7
219. Olha, Dima, Sam, Jack and Peter compared their watches. It turned out that
Sam's watch lags behind Dmitry's watch by three minutes. Olha's watch is one
minute behind to Dima's watch, Jack's watch is one minute behind the Sam's,
and Peter's watch isone minute behind to Olha's watch. If you compute an
average time of all five watches you will get a correct time. It is also known that
one of these watches shows the correct time. Which one?
(A) Olha
(B) Dima
(C) Sam
(D) Jack
(E) Peter
159
Grade – 5 & 6
MATH KANGAROO WORK BOOK
220. Anne imagined a number. She described the number as follows: "The number I
imagined is a three-digit number and is written with different digits. It is the
largest such number that is divisible by 2, 5 and 9. " Which number did Anna
imagine?
(A) 990
(B) 810
(C) 972
(D) 792
(E) 945
221. We have three identical rectangle mosaics. We place them alongside each
other as follows. In case "A", the ratio of the sides of the resulted rectangle is 18
to 7. What would be the ratio of length to width of the resulted rectangle in case
"B"?
(A) 7 : 2
(B) 7 : 3
(C) 8 : 3
(D) 8 : 5
(E) 7 : 3
222. Mohsen and Ali play the following game. Each time, Ali moves the pieces to
change the shape from "A" to other forms. Then, Mohsen tries to return the
pieces to their original form with minimum moves. If "B" is the shape that Ali has
created, what would be the minimum number of movements for Mohsen to
return them to "A"? (pieces can be put on any column without limit)
(A) 10 moves
(B) 8 moves
(C) 9 moves
(D) 6 moves
(E) 10 moves
160
Grade – 5 & 6
MATH KANGAROO WORK BOOK
223. According to the following figure, which comparison is true?
(A) The height of each person equals to one third of the giraffe's height.
(B) The average of the height of all three people equals to one third of the
giraffe's height.
(C) The average of the height of all three people is less than one third of the
giraffe's height.
(D) The average of the height of all three people is greater than one third of the
giraffe's height.
(E) The sum of the height of all three people equals the height of the giraffe.
224. Romina has put 7 domino pieces on a 4x4 table in a way that each piece covers
two squares of the table and in the end only the number of two squares are
visible. What two numbers can be those?
(A) 6 and 14
(B) 3 and 11
(C) 8 and 13
(D) 7 and 10
(E) 6 and 14
161
Grade – 5 & 6
MATH KANGAROO WORK BOOK
225. Which is the 50th shape?
(A)
(B)
(C)
(D)
(E)
226. Arash, Babak, Peyman, and Radman want to take a picture together. Arash
and Peyman want to be next to each other in the picture. Also, Peyman does
not wantto stand next to Babak. In how many ways can they take a picture?
(A) 10
(B) 7
(C) 8
(D) 9
(E) 10
227. A gas turbine creates energy by mixing air and fuel. The cross section of the
turbine is circular and there are 30 torches around it with same distances which
push the heat inside the turbine. The torches are numbered clockwise. If the top
torch (12 o'clock) is number 30, which torches are between 2 and 4 o'clock?
(A) torches 7, 8, 9, 10
(B) torches 6, 7, 8, 9
(C) torches 7, 8, 9, 10
(D) torches 6, 7, 8, 9, 10
(E) torches 7, 8, 9, 10, 11
228. The following square is made of 7 pieces. They are known as the Tangram
pieces. How many trapezoid are there?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
229. There are two squares ABCD and DEFG with lengths of 2 and 6. If T is the
middle of AF, what is the area of the ATG triangle?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
162
Grade – 5 & 6
MATH KANGAROO WORK BOOK
230. Sah and has made the following by sticking 9 same-size white cubes. If he
throws the whole thing into a bucket of red paint, how many sides of the cubes
will not be colored?
(A) 10
(B) 20
(C) 24
(D) 30
(E) 36
231. Nazanin went to the fruit shop this morning. There were the following labels on
the fruits.
If Nazanin has paid the same amount of money for both kinds of fruit and has
bought 4 more oranges than apples, how many apples has she bought?
("Toman" is the currency in country Nazanin lives).
(A) 20
(B) 24
(C) 30
(D) 36
(E) 40
232. The diagram shows a model which can be disassembled into parts (isosceles
triangle and semicircle) along dashed lines.
If the size of the angle
this model?
= 100, which fan can be assembled from the parts of
163
Grade – 5 & 6
MATH KANGAROO WORK BOOK
(A)
(B)
(C)
(D)
(E)
164
Grade – 5 & 6
MATH KANGAROO WORK BOOK
SPACE FOR ROUGH
165
Grade – 5 & 6
ANSWER
SECTION A: Pre-Foundation (3 POINT PROBLEMS)
1
D
27
B
53
A
79
B
105
C
131
E
2
C
28
C
54
C
80
C
106
D
132
D
3
A
29
B
55
E
81
B
107
D
133
D
4
C
30
D
56
C
82
C
108
C
134
C
5
C
31
A
57
D
83
A
109
C
135
B
6
C
32
D
58
A
84
A
110
A
136
A
7
C
33
B
59
B
85
B
111
A
137
D
8
A
34
C
60
B
86
E
112
C
138
D
9
B
35
C
61
E
87
D
113
B
139
C
10
D
36
C
62
C
88
E
114
A
140
D
11
B
37
C
63
C
89
A
115
A
141
D
12
D
38
B
64
B
90
A
116
C
142
E
13
C
39
B
65
E
91
C
117
C
143
A
14
C
40
B
66
B
92
E
118
C
144
B
15
A
41
C
67
B
93
A
119
E
145
B
16
D
42
C
68
E
94
C
120
E
146
A
17
C
43
A
69
C
95
E
121
E
147
B
18
B
44
B
70
C
96
B
122
D
148
B
19
A
45
E
71
C
97
D
123
D
149
E
20
C
46
E
72
D
98
C
124
B
150
B
21
D
47
D
73
D
99
C
125
C
151
C
22
B
48
A
74
A
100
B
126
A
152
D
23
A
49
E
75
A
101
B
127
B
153
B
24
D
50
B
76
D
102
C
128
C
154
C
25
C
51
C
77
B
103
D
129
C
155
C
26
C
52
C
78
B
104
E
130
E
156
B
GRADE 5 &6
ANSWER
SECTION A: Pre-Foundation (3 POINT PROBLEMS)
157
D
182
D
207
B
232
B
257
B
158
C
183
C
208
A
233
E
258
E
159
B
184
E
209
D
234
A
259
A
160
D
185
D
210
A
235
D
260
D
161
D
186
C
211
B
236
A
261
C
162
C
187
C
212
E
237
D
262
D
163
A
188
B
213
D
238
B
263
A
164
D
189
A
214
D
239
A
264
C
165
D
190
A
215
E
240
D
265
B
166
B
191
B
216
B
241
B
266
C
167
C
192
C
217
B
242
B
267
C
168
D
193
B
218
B
243
E
268
D
169
D
194
C
219
B
244
D
269
E
170
D
195
D
220
A
245
A
270
D
171
D
196
E
221
A
246
C
172
B
197
E
222
D
247
D
173
B
198
B
223
D
248
D
174
B
199
D
224
C
249
C
175
E
200
A
225
D
250
B
176
E
201
E
226
B
251
C
177
D
202
E
227
E
252
D
178
D
203
D
228
D
253
C
179
D
204
E
229
E
254
C
180
B
205
E
230
B
255
D
181
C
206
B
231
C
256
B
GRADE 5 &6
ANSWER
SECTION B: Foundation (4 POINT PROBLEMS)
1
B
27
B
53
D
79
E
105
C
131
A
2
C
28
A
54
C
80
A
106
E
132
C
3
D
29
D
55
D
81
D
107
E
133
B
4
B
30
A
56
D
82
E
108
C
134
C
5
D
31
C
57
C
83
C
109
D
135
A
6
D
32
D
58
D
84
C
110
C
136
D
7
A
33
D
59
A
85
D
111
C
137
C
8
D
34
D
60
C
86
C
112
B
138
D
9
D
35
C
61
C
87
B
113
D
139
A
10
C
36
D
62
C
88
C
114
B
140
D
11
D
37
D
63
D
89
E
115
B
141
A
12
B
38
B
64
B
90
B
116
A
142
C
13
B
39
B
65
E
91
A
117
D
143
B
14
D
40
A
66
B
92
C
118
E
144
D
15
C
41
D
67
D
93
C
119
D
145
D
16
B
42
B
68
A
94
D
120
B
146
E
17
C
43
E
69
C
95
B
121
B
147
B
18
D
44
C
70
D
96
E
122
B
148
E
19
B
45
D
71
E
97
A
123
E
149
D
20
B
46
B
72
B
98
D
124
C
150
C
21
C
47
B
73
D
99
A
125
C
151
A
22
D
48
C
74
B
100
C
126
D
152
D
23
A
49
D
75
B
101
E
127
C
153
D
24
A
50
E
76
D
102
B
128
C
154
B
25
D
51
D
77
A
103
C
129
C
155
D
26
C
52
B
78
D
104
A
130
B
156
C
GRADE 5 &6
ANSWER
SECTION B: Foundation (4 POINT PROBLEMS)
157
D
182
D
207
C
232
C
257
E
282
A
158
E
183
C
208
D
233
E
258
B
283
B
159
D
184
D
209
A
234
D
259
D
284
D
160
E
185
B
210
A
235
A
260
C
285
C
161
C
186
D
211
E
236
A
261
E
286
E
162
C
187
C
212
D
237
D
262
D
287
D
163
D
188
B
213
C
238
C
263
C
288
E
164
D
189
D
214
C
239
E
264
B
289
D
165
D
190
A
215
D
240
E
265
D
290
D
166
B
191
C
216
D
241
B
266
D
291
E
167
A
192
E
217
B
242
D
267
B
292
E
168
B
193
D
218
E
243
A
268
E
293
D
169
B
194
B
219
D
244
D
269
D
294
D
170
A
195
B
220
C
245
C
270
C
295
E
171
D
196
C
221
B
246
D
271
D
296
D
172
D
197
A
222
E
247
B
272
B
297
C
173
C
198
A
223
B
248
A
273
C
298
B
174
A
199
A
224
D
249
C
274
B
299
C
175
B
200
C
225
E
250
D
275
B
300
D
176
D
201
D
226
E
251
E
276
B
301
B
177
C
202
B
227
E
252
C
277
B
302
E
178
B
203
D
228
A
253
E
278
D
303
A
179
C
204
D
229
B
254
B
279
C
304
A
180
C
205
B
230
B
255
C
280
D
305
B
181
B
206
B
231
C
256
C
281
D
306
D
GRADE 5 &6
ANSWER
SECTION B: Foundation (4 POINT PROBLEMS)
307
E
321
D
335
C
349
C
308
A
322
E
336
D
350
D
309
E
323
E
337
D
351
E
310
A
324
E
338
E
352
A
311
B
325
C
339
E
353
D
312
A
326
D
340
C
354
B
313
C
327
B
341
E
355
D
314
D
328
B
342
C
356
D
315
C
329
B
343
A
357
A
316
A
330
C
344
E
317
D
331
E
345
E
318
E
332
B
346
D
319
C
333
C
347
C
320
D
334
C
348
B
GRADE 5 &6
ANSWER
SECTION C: Exploration (5 POINT PROBLEMS)
1
D
25
D
49
D
73
D
97
C
121
C
2
C
26
E
50
B
74
B
98
B
122
C
3
B
27
D
51
D
75
B
99
B
123
D
4
C
28
A
52
A
76
D
100
A
124
B
5
C
29
D
53
E
77
D
101
C
125
B
6
D
30
A
54
C
78
E
102
A
126
C
7
D
31
B
55
E
79
C
103
D
127
E
8
C
32
D
56
D
80
E
104
D
128
B
9
D
33
D
57
B
81
B
105
A
129
D
10
B
34
B
58
C
82
A
106
C
130
E
11
C
35
D
59
C
83
A
107
C
131
C
12
A
36
B
60
E
84
C
108
E
132
D
13
D
37
D
61
E
85
C
109
D
133
B
14
B
38
D
62
C
86
B
110
C
134
E
15
D
39
C
63
D
87
D
111
D
135
C
16
C
40
B
64
C
88
A
112
B
136
D
17
A
41
A
65
B
89
A
113
D
137
D
18
A
42
D
66
C
90
B
114
A
138
A
19
D
43
B
67
B
91
D
115
D
139
C
20
B
44
A
68
D
92
C
116
C
140
A
21
C
45
D
69
E
93
D
117
B
141
E
22
C
46
D
70
D
94
D
118
C
142
C
23
D
47
B
71
D
95
A
119
C
143
E
24
C
48
B
72
B
96
D
120
B
144
C
GRADE 5 &6
ANSWER
SECTION C: Exploration (5 POINT PROBLEMS)
145
C
169
B
193
A
217
B
146
E
170
C
194
A
218
B
147
C
171
C
195
E
219
E
148
A
172
E
196
B
220
B
149
D
173
D
197
B
221
A
150
D
174
B
198
C
222
C
151
B
175
C
199
B
223
D
152
C
176
D
200
C
224
C
153
D
177
A
201
B
225
B
154
C
178
B
202
A
226
C
155
C
179
C
203
C
227
B
156
D
180
B
204
A
228
E
157
D
181
C
205
C
229
B
158
C
182
E
206
B
230
C
159
D
183
E
207
B
231
D
160
B
184
A
208
B
232
C
161
A
185
C
209
C
162
D
186
B
210
D
163
B
187
B
211
D
164
B
188
A
212
E
165
A
189
C
213
B
166
B
190
A
214
E
167
A
191
E
215
B
168
D
192
A
216
B
GRADE 5 &6
MATHEMATICAL KANGAROO
Mathematical Kangaroo (also known as International Mathematical Kangaroo, or Kangourou sans frontieres in French) is an international
mathematical competition held across 92 countries in the world. There are twelve levels of participation, ranging from grade 1 to grade 12. The
key competence tested by Mathematical Kangaroo is not just pure knowledge of formulas, but the logical combination of concepts.
The Competition was established in 1991 by Andre Deledicq, a Professor of Mathematics at the University of Paris, and Jean-Pierre Boudine,
Professor of Mathematics at Marseille. The idea comes from the Australian Mathematics Competition, initiated in 1978 by Peter O'Halloran. It is
based on multiple-choice questions (MCQs), which were rarely used in France at that time. For this competition, Jean-Pierre Boudine and
Andre Deledicq were awarded the 1994 d'Alembert prize of the Mathematical Society of France.
The competition has now spread around the world Students from Sweden first took part in 1999. By 2011, 860,000 students from 9,000
schools took part in Germany, having grown rapidly from 549,000 in 2007. In 2014, the competition was hosted in Latin America. In 2017,
the Bulgarian association held a week-long Kangaroo summer camp In Canada, math contest clubs for elementary school children teach
“questions typical of the Math Kangaroo contest”, starting with those with a visual component and helping to develop logic and spatial
reasoning. Students in Pakistan took part for the first time in 2005, the numbers increasing each year since. In 2009, the Pittsburgh PostGazette noted that the competition was very popular in Europe and was
“finding its way into the United States”. Denmark first participated in 2015. India participated for the first time in 2019 under the
banner of International Olympiad Academy.
IOA WORKBOOK
INTERNATIONAL OLYMPIAD ACADEMY
A division of CSAR Learning Solutions Pvt. Ltd.
Registered Office: A-409, Durga Vihar, East of Sainik Farms, New Delhi-110080
Hand Held: +91 9810336335, +91 8368118421
Email: exam@internationalolympiadacademy.com
Website: www.internationalolympiadacaemy.com / www.mathkangaroo.in
OUR
PARTNERS
ITPL
HIPPO ENGLISH
OLYMPIAD
MATH KANGAROO
COMPETITION
CSAR Learning Solutions Pvt. Ltd.
TECHNOLOGY PARTNER