Mathe
ematical Kangarroo 201
15
Group Kadett (Gradess 7 and 8)
Austria ‐ 23. 3. 22015
‐ 3p
point questiions ‐
1. The worrd KANGARO
OO is written on the top oof my umbre
ella.
Which of the following pictures shows
s
my um
mbrella?
(A)
(C)
(
(B)
(D)
(E)
2. A rectangle is made of 4 equally sized, small rectangles. The
T smaller side
s has
side lenggth 10 cm. How long is th
he longer sidde?
(A) 10 cm
m
(B) 20
2 cm
(C)
( 30 cm
(D) 40 cm
m
(E) 50 cm
3. Which of the following numbers is closest to the productt of 2∙015  510∙2?
(A) 0,1
(B) 1
(C)
( 10
(D) 100
(E) 10
000
4. The diaggram shows the
t net of a cube
c
whose faces are numbered. Sasscha adds
the numbeers that are on
o opposite faces
f
of the ccube. Which three results
does he gett?
(A) 4, 6, 11
(B) 4,
4 5, 12
(C)
( 5, 6, 10
(D) 5, 7, 9
(E) 5, 8, 8
5. Which of the following fractions is not a whoole number?
(A)
(B)
(D)
(C)
(
(E)
6. The drivee from A‐village to B‐tow
wn via C‐housse takes 130
0 minutes. Th
he drive from
m A‐village to
o
C‐house takes 35 minuttes. How many minutes ddoes a drive from C‐housse to B‐townn take?
(A) 95
(B) 105
1
(D) 165
(C)
( 115
(E) 17
75
7. The diaggram shows the
t net of a three‐sided
t
pprism. Which
h line of the diagram form
ms an
edge of tthe prism together with line UV wheen the net is folded
f
up?
(A) WV
(B) XW
X
(C)
( XY
(D) QR
(E) RS
R
8. When simon the squ
uirrel comes down from hhis tree onto
o the floor, he
e never movves further th
han 5 m
away fro
om the trunkk of his tree. Furthermoree, he stays att least 5 m aw
way from thee dog kennel.
Which picture showss most accurrately the areea in which Simon
S
can be
e found?
(A)
(B)
(CC)
(D
D)
(E)
9. One corn
ner of a squaare piece of paper
p
is fold ed into the middle
m
of the
e square.
That wayy an irregular pentagon is created. Thhe numerical values of th
he areas of thhe
Pentagon and the sq
quare are con
nsecutive whhole numbers.
What is tthe area of the
t square?
(A) 2
(B) 4
(C)
( 8
(D) 16
2
(E) 32
10. The sidee lengths of a triangle are
e 6, 10 and 111. An equilateral triangle
e has the sam
me perimete
er as this
triangle. How long iss one side of the equilateeral triangle??
(A) 18
(B) 11
1
(C)
( 10
(D) 9
(E) 6
‐ 4p
point questiions ‐
11.A cyclist covers a disttance of 5 m in one secoond. The whe
eels of his bikke each havee a circumferrence of
125 cm. How many complete turns does eacch wheel do in 5 secondss?
(A) 4
(B) 5
(C)
( 10
(D) 20
(E) 25
5
12. All the b
boys in a classs are born on
o different ddays of the week
w
and all the
t girls are born in diffe
erent
months. If one new girl
g or boy jo
oins this classs, this is defin
nitely no longer true. Ho w many teen
nagers are
in this class?
(A) 18
(B) 19
1
(C)
( 20
(D) 24
(E) 25
5
13.The diaggram consistss of three squares each oone of side le
ength 1. The midpoint
of the to
opmost square is exactly above the coommon side of the two other
o
squarees.
What is tthe area of the
t section coloured greyy?
(A)
(B)
(C)
( 1
(D) 1
(E) 1
14.Each star in the equaation 2 ∗ 0 ∗ 1 ∗ 5 ∗ 2 ∗ 0 ∗ 1 ∗ 5 ∗ 2 ∗ 0 ∗ 1 ∗ 5
” so that the equation iss correct.
“” or “
What is tthe smallest number of stars
s
that cann be replaced by “”?
(A) 1
(B) 2
(C)
( 3
(D) 4
0 should bbe replaced by
b either
(E) 5
15.During a thunder sto
orm it rained 15 liters perr square metter. By how much
m
did thee water level of an
outdoor swimming pool
p
increase
e?
(A) 150 ccm
(B) 0,15
0 cm
(C)
( 15 cm
(D) 1,5 cm
m
(E) It dep
pends on thee size of the swimming p ool.
16.A bush h
has 10 twigs. Each twig has exactly 5 leaves or exaactly 2 leaves and a
flower. W
Which of the following nu
umbers couldd be the totaal number off leaves on
the bush
h?
(A) 45
(B) 39
3
(C)
( 37
(D) 31
(E) None of the n umbers from
m (A) to (D)
17.The 10 p
participants of
o a test achiieve on averaage 6 points. Exactly 6 off the particippants passed the test.
The averrage of the participants
p
that
t
passed tthe test was 8 points.
What is tthe average of the particcipants that ddid not pass the test?
(A) 1
(B) 2
(D) 4
(C)
( 3
(E) 5
18.Each sidee of each triaangle in the diagram is p ainted either blue, green
n or red.
Four of tthe sides aree already pain
nted. Which colour can the
t line markked „x" have,,
if each trriangle mustt have all side
es in differennt colours?
(A) onlyy green (B) only
o red
(C) only blue
(D) either red or blue
(E) The queestion canno
ot be solved.
19.Eva addeed the length
hs of three siides of a recttangle and obtained
o
44 cm.
c Ulli also aadded the le
engths of
three sid
des of the same rectangle
e and obtainned 40 cm. What
W
is the pe
erimeter of tthe rectangle
e?
(A) 42 cm
5 cm
(B) 56
(C)
( 64 cm
(D) 84 cm
m
(E) 11
12 cm
20. The teaccher asks fivee of her stud
dents, how m
many of them
m had studied
d the previouus day. Azra says:
“Nobody.” B
Berti says: “O
Only one.” Ch
hrista says: “ Exactly two.”” Doris says: “Exactly threee.” Emina says:
“Exactly fou
ur.” The teach
her knows th
hat students always lie if they haven’tt studied an d are alwayss truthful
when they h
have studied
d. How manyy of those stuudents had studied the previous day??
(A) 0
(B) 1
(C)
( 2
(D) 3
(E) 4
‐ 5p
point questiions ‐
21. In a group of kangarroos the two lightest onees weigh 25 % of the total weight of tthe whole gro
oup.
The threee heaviest ones
o
weight 60
6 % of the ttotal weight. How many kangaroos
k
arre in this group?
(A) 6
(B) 7
(C)
( 8
(D) 15
(E) 20
0
22.Five positive whole numbers,
n
wh
hich are not nnecessarily all
a different, are
a written oon five cards.
Peter calculates the sum of each pair of cardss. He obtainss only three different ressults, namelyy 57, 70 and
83. What is the biggeest number that
t
is writteen on one of the cards?
(A) 35
(B) 42
4
(C)
( 48
(D) 53
(E) 82
2
23. A squaree with area 30
3 is split intto two by its diagonal and
d then
Split into
o triangles ass shown in th
he diagram. SSome of the areas of the
e
triangless are given in
n the diagram
m. Which of tthe line segm
ments a, b, c,, d, e
of the diiagonal is thee longest?
(A) a
(B) b
(C)
( c
(D) d
(E) e
24. Riki wants to write one numberr in each of t he seven secctions of the diagram picctured.
Two zones are adjaceent if they sh
hare a part oof their outlin
ne. The number in each zzone
should b
be the sum of all numberrs of its adjaccent zones. Riki
R has already placed nuumbers
in two zo
ones. Which number doe
es she need tto write in th
he zone markked „?".
(A) 1
(B) 2
(C)
( 6
(D) 4
(E) 0
25.Florian h
has seven pieeces of wire of lengths 1 cm, 2 cm, 3 cm, 4 cm, 5 cm, 6 cm an d 7 cm.
He does not
He uses some of tho
ose pieces to form a wire model of a cube
c
with sid
de length 1. H
want anyy overlapping wire parts. What is thee smallest nu
umber of wire pieces thatt he can
use?
(A) 1
(B) 2
(C)
( 3
(D) 4
(E) 5
26.In the traapezium PQR
RS the sides PQ and SR a re parallel. Also
A
Q . What is thhe size of anggle PQR?
RSP = 1120° and RSS  SP  13 PQ
(A) 15°
(B) 22∙5°
2
(C)
( 25°
(D) 30°
(E) 45
5°
27.On a straaight line theere are five points.
p
Alex m
measures all the distance
es between eevery possible pair of
points. He o
obtains in asccending orde
er 2, 5, 6, 8, 99, k, 15, 17, 20 and 22. What
W
is the va
value of k?
(A) 10
(B) 11
1
(C)
( 12
(D) 13
(E) 14
4
28.I have no
oted down six digits of Errich’s seven‐ digit phone number in th
he correct orrder.
I don’t know which digit
d I have missed
m
out annd where I have missed it out. What iis the maxim
mum
ake to be surre that I have
e used the co
orrect phonee number?
number of tries that I have to ma
(Note: The first digit could also be
b 0!)
(A) 55
(B) 60
6
(C)
( 64
(D) 70
(E) 80
0
29.Maria divides 2015 by
b 1. Then sh
he divides 20015 by 2 and then in orde
er by 3, 4 etcc. up to and including
1000. Fo
or each division she write
es down the remainder. What
W
is the biggest
b
remaainder she ha
as noted
down?
(A) 15
2
(B) 215
(C)
( 671
(D) 1007
(E) an
nother valuee
30.Each possitive whole number is co
oloured in acccording to the following
g three rules::
umber is either red or greeen.
(i) Each nu
(ii) The sum
m of two diffe
erent red nuumbers resultts in a red nu
umber.
(iii) The sum
m of two diffe
erent green numbers is a green number.
How many ways are there to do this?
(A) 0
(B) 2
(C)
( 4
(D) 6
here are morre than six ways
(E) th