16th Pangea Mathematics Competition
Preliminary Round - Grade 6
1 point
Question 1
Numbers can be put in the square with nine fields such that they add up to 36 in
every row, every column and the two diagonals. Which number is in the field with the
question mark?
18
?
3
6
a) 3
d) 12
e) 15
Question 2
A farmer has 17 cows, 5 pigs and 1 horse. How old is the farmer?
1 point
a) 21 years
b) 6
c) 9
b) 22 years
c) 23 years
d) 85 years
1 point
Question 3
Which ratio does not fit?
a) 0.25
b)
1
4
e) not solvable
c) 4:8
d)
e)
2 points
Question 4
The big square with an area of 49 cm2 is built up
out of four equal sized rectangles and a small square
with area 1 cm2 . Find the area of one rectangle.
a) 12 cm2
b) 14 cm2
c) 24 cm2
1
d) 28 cm2
e) 48 cm2
Leipzig International School
2 points
Question 5
Decode the word using the secret code.
•
K
O
C
J
L
I
R
U
M
a) MATHE
•
•
•
•
B
Y
X
•
•
•
T
E
Z
•
D
G
P
F
•
•
N
S
•
G
•
•
•
W
V
A
b) MATIK
•
c) STERN
H
d) SUPER
e) SUPPE
2 points
Question 6
Two days before yesterday was Friday. What day of the week is it in two days?
a) Tuesday
b) Wednesday
c) Thursday
d) Friday
Question 7
In the diagram you see two addition-walls with 2 and 3 head stones resp.
2 head stones
e) Sunday
3 points
3 head stones
8
4
4 4
2 2 2
2 2
Which number you will find on the stone on the top in the addition-wall with 10 head
stones?
a) 400
b) 512
c) 800
d) 1024
e) 2048
3 points
Question 8
Distribute the digits 1, 2, 5, 6, 9 in the boxes so that the multiplication problem is
correct. Which digit is then after the multiplication sign?
= 45810
a) 1
b) 2
c) 5
2
d) 6
Leipzig International School
e) 9
3 points
Question 9
Kevin asks Luisa a number puzzle:: Remember a number. Now add 3 and then
”
multiply the sum with four. Finally, subtract 5. If you tell me the result, I give you
your imaginary number.“
Luisa says: My result is 35.“
”
Which number is Luisa’s imaginary number?
a) 3
b) 4
c) 5
d) 6
e) 7
4 points
Question 10
A rectangle has side lengths of 18 cm and 16 cm. Change it into a rectangle with equal
area such that its lengths is twice its width. Find the perimeter of that new rectangle.
a) 44 cm
b) 68 cm
c) 72 cm
d) 144 cm
4 points
Question 11
Find the area of the grey shaded triangle.
a) 8 boxes
b) 9 boxes
e) 288 cm
c)10 boxes
d) 11 boxes
e) 12 boxes
4 points
Question 12
The dice is rolled along the arrow. Which
number is at the bottom on the grey field?
a) 2
b) 3
c) 4
3
d) 5
Leipzig International School
e) 6
4 points
Question 13
Which number fits in the box such that the final result will be 1?
7 12
−
5
□
a) 5
b) 12
c) 20
d) 24
e) 30
5 points
Question 14
Luisa can put 24 different outfits out of her pants and sweaters. How many pants (p)
and sweaters (s) can Luisa not have?
a) 2 p 12 s
b) 3 p 8 s
c) 6 p 4 s
d) 8 p 3 s
e) 5 p 5 s
5 points
Question 15
There are 60 black, 26 red, 25 yellow, 3 green and 6 blue balls in a box. Lisa should
choose randomly without looking balls out of the box. How many balls does she need
to take out to make sure she has 8 balls of the same color?
a) 8
b) 16
c) 31
d) 32
e) 64
@
5 points
Question 16
A squared piece of paper is folded twice and cut as shown. What shape do you get after
unfolding the piece that was cut out?
a)
b)
c)
d)
e)
5 points
Question 17
Nina has two sand glasses: a small sand glass for 5 minutes and a large sand glass for
7 min. At the beginning the sand of both sand glasses is in the lower chamber. Nina
turns over both sand glasses at the same time. After the little sand glass runs out, Nina
turns it over again. After the big sand glass runs out, Nina turns both sand glasses
over and waits until the small sand glass is run out. What time has Nina measured?
a) 9 min
b) 12 min
c) 14 min
4
d) 17 min
e) 19 min
Leipzig International School
5 points
Question 18
Equal letters represent equal digits. Different letters represent different digits. How
many solutions you can find for the following equation?
AB : C = B
a) 4
b) 5
c) 6
5
d) 7
Leipzig International School
e) 8
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