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<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In the diagram we see 10 islands that are connected by 15 bridges. What is the minimum number of bridges that need to be closed off so that there is no connection from $A$ to $B$ anymore? | 3 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Four of the following five pictures show pieces of the graph of the same quadratic function. Which piece does not belong? | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The diagram shows a circle with centre $O$ and the diameters $A B$ and $C X$. Let $O B=$ $B C$. Which fraction of the circle area is shaded?
(A) $\frac{2}{5}$
(B) $\frac{1}{3}$
(C) $\frac{2}{7}$
(D) $\frac{3}{8}$
(E) $\frac{4}{11}$ | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Three circles with centres $A, B, C$ touch each other in pairs from the outside (see diagram). Their radii are 3,2 and 1. How big is the area of the triangle $A B C$? | 6 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The diagram shows the floor plan of Renate's house. Renate enters her house from the terrace (Terrasse) and walks through every door of the house exactly once. Which room does she end up in? | 2 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The faces of the prism shown, are made up of two triangles and three squares. The six vertices are labelled using the numbers 1 to 6. The sum of the four numbers around each square is always the same. The numbers 1 and 5 are given in the diagram. Which number is written at vertex $X$? | 2 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
On an idealised rectangular billiard table with side lengths $3 \mathrm{~m}$ and $2 \mathrm{m}$ a ball (point-shaped) is pushed away from point $M$ on the long side $A B$. It is reflected exactly once on each of the other sides as shown. at which distance from the vertex $A$ will the ball hit this side again if $B M=1.2 \mathrm{~m}$ and $B N=$ $0.8 m$?
(A) $2 \mathrm{~m}$
(B) $1.5 \mathrm{~m}$
(C) $1.2 \mathrm{~m}$
(D) $2.8 \mathrm{~m}$
(E) $1.8 \mathrm{~m}$ | E | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The diagram shows two adjoining squares with side lengths $a$ and $b$ (with $a<b$). How big is the area of the grey triangle?
(A) $\sqrt{a b}$
(B) $\frac{1}{2} a^{2}$
(C) $\frac{1}{2} b^{2}$
(D) $\frac{1}{4}\left(a^{2}+b^{2}\right)$
(E) $\frac{1}{2}\left(a^{2}+b^{2}\right)$ | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Three circles with radius 2 are drawn in such a way that each time one of the points of intersection of two circles is identical with the centre of the third circle. How big is the area of the grey zone?
(A) $\pi$
(B) $3 \pi$
(C) $\frac{\pi}{2}$
(D) $2 \pi$
(E) $4 \pi$ | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The pie chart beside refers to the number of inhabitants of the five zones of a city. The central zone has the same population as the north, west and east zones together and the south zone has half of the inhabitants of the west zone. What is the percentage difference between the inhabitants of the north and east zones?
(A) $6 \%$
(B) $11 \%$
(C) $12 \%$
(D) $13 \%$
(E) $18 \%$ | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The parabola in the figure has an equation of the form $y=a x^{2}+b x+c$ for some distinct real numbers $a, b$ and $c$. Which of the following equations could be an equation of the line in the figure?
(A) $y=b x+c$
(B) $y=c x+b$
(C) $y=a x+b$
(D) $y=a x+c$
(E) $y=c x+a$ | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
A triangle $A B C$ is divided into four parts by two straight lines, as shown. The areas of the smaller triangles are 1,3 and 3. What is the area of the original triangle? | 12 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
A cuboid with surface area $X$ is cut up along six planes parallel to the sides (see diagram). What is the total surface area of all 27 thus created solids?
(A) $X$
(B) $2 X$
(C) $3 X$
(D) $4 X$
(E) It depends on the position of the planes. | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Two equilateral triangles of different sizes are placed on top of each other so that a hexagon is formed on the inside whose opposite sides are parallel. Four of the side lengths of the hexagon are stated in the diagram. How big is the perimeter of the hexagon? | 70 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The diagram shows a spiral of consecutive numbers starting with 1. In which order will the numbers 625, 626 and 627 appear in the spiral?
(A) $625 \uparrow 626 \uparrow 627$
(B) $625 \uparrow 626 \rightarrow$
(C) $625 \rightarrow 626 \rightarrow 627$
(D) $625 \rightarrow 626 \uparrow 627$
(E) $625 \downarrow 626 \downarrow 627$ | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
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 $T$ | E | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
A butterfly sat down on a correctly solved exercise. What number is the butterfly covering? | 500 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In the diagram every of the eight kangaroos can jump to any empty square. What is the least number of kangaroos that must jump so that each row and each column have exactly two kangaroos? | 1 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
John has a chocolate tablet consisting of square pieces of $1 \mathrm{~cm} \times 1 \mathrm{~cm}$. He has eaten already some pieces in a corner (see the picture). How many pieces John still have? | 60 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The figure shows a rectangular garden with dimensions $16 \mathrm{~m}$ and $20 \mathrm{~m}$. The gardener has planted six identical flowerbeds (they are gray in the diagram). What is the perimeter (in metres) of each of the flowerbeds? | 24 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
How many cubes have been taken from the block? | 7 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In each of the nine cells of the square we will write down one of the digits 1 , 2 or 3. We will do this in such a way that in each horizontal row and vertical column each of the digits 1, 2 and 3 will be written. In the upper left cell we will start with 1. How many different squares can we then make? | 4 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Zita walks from left to right and puts the numbers into 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
(E) 1, 2 and 5 | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Which number has to be put into the dark cloud to have all the given calculations right? | 5 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Jane shoots two arrows at the target. In the drawing we see that her score is 5. If both arrows hit the target, how many different scores can she obtain? | 6 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Thomas has made a table out of small cubes. How many small cubes did he use? | 32 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
A large cube is made from 64 small cubes. The 5 visible faces of the large cube are green, the bottom face is red. How many of the small cubes have 3 green faces? | 4 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
lines are drawn on a piece of paper and some of the lines are given numbers. The paper is cut along some of these lines and then folded as shown in the picture. What is the total of the numbers on the lines that were cut? | 20 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Seven children stand in a circle. Nowhere are two boys found standing next to each other. Nowhere are three girls found standing next to each other. What is possible for the number of girls? The number of girls can...
(A) ... only be 3.
(B) ... be 3 or 4.
(C) ... be 4 or 5.
(D) ... only be 5.
(E) ... only be 4. | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Elisabeth sorts the following cards:
With each move she is allowed to swap any two cards with each other. What is the smallest number of moves she needs in order to get the word KANGAROO. | 3 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Heinzi the kangaroo has bought some toys. For this he gave 150 Kangoo-coins (KC) and received 20 kangoo-coins back. Just before leaving the shop he changed his mind, and exchanged one of the toys he had bought with another one. Therefore he received a further 5 kangoo-coins back from the shopkeeper. Which of the toys in the picture has Heinzi taken home with him?
(A) Carriage and Aeroplane
(B) Carriage and Bus
(C) Carriage and Tram
(D) Motorbike and Tram
(E) Bus, Motorbike and Tram | A | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In each box exactly one of the digits $0,1,2,3,4,5$ and 6 is to be written. Each digit will only be used once. Which digit has to be written in the grey box so that the sum is correct? | 5 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In the diagram you can see a very ragged island. Some of the frogs are sitting in the water. How many are sitting on the island? | 6 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Peter rides his bike along a cycle path in a park. He starts at point $S$ and rides in the direction of the arrow. At the first crossing he turns right, then at the next left, and then again to the right and then again to left. Which crossing does he not reach? | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Which picture shows a single large loop? | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In this square there are 9 dots. The distance between the points is always the same. You can draw a square by joining 4 points. How many different sizes can such squares have? | 3 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Chantal has placed numbers in two of the nine cells (see diagram). She wants to place the numbers 1, 2, 3 in every row and every column exactly once. How big is the sum of the two numbers in the grey cells? | 4 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Karin wants to place five bowls on a table so that they are ordered according to their weight. She has already placed the bowls $Q, R, S$ and $T$ in order, where $Q$ is lightest and $T$ is heaviest. Where does she have to place bowl Z?
(A) to the left of bowl Q
(B) between bowls Q and R
(C) between bowls R and S
(D) between bowls S and T
(E) to the right of bowl T | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Linda fixes 3 photos on a pin board next to each other. She uses 8 pins to do so. Peter wants to fix 7 photos in the same way. How many pins does he need for that? | 16 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
John paints the squares of the board next to it if the result of the calculation inside them is 24. How did the painting of the board look?
\begin{tabular}{|l|l|l|}
\hline $28-4$ & $4 \times 6$ & $18+6$ \\
\hline $19+6$ & $8 \times 3$ & $29-6$ \\
\hline
\end{tabular} | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Cynthia paints each region of the figure in a single color: red, blue or yellow. She paints with different colors the regions that touch each other. In how many different ways can Cyntia paint the figure? | 6 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
How many fish will have their heads pointing towards the ring when we straighten the line? | 6 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
7 cards are arranged as shown. Each card has 2 numbers on with 1 of them written upside down. The teacher wants to rearrange the cards so that the sum of the numbers in the top row is the same as the sum of the numbers in the bottom row. She can do this by turning one of the cards upside down. Which card must she turn?
(A) A
(B) B
(C) D
(D) F
(E) G | E | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
If a laser beam hits a mirror it changes its direction (see left diagram). Each mirror has mirrored sides on both sides. At which letter does the laser beam end? | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
A road leads away from each of the six houses (see diagram). A hexagon showing the roads in the middle is however, missing. Which hexagons fit in the middle so
that one can travel from $A$ to $B$ and to $E$, but not to $D$?
(A) 1 and 2
(B) 1 and 4
(C) 1 and 5
(D) 2 and 3
(E) 4 and 5 | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The sum of the numbers in each of the rings should be 55. Which number is $X$? | 10 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The composite board shown in the picture consists of 20 fields $1 \times 1$. How many possibilities are there exist to cover all 18 white fields with 9 rectangular stones $1 \times 2$ ? (The board cannot be turned. Two possibilities are called different if at least one stone lies in another way.) | 4 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Choose the picture where the angle between the hands of a watch is $150^{\circ}$. | E | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Six cars are parked on a parking. Someone wants to move from $S$ to $F$. His route must be as short as possible. Which of the following routes is the shortest?
(A) A
(B) B
(C) C
(D) D
(E) All routes are equal | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
On the faces of a cube are written letters. First figure represents one possibility of its net. What letter should be written instead of the question mark in the other version of its net?
(A) A
(B) B
(C) C
(D) E
(E) Impossible to determine | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Two squares $9 \mathrm{~cm} \times 9 \mathrm{~cm}$ overlap so as to form a rectangle $9 \mathrm{~cm} \times 13 \mathrm{~cm}$ as shown. Find the area of the region in which the two squares overlap.
(A) $36 \mathrm{~cm}^{2}$
(B) $45 \mathrm{~cm}^{2}$
(C) $54 \mathrm{~cm}^{2}$
(D) $63 \mathrm{~cm}^{2}$
(E) $72 \mathrm{~cm}^{2}$ | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
There are 5 boxes and each box contains some cards labeled K, M, H, P, T, as shown below. Peter wants to remove cards out of each box so that at the end each box contained only one card, and different boxes contained cards with different letters. Which card remains in the first box?
(A) It is impossible to do this
(B) T
(C) M
(D) H
(E) P | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
By shooting two arrows at the shown target on the wall, how many different scores can we obtain? | 9 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Suppose you make a trip over the squared board shown, and you visit every square exactly once. Where must you start, if you can move only horizontally or vertically, but not diagonally?
(A) Only in the middle square
(B) Only at a corner square
(C) Only at an unshaded square
(D) Only at a shaded square
(E) At any square | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The picture shows the plan of a town. There are four circular bus routes in the town. Bus 1 follows the route $C D E F G H C$, which is $17 \mathrm{~km}$ long. Bus 2 goes $A B C F G H A$, and covers $12 \mathrm{~km}$. The route of bus 3 is $A B C D E F G H A$, and is equal to $20 \mathrm{~km}$. Bus 4 follows the route $C F G H C$. How long is this route?
(A) $5 \mathrm{~km}$
(B) $8 \mathrm{~km}$
(C) $9 \mathrm{~km}$
(D) $12 \mathrm{~km}$
(E) $15 \mathrm{~km}$ | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The diagram shows squares of different sizes. The side length of the smallest square is $20 \mathrm{~cm}$. How long is the black line?
(A) $380 \mathrm{~cm}$
(B) $400 \mathrm{~cm}$
(C) $420 \mathrm{~cm}$
(D) $440 \mathrm{~cm}$
(E) $1680 \mathrm{~cm}$ | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Which of the following is made using more than one piece of string?
(A) I, III, IV and V
(B) III, IV and V
(C) I, III and V
(D) all
(E) None of these answers | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In the following figures you see five elastic bands, only one of which is tied in a knot. Which one? | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The numbers 1 to 7 should be written in the small circles so that the sum of the numbers along each line is the same. Which number should be written in the uppermost circle on the triangle? | 4 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Four cogs are connected to each other as shown in the picture. The first has 30 teeth, the second 15, the third 60 and the fourth 10 . How many turns will the last cog make for each full turn of the first cog? | 3 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Nick can turn right but not left on his bicycle. What is the least number of right turns he must make in order to get from $A$ to $B$? | 4 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
For the game of Chess a new piece, the Kangaroo, has been invented. With each jump the kangaroo jumps either 3 squares vertically and 1 Horizontally, or 3 horizontally and 1 vertically, as pictured. What is the smallest number of jumps the kangaroo must make to move from its current position to position $\mathrm{A}$ ? | 3 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
$A 10 \mathrm{~cm}$ long piece if wire is folded so that every part is equally long (see diagram). The wire is then cut through in the two positions marked. How long are the three pieces created in this way?
(A) $2 \mathrm{~cm}, 3 \mathrm{~cm}, 5 \mathrm{~cm}$
(B) $2 \mathrm{~cm}, 2 \mathrm{~cm}, 6 \mathrm{~cm}$
(C) $1 \mathrm{~cm}, 4 \mathrm{~cm}, 5 \mathrm{~cm}$
(D) $1 \mathrm{~cm}, 3 \mathrm{~cm}, 6 \mathrm{~cm}$
(E) $3 \mathrm{~cm}, 3 \mathrm{~cm}, 4 \mathrm{~cm}$ | A | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Jane, Kate and Lynn go for a walk. Jane walks at the very front, Kate in the middle and Lynn at the very back. Jane weighs $500 \mathrm{~kg}$ more than Kate and Kate weighs $1000 \mathrm{~kg}$ less than Lynn. Which of the following pictures shows Jane, Kate and Lynn in the right order?
(A) (A)
(B) (B)
(C) (C)
(D) (D)
(E) (E) | A | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
A furniture shop sells 3-seater, 2-seater and 1-seater sofas that each have an equally wide armrest on the left and the right hand side. Each seat is equally wide (see picture). Together with the armrests the 3-seater sofa is $220 \mathrm{~cm}$ and the 2-seater sofa $160 \mathrm{~cm}$ wide. How wide is the 1-seater sofa?
(A) $60 \mathrm{~cm}$
(B) $80 \mathrm{~cm}$
(C) $90 \mathrm{~cm}$
(D) $100 \mathrm{~cm}$
(E) $120 \mathrm{~cm}$ | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The faces of a die are either white, grey or black. Opposite faces are always a different colour. Which of the following nets does not belong to such a die? | E | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Benjamin writes a number into the first circle. He then carries out the calculations as instructed and each time writes down the results in the respective circles. How many of the six numbers are divisible by 3? | 2 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
When the bat Elisa left its cave at night, the digital clock showed . When she came back in the morning and hung herself upside down, she looked at her watch and saw . How long did she stay out of the cave?
(A) 2h 48m
(B) 2h 59m
(C) 3h 39m
(D) 3h 41m
(E) 3h 49m | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Ten people order an ice cream for each one. They ask for four vanilla ice creams, three chocolate ice creams, two lemon ice creams and one mango ice cream. As a topping, they ask for four umbrellas, three cherries, two wafers and a chocolate gum, one topping for each ice cream. Since they don't want two ice creams the same, which of the following combinations is possible?
(A) Chocolat and chocolate gum.
(B) Mango and cherry.
(C) Lemmon and wafer.
(D) Mango and wafer.
(E) Lemmon and cherry. | E | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
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 coloured $\frac{1}{8}$ of the large square. Which one is our coloring? | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Eva paddles around five buoys with her boat (see diagram). Which of the buoys does she paddle around in an anti-clockwise direction?
(A) 1 and 4
(B) 2, 3 and 5
(C) 2 and 3
(D) 1,4 and 5
(E) 1 and 3 | E | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
How much does this Ferris wheel need to turn so that a white gondola is on top for
the first time?
(A) $\frac{1}{2}$ turn
(B) $\frac{1}{3}$ turn
(C) $\frac{1}{6}$ turn
(D) $\frac{1}{12}$ turn
(E) $\frac{5}{6}$ turn | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In triangle $A B C$ (see picture) $A B=A C, A E=A D$, and $\angle B A D=30^{\circ}$. What is the measure of angle $C D E$?
(A) $10^{\circ}$
(B) $15^{\circ}$
(C) $20^{\circ}$
(D) $25^{\circ}$
(E) $30^{\circ}$ | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The section of a cube by a plane generates a plane figure. I have plotted this section in the development of the cube (see the picture). Can you find out what figure it is?
(A) An equilateral triangle
(B) A rectangle, but not a square
(C) A right triangle
(D) A square
(E) A hexagon | A | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
How many pieces of string are there in the picture? | 4 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Which of the following is made using more than one piece of string?
(A) I, III, IV and V
(B) I, III and V
(C) III, IV and V
(D) all
(E) None of these answers | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
How many lines of symmetry does this figure have? | 2 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In the quadrilateral $\mathrm{ABCD}, \mathrm{AD}=\mathrm{BC}, \angle \mathrm{DAC}=50^{\circ}$, $\angle \mathrm{DCA}=65^{\circ}$ and $\angle \mathrm{ACB}=70^{\circ}$. How big is $\angle \mathrm{ABC}$?
(A) $50^{\circ}$
(B) $55^{\circ}$
(C) $60^{\circ}$
(D) $65^{\circ}$
(E) It is not clear. | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The sides of the rectangle $A B C D$ are parallel to the co-ordinate axes. The rectangle is positioned below the $x$-axis and to the right of the $y$-axis, as shown in the picture. The co-ordinates of the points $A, B, C, D$ are whole numbers. For each of the points we calculate the value of ( $y$ co-ordinate) $\div$(x co-ordinate). Which of the points will give the smallest value?
(A) A
(B) B
(C) C
(D) D
(E) It depends on the rectangle. | A | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In triangle $A B C$ (see sketch) $A D$ is the angle bisector of the angle at $A$ and $B H$ is the height from side $A C$. The obtuse angle between $B H$ and $A D$ is four times the size of angle $\angle D A B$. How big is the angle $\angle C A B$?
(A) $30^{\circ}$
(B) $45^{\circ}$
(C) $60^{\circ}$
(D) $75^{\circ}$
(E) $90^{\circ}$ | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Valentin draws a zig-zag line inside a rectangle as shown in the diagram. For that he uses the angles $10^{\circ}, 14^{\circ}, 33^{\circ}$ and $26^{\circ}$. How big is angle $\varphi$?
(A) $11^{\circ}$
(B) $12^{\circ}$
(C) $16^{\circ}$
(D) $17^{\circ}$
(E) $33^{\circ}$ | A | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The diagram shows a rectangle and a straight line $x$, which is parallel to one of the sides of the rectangle. There are two points $A$ and $B$ on $x$ inside the rectangle. The sum of the areas of the two triangles shaded in grey is $10 \mathrm{~cm}^{2}$. How big is the area of the rectangle?
(A) $18 \mathrm{~cm}^{2}$
(B) $20 \mathrm{~cm}^{2}$
(C) $22 \mathrm{~cm}^{2}$
(D) $24 \mathrm{~cm}^{2}$
(E) It depends on the position of the points A and B. | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The points $N, M$ and $L$ lie on the sides of an equilateral triangle $A B C$ so that $\mathrm{NM} \perp \mathrm{BC}, \mathrm{ML} \perp \mathrm{AB}$ and $\mathrm{LN} \perp \mathrm{AC}$ holds true. The area of the triangle $\mathrm{ABC}$ is $36 \mathrm{~cm}^{2}$. What is the area of the triangle LMN?
(A) $9 \mathrm{~cm}^{2}$
(B) $12 \mathrm{~cm}^{2}$
(C) $15 \mathrm{~cm}^{2}$
(D) $16 \mathrm{~cm}^{2}$
(E) $18 \mathrm{~cm}^{2}$ | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Five squares are positioned as shown. The small square indicated has area 1. What is the value of $h$?
(A) $3 \mathrm{~m}$
(B) $3.5 \mathrm{~m}$
(C) $4 \mathrm{~m}$
(D) $4.2 \mathrm{~m}$
(E) $4.5 \mathrm{~m}$ | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Meike paddles around five buoys with her boat (see diagram). Which of the buoys does she paddle around in a clockwise direction?
(A) 2, 3 and 4
(B) 1, 2 and 3
(C) 1, 3 and 5
(D) 2, 4 and 5
(E) 2, 3 and 5 | E | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Anna has five circular discs that are all of different sizes. She wants to build a tower using three discs where a smaller disc always has to lie on top of a bigger disc. How many ways are there for Anna to build the tower? | 10 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The digits 0 to 9 can be formed using matchsticks (see diagram). How many different positive whole numbers can be formed this way with exactly 6 matchsticks? | 6 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
An ant walks along the sides of an equilateral triangle (see diagram). Its velocity is $5 \mathrm{~cm} / \mathrm{min}$ along the first side, $15 \mathrm{~cm} / \mathrm{min}$ along the second and $20 \mathrm{~cm} / \mathrm{min}$ along the third. With which average velocity in $\mathrm{cm} / \mathrm{min}$ does the ant walk once around the entire triangle?
(A) $10$
(B) $\frac{80}{11}$
(C) $\frac{180}{19}$
(D) $15$
(E) $\frac{40}{3}$ | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
What is the sum of the 10 angles marked in the picture?
(A) $720^{\circ}$
(B) $600^{\circ}$
(C) $450^{\circ}$
(D) $360^{\circ}$
(E) $300^{\circ}$ | A | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
How many routes are possible for the king to travel from the top left square to the bottom right square of the grid with the minimum number of moves. (The king can move to any adjacent square, including that adjacent diagonally.) | 4 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In the diagram one should go from A to B along the arrows. Along the way calculate the sum of the numbers that are stepped on. How many different results can be obtained? | 2 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
A circle of radius $4 \mathrm{~cm}$ is divided, as shown, by four semicircles with radius $2 \mathrm{~cm}$ into four congruent parts. What is the perimeter of one of these parts?
(A) $2 \pi$
(B) $4 \pi$
(C) $6 \pi$
(D) $8 \pi$
(E) $12 \pi$ | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The area of the grey rectangle shown on the right is $13 \mathrm{~cm}^{2}. X$ and $Y$ are the midpoints of the sides of the trapezium. How big is the area of the trapezium?
(A) $24 \mathrm{~cm}^{2}$
(B) $25 \mathrm{~cm}^{2}$
(C) $26 \mathrm{~cm}^{2}$
(D) $27 \mathrm{~cm}^{2}$
(E) $28 \mathrm{~cm}^{2}$ | C | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Which of the shapes to the right has the largest area?
(A) A
(B) B
(C) C
(D) D
(E) All shapes have the same area. | E | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Mr. Hide wants to find a treasure that he buried years before. He can only remember that he buried the treasure at least $5 \mathrm{~m}$ away from the hedge and no more than $5 \mathrm{~m}$ away from the old pear tree. Which picture shows best the area where Mr. Hide has to look for the treasure? | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
In the diagram one can see my decision-die in three different positions. What is the probability I get a "YES", when rolling this die once.
(A) $\frac{1}{3}$
(B) $\frac{1}{2}$
(C) $\frac{5}{9}$
(D) $\frac{2}{3}$
(E) $\frac{5}{6}$ | B | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Lines parallel to the base $A C$ of triangle $A B C$ are drawn through $X$ and $Y$. In each case, the areas of the grey parts are equal in siz. The ratio $B X: X A=4: 1$ is known. What is the ratio $B Y: Y A$?
(A) $1: 1$
(B) $2: 1$
(C) $3: 1$
(D) $3: 2$
(E) $4: 3$ | D | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Peter wants to colour in the cells of a $3 \times 3$ square so that every row, every column and both diagonals each have three cells with three different colours. What is the smallest number of colours with which Peter can achieve this? | 5 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
The rings shown are partially interlinked. How long is the longest chain built this way which also contains the thick light ring? | 5 | |
<image>Please solve the problem step by step and put your answer in one "\boxed{}". If it is a multiple choice question, only one letter is allowed in the "\boxed{}".
Five identical measuring jugs are filled with water. Four of them contain exactly the same amount of water. Which measuring jug contains a different amount? | B |
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