Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>Question: Petra crafts a piece of jewellery out of two black and two white hearts. The hearts have areas of $1 \mathrm{~cm}^{2}, 4 \mathrm{~cm}^{2}, 9 \mathrm{~cm}^{2}$ and $16 \mathrm{~cm}^{2}$ respectively. She places the hearts on top of each other as shown in the diagram and glues them together. How big is the total area of the visible black parts?
<image1>
Choices:
A. $9 \mathrm{~cm}^{2}$
B. $10 \mathrm{~cm}^{2}$
C. $11 \mathrm{~cm}^{2}$
D. $12 \mathrm{~cm}^{2}$
E. $13 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: Ant Annie starts at the left end of the stick and crawls $\frac{2}{3}$ of the length of the stick. Ladybird Bob starts at the right end of the stick und crawls $\frac{3}{4}$ of the length of the stick. Which fraction of the length of the stick are they then apart from each other?
<image1>
Choices:
A. $\frac{3}{8}$
B. $\frac{1}{12}$
C. $\frac{5}{7}$
D. $\frac{5}{12}$
E. $\frac{7}{12}$
Answer: D
Problem: <image>Question: The black and the dashed line together form seven equilateral triangles. The dashed line is $20 \mathrm{~cm}$ long. How long is the black line?
<image1>
Choices:
A. $25 \mathrm{~cm}$
B. $30 \mathrm{~cm}$
C. $35 \mathrm{~cm}$
D. $40 \mathrm{~cm}$
E. $45 \mathrm{~cm}$
Answer: D
Problem: <image>Question: Ria wants to write a number into each box. She has already written two numbers. The sum of all five numbers should be 35, the sum of the first three numbers should be 22, the sum of the last three numbers should be 25. What is the product Ria gets, if she multiplies the two numbers in the grey boxes?
<image1>
Answer: 63
Problem: <image>Question: Two $1 \mathrm{~cm}$ long segments are marked on opposite sides of a square with side length 8 $\mathrm{cm}$. The end points of the segments are connected with each other as shown in the diagram. How big is the area of the grey part?
<image1>
Choices:
A. $2 \mathrm{~cm}^{2}$
B. $4 \mathrm{~cm}^{2}$
C. $6.4 \mathrm{~cm}^{2}$
D. $8 \mathrm{~cm}^{2}$
E. $10 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: Emily wants to insert nine numbers into the $3 \times 3$ table so that the sum of the numbers in two adjacent cells (with a common side) is always the same. She has already written two numbers into the table. How big is the sum of all nine numbers?
<image1>
Answer: 22
Problem: <image>Question: There are 10 kangaroos in a row, as seen in the picture. Two kangaroos, that are standing next to each other and can see each other are allowed to change places by hopping past each other. This is carried out until no more jumps are allowed. How often do two kangaroos swap places?
<image1>
Answer: 18
Problem: <image>Question: The diagram shows Maria's square tablecloth to scale. All small light squares are equally big and their diagonals are parallel to the sides of the table cloth. Which part of the whole table cloth is black?
<image1>
Choices:
A. $16 \%$
B. $24 \%$
C. $25 \%$
D. $32 \%$
E. $36 \%$
Answer: D
Problem: <image>Question: Mike has 125 small, equally big cubes. He glues some of them together in such a way that one big cube with exactly nine tunnels is created (see diagram). The tunnels go all the way straight through the cube. How many of the 125 cubes is he not using?
<image1>
Answer: 39
Problem: <image>Question: Sarah wants to write a positive whole number onto every tile in the number wall shown, so that every number is equal to the sum of the two numbers on the tiles that are directly below. What is the maximum number of odd numbers Sarah can write on the tiles?
<image1>
Answer: 10
Problem: <image>Question: The parallelogram has area 1. The two diagonals intersect each other at point M. Another point $P$ lies on the side DC. $E$ is the point of intersection of the segments $A P$ and $B D$, and $F$ is the point of intersection of the segments $B P$ and $A C$. What is the area of the quadrilateral EMFP, if the sum of the areas of the triangles $A E D$ and BFC is $\frac{1}{3}$?
<image1>
Choices:
A. $\frac{1}{6}$
B. $\frac{1}{8}$
C. $\frac{1}{10}$
D. $\frac{1}{12}$
E. $\frac{1}{14}$
Answer: D
Problem: <image>Question: If the letters of the Word MAMA are written underneath each other then the word has a vertical axis of symmetry. For which of these words does that also hold true?
<image1>
Choices:
A. ADAM
B. BAUM
C. BOOT
D. LOGO
E. TOTO
Answer: E
Problem: <image>Question: The fence on the right has many holes. One morning the fence falls over and lies on the floor. Which of the following pictures shows the fallen down fence?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: Bernd produces steps for a staircase which are $15 \mathrm{~cm}$ high and $15 \mathrm{~cm}$ deep (see diagram). The staircase should reach from the ground floor to the first floor which is $3 \mathrm{~m}$ higher. How many steps does Bernd have to produce?
<image1>
Answer: 20
Problem: <image>Question: In a game of luck, A ball rolls downwards towards hammered nails and is diverted either to the right or the left by a nail immediately below it. One possible path is shown in the diagram. How many different ways are there for the ball to reach the second compartment from the left?
<image1>
Answer: 4
Problem: <image>Question: A large rectangle is made up of 9 equally big rectangles. The longer side of each small rectangle is $10 \mathrm{~cm}$ long. What is the perimeter of the large rectangle?
<image1>
Choices:
A. $40 \mathrm{~cm}$
B. $48 \mathrm{~cm}$
C. $76 \mathrm{~cm}$
D. $81 \mathrm{~cm}$
E. $90 \mathrm{~cm}$
Answer: C
Problem: <image>Question: Two circles are inscribed into an $11 \mathrm{~cm}$ long and $7 \mathrm{~cm}$ wide rectangle so that they each touch three sides of the rectangle. How big is the distance between the centres of the two circles?
<image1>
Choices:
A. $1 \mathrm{~cm}$
B. $2 \mathrm{~cm}$
C. $3 \mathrm{~cm}$
D. $4 \mathrm{~cm}$
E. $5 \mathrm{~cm}$
Answer: D
Problem: <image>Question: The square $A B C D$ has side length $3 \mathrm{~cm}$. The points $M$ and $N$, which lie on the sides $A D$ and $A B$ respectively, are joined to the corner $C$. That way the square is split up into three parts with equal area. How long is the line segment DM?
<image1>
Choices:
A. $0.5 \mathrm{~cm}$
B. $1 \mathrm{~cm}$
C. $1.5 \mathrm{~cm}$
D. $2 \mathrm{~cm}$
E. $2.5 \mathrm{~cm}$
Answer: D
Problem: <image>Question: Martina multiplies two, two-digit numbers and then paints over some of the digits. How big is the sum of the three digits that Martina has painted over?
<image1>
Answer: 6
Problem: <image>Question: 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 $\varphi$?
<image1>
Choices:
A. $11^{\circ}$
B. $12^{\circ}$
C. $16^{\circ}$
D. $17^{\circ}$
E. $33^{\circ}$
Answer: A
Problem: <image>Question: 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?
<image1>
Choices:
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.
Answer: B
Problem: <image>Question: Jakob writes one of the natural numbers 1 to 9 into each cell of the $3 \times 3$-table. Then he works out the sum of the numbers in each row and in each column. Five of his results are 12, 13, 15, 16 and 17. What is the sixth sum?
<image1>
Answer: 17
Problem: <image>Question: The diagram shows the net of a box consisting only of rectangles. How big is the volume of the box?
<image1>
Choices:
A. $43 \mathrm{~cm}^{3}$
B. $70 \mathrm{~cm}^{3}$
C. $80 \mathrm{~cm}^{3}$
D. $100 \mathrm{~cm}^{3}$
E. $1820 \mathrm{~cm}^{3}$
Answer: C
Problem: <image>Question: Rita wants to write a number into every square of the diagram shown. Every number should be equal to the sum of the two numbers from the adjacent squares. Squares are adjacent if they share one edge. Two numbers are already given. Which number is she going to write into the square marked with $x$?
<image1>
Answer: 7
Problem: <image>Question: Simon runs along the edge round a $50 \mathrm{~m}$ long rectangular swimming pool, while at the same time Jan swims lengths in the pool. Simon runs three times as fast as Jan swims. While Jan swims 6 lengths, Simon manages 5 rounds around the pool. How wide is the swimming pool?
<image1>
Choices:
A. $25 \mathrm{~m}$
B. $40 \mathrm{~m}$
C. $50 \mathrm{~m}$
D. $80 \mathrm{~m}$
E. $180 \mathrm{~m}$
Answer: B
Problem: <image>Question: Lisas aviation club designs a flag with a flying "dove" on a $4 \times 6$-grid. The area of the "dove" is $192 \mathrm{~cm}^{2}$. The perimeter of the "dove" is made up of straight lines and circular arcs. What measurements does the flag have?
<image1>
Choices:
A. $6 \mathrm{~cm} \times 4 \mathrm{~cm}$
B. $12 \mathrm{~cm} \times 8 \mathrm{~cm}$
C. $20 \mathrm{~cm} \times 12 \mathrm{~cm}$
D. $24 \mathrm{~cm} \times 16 \mathrm{~cm}$
E. $30 \mathrm{~cm} \times 20 \mathrm{~cm}$
Answer: D
Problem: <image>Question: 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?
<image1>
Choices:
A. $9 \mathrm{~cm}^{2}$
B. $12 \mathrm{~cm}^{2}$
C. $15 \mathrm{~cm}^{2}$
D. $16 \mathrm{~cm}^{2}$
E. $18 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: In the isosceles triangle $A B C$ (with base $A C$ ) the points $K$ and $L$ are added on the sides $A B$ and $B C$ respectively so that $A K=K L=\angle B$ and $K B=A C$. How big is the angle $\angle A B C$?
<image1>
Choices:
A. $30^{\circ}$
B. $35^{\circ}$
C. $36^{\circ}$
D. $40^{\circ}$
E. $44^{\circ}$
Answer: C
Problem: <image>Question: In a game of dominoes the tiles always have to be placed so that the touching halves of two adjacent domino tiles show the same number of dots. Paul has six domino tiles in front of him (see diagram).
<image1>
In several steps Paul tries to arrange them in a correct order. In each step he is either allowed to swap any two domino tiles or he is allowed to turn one domino tile $180^{\circ}$ around. What is the minimum number of steps he needs in order to arrange the domino tiles correctly?
Answer: 3
Problem: <image>Question: Which cloud contains even numbers only?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: A $3 \times 3 \times 3$ cube is made up of small $1 \times 1 \times 1$ cubes. Then the middle cubes from front to back, from top to bottom and from right to left are removed (see diagram). How many $1 \times 1 \times 1$ - cubes remain?
<image1>
Answer: 20
Problem: <image>Question: Three rings are connected to each other as shown. Which of the following pictures also shows three rings connected in the same way?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Four of the following five diagrams can be drawn without lifting the pencil and without going over a line twice. For one diagram this is not true. Which one is it?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: A big square is divided up into smaller squares of different sizes as shown. Some of the smaller squares are shaded in grey. Which fraction of the big square is shaded in grey?
<image1>
Choices:
A. $\frac{2}{3}$
B. $\frac{2}{5}$
C. $\frac{4}{7}$
D. $\frac{4}{9}$
E. $\frac{5}{12}$
Answer: D
Problem: <image>Question: Three four-digit numbers are written onto three separate pieces of paper as shown. The sum of the three numbers is 10126. Three of the digits in the picture are hidden. Which are the hidden digits?
<image1>
Choices:
A. 5,6 and 7
B. 4,5 and 7
C. 4,6 and 7
D. 4,5 and 6
E. 3,5 and 6
Answer: A
Problem: <image>Question: The following information is known about triangle PSQ: $\angle Q P S=20^{\circ}$. The triangle PSQ has been split up into two smaller triangles by the line $Q R$ as shown. It is known that $P Q=P R=Q S$. How big is the angle RQS?
<image1>
Choices:
A. $50^{\circ}$
B. $60^{\circ}$
C. $65^{\circ}$
D. $70^{\circ}$
E. $75^{\circ}$
Answer: B
Problem: <image>Question: A $4 \times 4$ square is made up of the two pieces shown. Which of the following $4 \times 4$ squares cannot be made this way?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Kathi folds a square piece of paper twice and subsequently cuts it along the two lines as shown in the picture. The resulting pieces of paper are then unfolded if possible. How many of the pieces of paper are squares?
<image1>
Answer: 5
Problem: <image>Question: Mia draws some congruent rectangles and one triangle. She then shades in grey those parts of the rectangles that lie outside the triangle (see diagram). How big is the resulting grey area?
<image1>
Choices:
A. $10 \mathrm{~cm}^{2}$
B. $12 \mathrm{~cm}^{2}$
C. $14 \mathrm{~cm}^{2}$
D. $15 \mathrm{~cm}^{2}$
E. $21 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: Anna has placed matches along the dotted lines to create a path. She has placed the first match as shown in the diagram. The path is in such a way that in the end it leads back to the left end of the first match. The numbers in the small squares state how many sides of the square she has placed matches on. What is the minimum number of matches she has used?
<image1>
Answer: 16
Problem: <image>Question: n number of buttons are placed evenly around a circle. The buttons are labelled clockwise in order with the numbers 1 to $n$. The button with the number 7 is exactly opposite the button with the number 23. How big is $n$?
<image1>
Answer: 32
Problem: <image>Question: Natascha has some blue, red, yellow and green sticks of $1 \mathrm{~cm}$ length. She wants to make a $3 \times 3$ grid as shown in such a way that the four sides of each $1 \times 1-$ square in the grid each are of a different colour. What is the minimum number of green sticks she can use?
<image1>
Answer: 5
Problem: <image>Question: An ant crawls along a closed line on the surface of a cube until it reaches its starting point. Which of the following nets of a cube belongs to the cube that the ant is crawling on?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Peter colours in each of the eight circles in one of the colours red, yellow or blue. Two circles that are directly connected by a line, are not allowed to be of the same colour. Which two circles does Peter definitely have to colour in the same colour?
<image1>
Choices:
A. 5 and 8
B. 1 and 6
C. 2 and 7
D. 4 and 5
E. 3 and 6
Answer: A
Problem: <image>Question: In square $A B C D, P, Q$ and $R$ are the midpoints of the edges $D A, B C$ and $C D$. Which fraction of the square $A B C D$ is shaded in the diagram?
<image1>
Choices:
A. $\frac{3}{4}$
B. $\frac{5}{8}$
C. $\frac{1}{2}$
D. $\frac{7}{16}$
E. $\frac{3}{8}$
Answer: E
Problem: <image>Question: One square was divided into four equal squares, containing other equal colored squares and equal colored triangles, as shown in the picture. What fraction of the original square does the colored part represent?
<image1>
Choices:
A. $\frac{1}{3}$
B. $\frac{1}{2}$
C. $\frac{4}{9}$
D. $\frac{5}{8}$
E. $\frac{3}{4}$
Answer: B
Problem: <image>Question: The figure of side 1 is formed by six equal triangles, made with 12 sticks. How many matchsticks are needed to complete the figure of side 2, partially represented?
<image1>
Answer: 36
Problem: <image>Question: Juca wrote a whole number greater than zero in each of the boxes on the $3 \times 3$ board on the right, so that the sums of the numbers in each row and in each column are equal. The only thing Juca remembers is that there are no three numbers repeated. What number is written in the box of the center?
<image1>
Answer: 4
Problem: <image>Question: In the figure, formed by a square and an equilateral triangle, the letters indicate the measurements of the angles. Which of the following equality is true?
<image1>
Choices:
A. $a=d$
B. $b+c=d$
C. $a+c=d+e$
D. $a+b=d+e$
E. $e+d=a$
Answer: E
Problem: <image>Question: As soon as he left his city towards Caecá, Charles saw the sign on the left. When he came back from Caecá, he saw the sign on the right. At that point, how far was it to get to his city?
<image1>
Choices:
A. $12 \mathrm{~km}$
B. $21 \mathrm{~km}$
C. $29 \mathrm{~km}$
D. $41 \mathrm{~km}$
E. $52 \mathrm{~km}$
Answer: D
Problem: <image>Question: Which of the pictures below shows what you will see if you look from above the piece represented on the right?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: The garden of Sonia's house is shaped like a 12-meter square and is divided into three lawns of the same area. The central lawn is shaped like a parallelogram, whose smaller diagonal is parallel to two sides of the square, as shown in the picture. What is the length of this diagonal, in meters?
<image1>
Answer: 8.0
Problem: <image>Question: Andrew bought 27 little cubes of the same color, each with three adjacent faces painted red and the other three of another color. He wants to use all these little cubes to build a bigger cube. What is the largest number of completely red faces that he can get for this cube?
<image1>
Answer: 6
Problem: <image>Question: A square is formed by four identical rectangles and a central square, as in the figure. The area of the square is $81 \mathrm{~cm}^{2}$ and the square formed by the diagonals of these rectangles has an area equal to $64 \mathrm{~cm}^{2}$. What is the area of the central square?
<image1>
Choices:
A. $25 \mathrm{~cm}^{2}$
B. $27 \mathrm{~cm}^{2}$
C. $36 \mathrm{~cm}^{2}$
D. $47 \mathrm{~cm}^{2}$
E. $49 \mathrm{~cm}^{2}$
Answer: D
Problem: <image>Question: Irene made a "city" using identical wooden cubes. We have, beside, a view from above and a side view of this "city". We do not know which side of the "city" is being shown. What is the smallest amount of cubes Irene may have used to make its assembly?
<image1>
Answer: 15
Problem: <image>Question: Amelia has a paper strip with five equal cells containing different drawings, according to the figure. She folds the strip in such a way that the cells overlap in five layers. Which of the sequences of layers, from top to bottom, is not possible to obtain?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: Zilda took a square sheet of paper of side 1 and made two folds taking two consecutive sides of the sheet to a diagonal of it, as shown in the picture, obtaining a quadrilateral (highlighted outline). What is the area of this quadrilateral?
<image1>
Choices:
A. $\frac{7}{10}$
B. $2-\sqrt{2}$
C. $\frac{3}{5}$
D. $\sqrt{2}-1$
E. $\frac{\sqrt{2}}{2}$
Answer: B
Problem: <image>Question: Cleuza assembled the $2 \times 2 \times 2$ block formed by equal balls beside, using one drop of glue at each contact point between two balls, in a total of 12 drops. She then glued a few more spheres until she completed a $4 \times 3 \times 2$ block. How many extra drops of glue did she get to use?
<image1>
Answer: 34
Problem: <image>Question: Which of the following symbols for signs of the Zodiac has an axis of symmetry?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: The figure shows three concentric circles with four lines passing through their common centre. What percentage of the figure is shaded?
<image1>
Choices:
A. $30 \%$
B. $35 \%$
C. $40 \%$
D. $45 \%$
E. $50 \%$
Answer: E
Problem: <image>Question: When the 5 pieces <image1> are fitted together correctly, the result is a rectangle with a calculation written on it. What is the answer to this calculation?
Answer: -100
Problem: <image>Question: Each of the five vases shown has the same height and each has a volume of 1 litre. Half a litre of water is poured into each vase. In which vase would the level of the water be the highest?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: A cube $3 \times 3 \times 3$ is made from $1 \times 1 \times 1$ white, grey and black cubes, as shown in the first diagram. The other two diagrams show the white part and the black part of the cube. Which of the following diagrams shows the grey part?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: A bike lock has four wheels numbered with the digits 0 to 9 in order. Each of the four wheels is rotated by $180^{\circ}$ from the code shown in the first diagram to get the correct code. What is the correct code for the bike lock?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: The area of the large square is $16 \mathrm{~cm}^{2}$ and the area of each small square is $1 \mathrm{~cm}^{2}$. What is the total area of the central flower in $\mathrm{cm}^{2}$?
<image1>
Answer: 4
Problem: <image>Question: Costa is building a new fence in his garden. He uses 25 planks of wood, each of which are $30 \mathrm{~cm}$ long. He arranges these planks so that there is the same slight overlap between any two adjacent planks. The total length of Costa's new fence is 6.9 metres. What is the length in centimetres of the overlap between any pair of adjacent planks?
<image1>
Answer: 2.5
Problem: <image>Question: Five identical right-angled triangles can be arranged so that their larger acute angles touch to form the star shown in the diagram. It is also possible to form a different star by arranging more of these triangles so that their smaller acute angles touch. How many triangles are needed to form the second star?
<image1>
Answer: 20
Problem: <image>Question: Five squares are positioned as shown. The small square indicated has area 1. What is the value of $h$?
<image1>
Choices:
A. $3 \mathrm{~m}$
B. $3.5 \mathrm{~m}$
C. $4 \mathrm{~m}$
D. $4.2 \mathrm{~m}$
E. $4.5 \mathrm{~m}$
Answer: C
Problem: <image>Question: A rectangular strip of paper of dimensions $4 \mathrm{~cm} \times 13 \mathrm{~cm}$ is folded as shown in the diagram. 2 rectangles are formed with areas $P$ and $Q$ where $P=2 Q$. What is the value of $x$?
<image1>
Choices:
A. $5 \mathrm{~cm}$
B. $5.5 \mathrm{~cm}$
C. $6 \mathrm{~cm}$
D. $6.5 \mathrm{~cm}$
E. $4 \sqrt{2} \mathrm{~cm}$
Answer: C
Problem: <image>Question: 5 friends talk about their collected <image1>. Xenia says: "I have an even number of pins", Zach: "Half of my pins are planets, Sue: "I don't have any moons", Paul: "I have more moons than stars" and Yvonne: "I have more stars than planets". Below are the collections of the 5 friends. Which set of pins belongs to Yvonne?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: A triangular pyramid is built with 20 cannon balls, as shown. Each cannon ball is labelled with one of $A, B, C, D$ or $E$. There are 4 cannon balls with each type of label. The picture shows the labels on the cannon balls on 3 of the faces of the pyramid. What is the label on the hidden cannon ball in the middle of the fourth face?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: A $3 \times 4 \times 5$ cuboid consists of 60 identical small cubes. A termite eats its way along the diagonal from $P$ to $Q$. This diagonal does not intersect the edges of any small cube inside the cuboid. How many of the small cubes does it pass through on its journey?
<image1>
Answer: 10
Problem: <image>Question: In a tournament each of the 6 teams plays one match against every other team. In each round of matches, 3 take place simultaneously. A TV station has already decided which match it will broadcast for each round, as shown in the diagram. In which round will team D play against team F?
<image1>
Answer: 1
Problem: <image>Question: The diagram shows a quadrilateral divided into 4 smaller quadrilaterals with a common vertex $K$. The other labelled points divide the sides of the large quadrilateral into three equal parts. The numbers indicate the areas of the corresponding small quadrilaterals. What is the area of the shaded quadrilateral?
<image1>
Answer: 6