Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>Question: The cells of the table are being coloured red (R) and green (G). In each row and in each column there must be two red and two green cells. What will the lowest row look like after colouring the table?
<image1>
Choices:
A. GRGR
B. RGRG
C. GRRG
D. RGGR
E. GGRR
Answer: A
Problem: <image>Question: The diagram on the right shows a triangle $A B C$ where two lines are drawn to the opposite sides from each of the two vertices $A$ and $B$. This divides the triangle into nine non-overlapping sections. If eight lines are drawn to the opposite sides, four from $A$ and four from $B$, what is the number of nonoverlapping sections the triangle is divided into?
<image1>
Answer: 25
Problem: <image>Question: An $8 \mathrm{~m}$ long rope is fastened to the corner of the house. A dog is fastened to the rope. Find the perimeter of the area, where the dog can be found.
<image1>
Choices:
A. $15 \pi+16$
B. $15 \pi+20$
C. $15 \pi$
D. $15 \pi+18$
E. $30 \pi+16$
Answer: A
Problem: <image>Question: How many different ways can you follow from point $A$ to point $B$ if you you can go only down, right or down diagonally by the sides of small triangles?
<image1>
Answer: 90
Problem: <image>Question: A coin with diameter $1 \mathrm{~cm}$ rolls around the contour outside of a regular hexagon with sides $1 \mathrm{~cm}$ long, as shown. How long is the path traced by the centre of the coin (in $\mathrm{cm}$ )?
<image1>
Choices:
A. $6+\frac{\pi}{2}$
B. $6+\pi$
C. $12+\pi$
D. $6+2 \pi$
E. $12+2 \pi$
Answer: B
Problem: <image>Question: An equilateral triangle and a regular hexagon are inscribed in a circle, the latter beeing inscribed in an equilateral triangle (see the picture). $S$ is the area of the big triangle, $s$ the area of the little one and $Q$ is the area of the hexagon. What is true?
<image1>
Choices:
A. $Q=\sqrt{S \cdot s}$
B. $Q=\frac{S+s}{2}$
C. $S=s+Q$
D. $Q=\sqrt{S^{2}+s^{2}}$
E. $S=Q+3 s$
Answer: A
Problem: <image>Question: Two circles have their centres on the same diagonal of a square. They touch each other and the sides of the square as shown. The side of the square is $1 \mathrm{~cm}$ long. What is the sum of the lengths of the radii of the circles in centimetres?
<image1>
Choices:
A. $\frac{1}{2}$
B. $\frac{1}{\sqrt{2}}$
C. $\sqrt{2}-1$
D. $2-\sqrt{2}$
E. It depends on sizes of the circles
Answer: D
Problem: <image>Question: The distance of two not-crossing edges of a regular tetrahedron (triangular pyramid with all the six edges equal) is $6 \mathrm{~cm}$. What is the volume of the tetrahedron $\left(\right.$ in $\left.\mathrm{cm}^{3}\right)$?
<image1>
Answer: 72
Problem: <image>Question: To meet the New Year day 2008, Basil put on a T-shirt with <image1> on it, and stood in front of a mirror on his hands, with his feet up. What number did Nick standing on his feet behind Basil see in the mirror?
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: What is the length of line $A B$ if the side of each of the four squares shown is 1?
<image1>
Choices:
A. 5
B. $\sqrt{13}$
C. $\sqrt{5}+\sqrt{2}$
D. $\sqrt{5}$
E. None of the previous
Answer: B
Problem: <image>Question: In the picture any letter stands for some digit (different letters for different digits, equal letters for equal digits). Which digit is $\mathrm{K}$?
<image1>
Answer: 9
Problem: <image>Question: Rectangle $A B C D$ intersects the circle at points $E, F$, $G, H$. If $A E=4 \mathrm{~cm}, E F=5 \mathrm{~cm}, D H=3 \mathrm{~cm}$, then the length of $H B$ is
<image1>
Choices:
A. $6 \mathrm{~cm}$
B. $7 \mathrm{~cm}$
C. $\frac{20}{3} \mathrm{~cm}$
D. $8 \mathrm{~cm}$
E. $9 \mathrm{~cm}$
Answer: B
Problem: <image>Question: In the figure, two regular hexagons are equal to each other. What part of the parallelogram's area is shaded?
<image1>
Choices:
A. $\frac{1}{2}$
B. $\frac{1}{3}$
C. $\frac{1}{4}$
D. $\frac{1}{5}$
E. $\frac{1}{6}$
Answer: A
Problem: <image>Question: Six integers are marked on the real line (see the fig.). It is known that at least two of them are divisible by 3, and at least two of them are divisible by 5. Which numbers are divisible by 15?
<image1>
Choices:
A. $A$ and $F$
B. $B$ and $D$
C. $C$ and $E$
D. All the six numbers
E. Only one of them
Answer: A
Problem: <image>Question: The picture shows an isosceles triangle with $A B=A C$. If $\angle B P C=120^{\circ}, \angle A B P=50^{\circ}$, then what is angle $P B C$?
<image1>
Choices:
A. $5^{\circ}$
B. $10^{\circ}$
C. $15^{\circ}$
D. $20^{\circ}$
E. $25^{\circ}$
Answer: A
Problem: <image>Question: Find the length of the arc denoted by the interrogation sign.
<image1>
Choices:
A. $\frac{5 \pi}{4}$
B. $\frac{5 \pi}{3}$
C. $\frac{\pi}{2}$
D. $\frac{3 \pi}{2}$
E. $\frac{2 \pi}{3}$
Answer: D
Problem: <image>Question: This network of eight equilateral triangles can be folded to form a regular octahedron. To construct a magic octahedron, replace the letters $A, B, C, D$, and $E$ with the numbers 2, 4, 6,7, and 8 (without repetition) so that each sum of the four numbers on the four faces that share a vertex were the same. On your magic octahedron, what does $B+D$ equal?
<image1>
Answer: 6
Problem: <image>Question: A 3-pyramid is a stack of the following 3 layers of balls. In the same way we have a 4-pyramid, a 5-pyramid, etc. All the outside balls of an 8-pyramid are removed. What kind of figure form the rest balls?
<image1>
Choices:
A. 3-pyramid
B. 4-pyramid
C. 5-pyramid
D. 6-pyramid
E. 7-pyramid
Answer: B
Problem: <image>Question: A square $4 \times 4$ table is divided into 16 unit squares (see the fig.) Find the maximum possible number of diagonals one can draw in these unit squares so that neither two of them had any common point (including endpoints).
<image1>
Answer: 10
Problem: <image>Question: In the picture $A B C D$ is a square of side 1 and the semicircles have centers on $A, B, C$ and $D$. What is the length of $P Q$?
<image1>
Choices:
A. $2-\sqrt{2}$
B. $\frac{3}{4}$
C. $\sqrt{5}-\sqrt{2}$
D. $\frac{\sqrt{3}}{3}$
E. $\sqrt{3}-1$
Answer: E
Problem: <image>Question: What is the minimum number of points which have to be removed from the adjacent diagram so that in the remaining picture no three points lie in one line?
<image1>
Answer: 3
Problem: <image>Question: The diagram on the right shows a solid made up of 6 triangles. Each vertex is assigned a number, two of which are indicated. The total of the three numbers on each triangle is the same. What is the total of all five numbers?
<image1>
Answer: 17
Problem: <image>Question: The area of the shown triangle equals $80 \mathrm{~m}^{2}$. Each circle has a radius of $2 \mathrm{~m}$ and itôs centre is in one of the vertices of the triangles. What is the area of the grey shaded region (in $\mathrm{m}^{2}$)?
<image1>
Choices:
A. 76
B. $80-2 \pi$
C. $40-4 \pi$
D. $80-\pi$
E. $78 \pi$
Answer: B
Problem: <image>Question: In the triangle illustrated one internal angle measures $68^{\circ}$. The three angle bisectors of the triangle are shown. What is the size of the angle indicated with a question mark?
<image1>
Choices:
A. $120^{\circ}$
B. $124^{\circ}$
C. $128^{\circ}$
D. $132^{\circ}$
E. $136^{\circ}$
Answer: B
Problem: <image>Question: The "Borromaic Rings" have an extraordinary property. Although no two are interlocked, they are strongly connected within each other. If one ring is cut through, the other two fall apart. Which of the following diagrams shows the picture of "Borromaic Rings"?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: The centres of the four illustrated circles are in the corners of the square. The two big circles touch each other and also the two little circles. With which factor do you have to multiply the radii of the little circles to obtain the radius of the big circles?
<image1>
Choices:
A. $\frac{2}{9}$
B. $\sqrt{5}$
C. $0.8 \cdot \pi$
D. 2.5
E. $1+\sqrt{2}$
Answer: E
Problem: <image>Question: There are three great circles on a sphere that intersect each other in a right angle. Starting in point S a little bug moves along the great circles in the direction indicated. At crossings it turns alternately to the right or left. How many quarter circles does it crawl along until it is back in point S?
<image1>
Answer: 6
Problem: <image>Question: Robert wants to place stones on a $4 \times 4$ gameboard so that the number of stones in each row and column is different; i.e. there are 8 different amounts. To achieve this he can place one or several stones in any one field or even leave single fields empty. What is the minimum number of stones needed to do this?
<image1>
Answer: 14
Problem: <image>Question: The object pictured is made up of four equally sized cubes. Each cube has a surface area of $24 \mathrm{~cm}^{2}$. What is the surface area of the object pictured?
<image1>
Choices:
A. $80 \mathrm{~cm}^{2}$
B. $64 \mathrm{~cm}^{2}$
C. $40 \mathrm{~cm}^{2}$
D. $32 \mathrm{~cm}^{2}$
E. $24 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: Six points are marked on a square grid as pictured. Which geometric figure cannot be drawn if only the marked points are allowed to be used as cornerpoints of the figure?
<image1>
Choices:
A. square
B. parallelogram with different long sides
C. acute triangle
D. obtuse triangle
E. all figures are possible
Answer: E
Problem: <image>Question: In the picture opposite we see that $1+3+5+7=4 \times 4$. How big is $1+3+5+7+\ldots+17+19$?
<image1>
Choices:
A. $10 \times 10$
B. $11 \times 11$
C. $12 \times 12$
D. $13 \times 13$
E. $14 \times 14$
Answer: A
Problem: <image>Question: In the figure, $\mathrm{ABCE}$ is a square. $\mathrm{CDE}$ and $\mathrm{BCF}$ are equilateral triangles. The length of $\mathrm{AB}$ is 1. How long is $\mathrm{FD}$?
<image1>
Choices:
A. $\sqrt{2}$
B. $\frac{\sqrt{3}}{2}$
C. $\sqrt{3}$
D. $\sqrt{5}-1$
E. $\sqrt{6}-1$
Answer: A
Problem: <image>Question: How big is the angle indicated with a question mark?
<image1>
Choices:
A. $10^{\circ}$
B. $20^{\circ}$
C. $30^{\circ}$
D. $40^{\circ}$
E. $50^{\circ}$
Answer: D
Problem: <image>Question: 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?
<image1>
Answer: 2
Problem: <image>Question: 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?
<image1>
Choices:
A. $2 \pi$
B. $4 \pi$
C. $6 \pi$
D. $8 \pi$
E. $12 \pi$
Answer: C
Problem: <image>Question: Five students carry out a run. Their results are recorded in the graph opposite, according to the time taken (Zeit) and the distance covered (Strecke). Who had the greatest average speed?
<image1>
Choices:
A. Anja
B. Bernd
C. Chris
D. Doris
E. Ernst
Answer: D
Problem: <image>Question: A triangle is folded along the dashed line as shown. The area of the triangle is 1.5 times the area of the resulting figure. We know that the total area of the grey parts is 1. Determine the area of the starting triangle.
<image1>
Answer: 3
Problem: <image>Question: In front of a supermarket there are two rows of interconnected trolleys.The first one is $2.9 \mathrm{~m}$ long and consists of 10 trolleys. The second one is $4.9 \mathrm{~m}$ long and consists of twenty trolleys. How long is one trolley?
<image1>
Choices:
A. $0.8 \mathrm{~m}$
B. $1 \mathrm{~m}$
C. $1.1 \mathrm{~m}$
D. $1.2 \mathrm{~m}$
E. $1.4 \mathrm{~m}$
Answer: C
Problem: <image>Question: Lines drawn parallel to the base of the triangle pictured, separate the other two sides into 10 equally large parts. What percentage of the triangle is grey?
<image1>
Choices:
A. $41.75 \%$
B. $42.5 \%$
C. $45 \%$
D. $46 \%$
E. $47.5 \%$
Answer: C
Problem: <image>Question: In the figure $\alpha=7^{\circ}$. All lines $\mathrm{OA}_{1}, \mathrm{~A}_{1} \mathrm{~A}_{2}, \mathrm{~A}_{2} \mathrm{~A}_{3}, \ldots$ are equally long. What is the maximum number of lines that can be drawn in this way if no two lines are allowed to intersect each other?
<image1>
Answer: 13
Problem: <image>Question: A barcode as pictured is made up of alternate black and white stripes. The code always starts and ends with a black stripe. Each stripe (black or white) has the width 1 or 2 and the total width of the barcode is 12. How many different barcodes of this kind are there if one reads from left to right?
<image1>
Answer: 114
Problem: <image>Question: 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?
<image1>
Choices:
A. $24 \mathrm{~cm}^{2}$
B. $25 \mathrm{~cm}^{2}$
C. $26 \mathrm{~cm}^{2}$
D. $27 \mathrm{~cm}^{2}$
E. $28 \mathrm{~cm}^{2}$
Answer: C
Problem: <image>Question: In the picture on the right a number should be written next to each point. The sum of the numbers on the corners of each side of the hexagon should be equal. Two numbers have already been written. Which number should be in the place marked ' $x$ '?
<image1>
Answer: 1
Problem: <image>Question: The two bold lines on the right are rotations of each other. Which of the given points could be the centre of this rotation?
<image1>
Choices:
A. only $X$
B. $X$ and $Z$
C. $X$ and $T$
D. only $T$
E. $X, Y, Z$ and $T$
Answer: C
Problem: <image>Question: Given are a regular hexagon with side-length 1, six squares and six equilateral triangles as shown on the right. What is the perimeter of this tessellation?
<image1>
Answer: 12
Problem: <image>Question: In the picture on the left we see three dice on top of each other. The sum of the points on opposite sides of the dice is 7 as usual. The sum of the points of areas that face each other is always 5. How many points are on the area marked $\mathrm{X}$?
<image1>
Answer: 6
Problem: <image>Question: A marble of radius 15 is rolled into a cone-shaped hole. It fits in perfectly. From the side the cone looks like an equilateral triangle. How deep is the hole?
<image1>
Answer: 45
Problem: <image>Question: The cells of the $4 \times 4$-table on the right should be coloured either in black or white. The numbers determine how many cells in each row/column should be black. How many ways are there to do the colouring in?
<image1>
Answer: 5
Problem: <image>Question: Nick wants to write whole numbers into the cells of the $3 \times 3$-table on the right so that the sum of the digits in each in each $2 \times 2$-sub-table is always 10. Five numbers have already been written. Determine the sum of the remaining four numbers.
<image1>
Answer: 12
Problem: <image>Question: In the triangle $W X Y$ points $Z$ on $X Y$ and $T$ on $W Z$ are, as shown on the right. If one connects $\mathrm{T}$ with $\mathrm{X}$, a figure with nine internal angles is created as shown in the figure on the right. From those 9 angles, what is the smallest number that could be a different size to each other
<image1>
Answer: 3
Problem: <image>Question: Simon has a cube with side length $1 \mathrm{dm}$ made of glass. He sticks several equally big black squares on it, as shown on the right so that all faces look the same. How many $\mathrm{cm}^{2}$ were covered over?
<image1>
Answer: 225
Problem: <image>Question: Three big boxes $P, Q$ and $R$ are stored in a warehouse. The upper picture on the right shows their placements from above. The boxes are so heavy that they can only be rotated $90^{\circ}$ around a vertical edge as indicated in the pictures below. Now the boxes should be rotated to stand against the wall in a certain order. Which arrangement is possible?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. All four arrangements are possible.
Answer: B
Problem: <image>Question: The two circles shown on the right intersect each other at $X$ and $Y$. Thereby $X Y$ is the diameter of the small circle. The centre $S$ of the large circle (with radius $r$ ) is on the small circle. How big is the area of the grey region?
<image1>
Choices:
A. $\frac{\pi}{6} r^{2}$
B. $\frac{\sqrt{3} \pi}{12} r^{2}$
C. $\frac{1}{2} r^{2}$
D. $\frac{\sqrt{3}}{4} r^{2}$
E. another number
Answer: C
Problem: <image>Question: Which of the shapes to the right has the largest area?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. All shapes have the same area.
Answer: E
Problem: <image>Question: $\mathrm{M}$ and $\mathrm{N}$ are the midpoints of the equal sides of an isosceles triangle. How big is the area of the quadrilateral (marked?)?
<image1>
Answer: 6
Problem: <image>Question: A cuboid is formed from 3 pieces (see picture). Each piece is made from 4 cubes of the same colour. What shape does the white piece have?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: The quadrilateral $A B C D$ with side length $4 \mathrm{~cm}$ has the same area as triangle $E C D$. What is the perpendicular distance from point $E$ to the line $g$?
<image1>
Choices:
A. $8 \mathrm{~cm}$
B. $(4+2 \sqrt{3}) \mathrm{cm}$
C. $12 \mathrm{~cm}$
D. $10 \times \sqrt{2} \mathrm{~cm}$
E. It depends on the position of $\mathrm{E}$.
Answer: C
Problem: <image>Question: One of the two sides of a rectangle has length $6 \mathrm{~cm}$. In the rectangle circles are drawn next to each other in such a way that their centres form an equilateral triangle. What is the shortest distance between the two grey circles (in $\mathrm{cm}$ )?
<image1>
Choices:
A. 1
B. $\sqrt{2}$
C. $2 \sqrt{3}-2$
D. $\frac{\pi}{2}$
E. 2
Answer: C
Problem: <image>Question: The diagram shows a right-angled triangle with side lengths 5,12 and 13. What is the length of the radius of the inscribed semi-circle?
<image1>
Choices:
A. $7 / 3$
B. $10 / 3$
C. $12 / 3$
D. $13 / 3$
E. $17 / 3$
Answer: B
Problem: <image>Question: A number from 1 to 9 is to written into each of the 12 fields of the table so that the sum of each column is the same. Also the sum of each row must be the same. A few numbers have already been written in. Which number should be written in the grey square?
<image1>
Answer: 4
Problem: <image>Question: A goldsmith has 12 double-links of chain. Out of these he wants to make a single closed chain with 24 links. What is the minimum number of links that he must open (and close again)?
<image1>
Answer: 8
Problem: <image>Question: A rectangle $A B C D$ with dimensions $16 \mathrm{~cm}$ by $4 \mathrm{~cm}$ was folded along the line MN so that corner C meets corner A. What is the area of the Pentagon ABNMD'?
<image1>
Choices:
A. $17 \mathrm{~cm}^{2}$
B. $27 \mathrm{~cm}^{2}$
C. $37 \mathrm{~cm}^{2}$
D. $47 \mathrm{~cm}^{2}$
E. $57 \mathrm{~cm}^{2}$
Answer: D
Problem: <image>Question: The shape pictured, is made out of two squares with side lengths $4 \mathrm{~cm}$ and $5 \mathrm{~cm}$ respectively, a triangle with area $8 \mathrm{~cm}^{2}$ and the grey parallelogram. What is the area of the parallelogram?
<image1>
Choices:
A. $15 \mathrm{~cm}^{2}$
B. $16 \mathrm{~cm}^{2}$
C. $18 \mathrm{~cm}^{2}$
D. $20 \mathrm{~cm}^{2}$
E. $21 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: The natural numbers from 1 to 120 were written as shown into a table with 15 columns. In which column (counting from left) is the sum of the numbers the largest?
<image1>
Answer: 5
Problem: <image>Question: Maria has six equally big square pieces of plain paper. On each piece of paper she draws one of the figures shown below. How many of these figures have the same perimeter as the plain piece of paper itself?
<image1>
Answer: 4
Problem: <image>Question: Mrs. Maisl buys four pieces of corn-on-the-cob for each of the four members of her family and get the discount offered. How much does she end up paying?
<image1>
Choices:
A. $0.80 €$
B. $1.20 €$
C. $2.80 €$
D. $3.20 €$
E. $80 €$
Answer: C
Problem: <image>Question: On a square grid made up of unit squares, six points are marked as shown on the right. Three of which form a triangle with the least area. How big is this smallest area?
<image1>
Choices:
A. $1 / 2$
B. $1 / 3$
C. $1 / 4$
D. 1
E. 2
Answer: A
Problem: <image>Question: A cube is coloured on the outside as if it was made up of four white and four black cubes where no cubes of the same colour are next to each other (see picture). Which of the following figures represents a possible net of the coloured cube?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: In a drawing we can see a three quarter circle with centre M and an indicated orientation arrow. This three-quarter circle is first turned $90^{\circ}$ anti-clockwise about M and then reflected in the x - axis. Which is the resulting picture?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Triangle RZT is generated by rotating the equilateral triangle AZC about point Z. Angle $\beta=\angle \mathrm{CZR}=70^{\circ}$. Determine angle $\alpha=\angle \mathrm{CAR}$.
<image1>
Choices:
A. $20^{\circ}$
B. $25^{\circ}$
C. $30^{\circ}$
D. $35^{\circ}$
E. $40^{\circ}$
Answer: D
Problem: <image>Question: The figure on the right is made up of six unit squares. Its perimeter is $14 \mathrm{~cm}$. Squares will be added to this figure in the same way until it is made up of 2013 unit squares (zigzag: alternating bottom right and top right). How big is the perimeter of the newly created figure?
<image1>
Answer: 4028
Problem: <image>Question: A and B are opposite vertices of a regular six-side shape, the points $C$ and $D$ are the midpoints of two opposite sides. The area of the regular six-sided shape is 60. Determine the product of the lengths of the lines $A B$ and $C D$!
<image1>
Answer: 80
Problem: <image>Question: The sides of the rectangle $A B C D$ are parallel to the co-ordinate axis. The rectangle lies below the $\mathrm{x}$-axis and to the right of the $\mathrm{y}$-axis, as shown in the diagram. For each of the points A, B, C, D the quotient (y-coordinate):(x-coordinate) is calculated. For which point will you obtain the smallest quotient?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. It depends on the position of the rectangle and its side lengths.
Answer: D
Problem: <image>Question: Tarzan wanted to draw a rhombus made up of two equilateral triangles. He drew the line segments inaccurately. When Jane checked the measurements of the four angles shown, she sees that they are not equally big (see diagram). Which of the five line segments in this diagram is the longest?
<image1>
Choices:
A. AD
B. AC
C. AB
D. BC
E. BD
Answer: A
Problem: <image>Question: How many different ways are there in the diagram shown, to get from point $A$ to point $B$ if you are only allowed to move in the directions indicated?
<image1>
Answer: 12
Problem: <image>Question: $a, b$ and $c$ show the lengths of the different of pieces of wire pictured. Which of the following inequalities is correct?
<image1>
Choices:
A. $a<b<c$
B. $a<c<b$
C. $b<a<c$
D. $b<c<a$
E. $c<b<a$
Answer: E
Problem: <image>Question: The side lengths of the large regular hexagon are twice the length of those of the small regular hexagon. What is the area of the large hexagon if the small hexagon has an area of $4 \mathrm{~cm}^{2}$?
<image1>
Choices:
A. $16 \mathrm{~cm}^{2}$
B. $14 \mathrm{~cm}^{2}$
C. $12 \mathrm{~cm}^{2}$
D. $10 \mathrm{~cm}^{2}$
E. $8 \mathrm{~cm}^{2}$
Answer: A
Problem: <image>Question: The circumference of the large wheel measures $4.2 \mathrm{~m}$, and that of the small wheel $0.9 \mathrm{~m}$. To begin with the valves on both wheels are at the lowest point, and then the bicycle moves to the left. After a few metres both valves are again at the lowest point at the same time. After how many metres does this happen for the first time?
<image1>
Choices:
A. $4.2 \mathrm{~m}$
B. $6.3 \mathrm{~m}$
C. $12.6 \mathrm{~m}$
D. $25.2 \mathrm{~m}$
E. $37.8 \mathrm{~m}$
Answer: C
Problem: <image>Question: Paul hangs rectangular pictures on a wall. For each picture he hammers a nail into the wall $2.5 \mathrm{~m}$ above the floor. He ties a $2 \mathrm{~m}$ long string to the upper corners of each picture (see diagram). which picture size (width in $\mathrm{cm} \times$ height in $\mathrm{cm}$ ) has its lower edge nearest to the floor?
<image1>
Choices:
A. $60 \times 40$
B. $120 \times 50$
C. $120 \times 90$
D. $160 \times 60$
E. $160 \times 100$
Answer: C