Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>Question: The diagram shows a circle with centre $O$ as well as a tangent that touches the circle in point $P$. The arc $A P$ has length 20, the arc $B P$ has length 16. What is the size of the angle $\angle A X P$?
<image1>
Choices:
A. $30^{\circ}$
B. $24^{\circ}$
C. $18^{\circ}$
D. $15^{\circ}$
E. $10^{\circ}$
Answer: E
Problem: <image>Question: In this number pyramid each number in a higher cell is equal to the product of the two numbers in the cells immediately underneath that number. Which of the following numbers cannot appear in the topmost cell, if the cells on the bottom row hold natural numbers greater than 1 only?
<image1>
Choices:
A. 56
B. 84
C. 90
D. 105
E. 220
Answer: D
Problem: <image>Question: The square shown in the diagram has a perimeter of 4. The perimeter of the equilateral triangle is
<image1>
Choices:
A. 4
B. $3+\sqrt{3}$
C. 3
D. $3+\sqrt{2}$
E. $4+\sqrt{3}$
Answer: B
Problem: <image>Question: Each of the ten points in the diagram is labelled with one of the numbers 0,1 or 2. It is known that the sum of the numbers in the corner points of each white triangle is divisible by 3, while the sum of the numbers in the corner points of each black triangle is not divisible by 3. Three of the points are already labeled as shown in the diagram. With which numbers can the inner point be labeled?
<image1>
Choices:
A. only 0
B. only 1
C. only 2
D. only 0 and 1
E. either 0 or 1 or 2
Answer: A
Problem: <image>Question: Bettina chooses five points $A, B, C, D$ and $E$ on a circle and draws the tangent to the circle at point $A$. She realizes that the five angles marked $x$ are all equally big. (Note that the diagram is not drawn to scale!) How big is the angle $\angle A B D$?
<image1>
Choices:
A. $66^{\circ}$
B. $70.5^{\circ}$
C. $72^{\circ}$
D. $75^{\circ}$
E. $77.5^{\circ}$
Answer: C
Problem: <image>Question: How many quadratic functions $y=a x^{2}+b x+c$ (with $a \neq 0$ ) have graphs that go through at least 3 of the marked points?
<image1>
Answer: 22
Problem: <image>Question: A rectangular piece of paper $A B C D$ is $5 \mathrm{~cm}$ wide and $50 \mathrm{~cm}$ long. The paper is white on one side and grey on the other. Christina folds the strip as shown so that the vertex $B$ coincides with $M$ the midpoint of the edge $C D$. Then she folds it so that the vertex $D$ coincides with $N$ the midpoint of the edge $A B$. How big is the area of the visible white part in the diagram?
<image1>
<image2>
<image3>
Choices:
A. $50 \mathrm{~cm}^{2}$
B. $60 \mathrm{~cm}^{2}$
C. $62.5 \mathrm{~cm}^{2}$
D. $100 \mathrm{~cm}^{2}$
E. $125 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: We consider a $5 \times 5$ square that is split up into 25 fields. Initially all fields are white. In each move it is allowed to change the colour of three fields that are adjacent in a horizontal or vertical line (i.e. white fields turn black and black ones turn white). What is the smallest number of moves needed to obtain the chessboard colouring shown in the diagram?
<image1>
Choices:
A. less than 10
B. 10
C. 12
D. more than 12
E. This colouring cannot be obtained.
Answer: A
Problem: <image>Question: On the number wall shown the number on each tile is equal to the sum of the numbers on the two tiles directly below it. Which number is on the tile marked with "?"?
<image1>
Answer: 16
Problem: <image>Question: 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?
<image1>
Answer: 3
Problem: <image>Question: Four of the following five pictures show pieces of the graph of the same quadratic function. Which piece does not belong?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: 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?
<image1>
Choices:
A. $\frac{2}{5}$
B. $\frac{1}{3}$
C. $\frac{2}{7}$
D. $\frac{3}{8}$
E. $\frac{4}{11}$
Answer: B
Problem: <image>Question: A $4 \times 1 \times 1$ cuboid is made up of 2 white and 2 grey cubes as shown. Which of the following cuboids can be build entirely out of such $4 \times 1 \times 1$ cuboids?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: Which quadrant contains no points of the graph of the linear function $f(x)=-3.5 x+7$?
<image1>
Choices:
A. I
B. II
C. III
D. IV
E. Every quadrant contains at least one point of the graph.
Answer: C
Problem: <image>Question: 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 $A B C$?
<image1>
Answer: 6
Problem: <image>Question: Each face of the polyhedron shown is either a triangle or a square. Each square borders 4 triangles, and each triangle borders 3 squares. The polyhedron has 6 squares. How many triangles does it have?
<image1>
Answer: 8
Problem: <image>Question: Julia has 2017 round discs available: 1009 black ones and 1008 white ones. Using them, she wants to lay the biggest square pattern (as shown) possible and starts by using a black disc in the left upper corner. Subsequently she lays the discs in such a way that the colours alternate in each row and column. How many discs are left over
when she has laid the biggest square possible?
<image1>
Choices:
A. none
B. 40 of each colour
C. 40 black and 41 white ones
D. 41 of each colour
E. 40 white and 41 black ones
Answer: E
Problem: <image>Question: The diagram shows a regular hexagon with side length 1. The grey flower is outlined by circular arcs with radius 1 whose centre's lie in the vertices of the hexagon. How big is the area of the grey flower?
<image1>
Choices:
A. $\frac{\pi}{2}$
B. $\frac{2 \pi}{3}$
C. $2 \sqrt{3}-\pi$
D. $\frac{\pi}{2}+\sqrt{3}$
E. $2 \pi-3 \sqrt{3}$
Answer: E
Problem: <image>Question: We look at a regular tetrahedron with volume 1. Its four vertices are cut off by planes that go through the midpoints of the respective edges (see diagram). How big is the volume of the remaining solid?
<image1>
Choices:
A. $\frac{4}{5}$
B. $\frac{3}{4}$
C. $\frac{2}{3}$
D. $\frac{1}{2}$
E. $\frac{1}{3}$
Answer: D
Problem: <image>Question: Nine whole numbers were written into the cells of a $3 \times 3$-table. The sum of these nine numbers is 500. We know that the numbers in two adjacent cells (with a common sideline) differ by exactly 1. Which number is in the middle cell?
<image1>
Answer: 56
Problem: <image>Question: In the diagram you can see the calendar page of a certain month. Unfortunately ink has run across parts of the page. Which day of the week does the 27th of that month fall on?
<image1>
Choices:
A. Monday
B. Wednesday
C. Thursday
D. Saturday
E. Sunday
Answer: A
Problem: <image>Question: 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?
<image1>
Answer: 2
Problem: <image>Question: The diagram shows an object made up of 12 dice glued-together. The object is dipped into some colour so that the entire outside is coloured in this new colour. How many of the small dice will have exactly four faces coloured in?
<image1>
Answer: 10
Problem: <image>Question: Four identical rhombuses (diamonds) and two squares are fitted together to form a regular octagon as shown. How big are the obtuse interior angles in the rhombuses?
<image1>
Choices:
A. $135^{\circ}$
B. $140^{\circ}$
C. $144^{\circ}$
D. $145^{\circ}$
E. $150^{\circ}$
Answer: A
Problem: <image>Question: The faces of the brick have the areas A, B and C as shown. How big is the volume of the brick?
<image1>
Choices:
A. $A B C$
B. $\sqrt{A B C}$
C. $\sqrt{A B+B C+C A}$
D. $\sqrt[3]{A B C}$
E. $2(A+B+C)$
Answer: B
Problem: <image>Question: Two dice with volumes $V$ and $W$ intersect each other as shown. $90 \%$ of the volume of the die with volume $V$ does not belong to both dice. $85 \%$ of the volume of the die with volume $W$ does not belong to both dice. What is the relationship between the volumes of the two dice?
<image1>
Choices:
A. $V=\frac{2}{3} W$
B. $V=\frac{3}{2} W$
C. $V=\frac{85}{90} \mathrm{~W}$
D. $V=\frac{90}{85} W$
E. $V=W$
Answer: B
Problem: <image>Question: The five vases shown are filled with water. The filling rate is constant. For which of the five vases does the graph shown describe the height of the water $h$ as a function of the time t?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: An octahedron is inscribed into a die with side length 1. The vertices of the octahedron are the midpoints of the faces of the die. How big is the volume of the octahedron?
<image1>
Choices:
A. $\frac{1}{3}$
B. $\frac{1}{4}$
C. $\frac{1}{5}$
D. $\frac{1}{6}$
E. $\frac{1}{8}$
Answer: D
Problem: <image>Question: The vertices of a triangle have the co-ordinates $A(p \mid q), B(r \mid s)$ and $C(t \mid u)$ as shown. The midpoints of the sides of the triangle are the points $\mathrm{M}(-2 \mid 1), \mathrm{N}(2 \mid-1)$ and $\mathrm{P}(3 \mid 2)$. Determine the value of the expression $p+q+r+s+t+u$
<image1>
Answer: 5
Problem: <image>Question: A regular pentagon is cut out of a page of lined paper. Step by step this pentagon is then rotated $21^{\circ}$ counter clockwise about its midpoint. The result after step one is shown in the diagram. Which of the diagrams shows the situation when the pentagon fills the hole entirely again for the first time?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>Question: Three of the cards shown will be dealt to Nadia, the rest to Riny. Nadia multiplies the three values of her cards and Riny multiplies the two values of his cards. It turns out that the sum of those two products is a prime number. Determine the sum of the values of Nadia's cards.
<image1>
Answer: 13
Problem: <image>Question: Two rectangles form the angles $40^{\circ}$ and $30^{\circ}$ respectively, with a straight line (see diagram). How big is angle $\alpha$?
<image1>
Choices:
A. $105^{\circ}$
B. $120^{\circ}$
C. $130^{\circ}$
D. $135^{\circ}$
E. another value
Answer: E
Problem: <image>Question: 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 $X$?
<image1>
Answer: 2
Problem: <image>Question: 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 $B N=$ $0.8 m$?
<image1>
Choices:
A. $2 \mathrm{~m}$
B. $1.5 \mathrm{~m}$
C. $1.2 \mathrm{~m}$
D. $2.8 \mathrm{~m}$
E. $1.8 \mathrm{~m}$
Answer: E
Problem: <image>Question: $A B C D E F$ is a regular hexagon, as shown in the diagram. $G$ is the midpoint of $A B. H$ and I are the intercepts of the line segments GD and GE respectively, with the line segment FC. How big is the ratio of the areas of the triangle GIF and the trapezium IHDE?
<image1>
Choices:
A. $\frac{1}{2}$
B. $\frac{1}{3}$
C. $\frac{1}{4}$
D. $\frac{\sqrt{3}}{3}$
E. $\frac{\sqrt{3}}{4}$
Answer: A
Problem: <image>Question: Archimedes has calculated 15!. The result is on the board. Unfortunately two of the digits, the second and the tenth, cannot be read. What are the two missing digits? (Remark: $15 !=15 \cdot 14 \cdot 13 \cdot \ldots \cdot 2 \cdot 1$ )
<image1>
Choices:
A. 2 and 0
B. 4 and 8
C. 7 and 4
D. 9 and 2
E. 3 and 8
Answer: E
Problem: <image>Question: The flag of Kangoraland is a rectangle which is split into three equal rectangles as shown. How big is the ratio of the side lengths of the white rectangle?
<image1>
Choices:
A. $1: 2$
B. $2: 3$
C. $2: 5$
D. $3: 7$
E. $4: 9$
Answer: A
Problem: <image>Question: The numbers $1,2,3$ and 4 are inserted into different cells of the $2 \times 2$ table shown. Then the sums of the numbers in each row and column are determined. Two of these sums are 4 and 5. How big are the two remaining sums?
<image1>
Choices:
A. 6 and 6
B. 3 and 5
C. 4 and 5
D. 4 and 6
E. 5 and 6
Answer: E
Problem: <image>Question: A rectangle is coloured in five different ways as shown. In which picture is the grey area biggest?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Three triangles are connected to each other as shown. In which of the following pictures are the three triangles connected in the same way?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
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 11126. Three of the digits in the picture are hidden. Which are the three hidden digits?
<image1>
Choices:
A. 1,4 and 7
B. 1,5 and 7
C. 3,3 and 3
D. 4,5 and 6
E. 4,5 and 7
Answer: B
Problem: <image>Question: Each side of a die is marked with either 1,2 or 3 dots so that the probability of rolling a 1 is equal to $\frac{1}{2}$, the probability of rolling a 2 is equal to $\frac{1}{3}$ and the probability of rolling a 3 is equal to $\frac{1}{6}$. Which of these pictures cannot be a picture of this particular die?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: A cuboid-shaped container that is not filled completely contains $120 \mathrm{~m}^{3}$ of water. The depth of the water is either $2 \mathrm{~m}$ or $3 \mathrm{~m}$ or $5 \mathrm{~m}$, depending on which side the container is actually standing on (drawings not to scale). How big is the volume of the container?
<image1>
Choices:
A. $160 \mathrm{~m}^{3}$
B. $180 \mathrm{~m}^{3}$
C. $200 \mathrm{~m}^{3}$
D. $220 \mathrm{~m}^{3}$
E. $240 \mathrm{~m}^{3}$
Answer: E
Problem: <image>Question: The system shown consists of three pulleys that are connected to each other via two ropes. $P$, the end of one rope, is pulled down by $24 \mathrm{~cm}$. By how many centimeters does point $Q$ move upwards?
<image1>
Answer: 6
Problem: <image>Question: The diagram shows two adjoining squares with side lengths $a$ and $b$ (with $a<b$). How big is the area of the grey triangle?
<image1>
Choices:
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. $\frac{1}{2}\left(a^{2}+b^{2}\right)$
Answer: B
Problem: <image>Question: The points of intersection of the network of bars shown are labelled with the numbers 1 to 10. The sums $S$ of the four numbers on the vertices of each square are
all the same. What is the minimum value of $S$?
<image1>
Answer: 20
Problem: <image>Question: A path $D E F B$ with $D E \perp E F$ and $E F \perp F B$ lies within the square $A B C D$ as shown. We know that $D E=5, E F=1$ and $F B=2$. What is the side length of the square?
<image1>
Choices:
A. $3 \sqrt{2}$
B. $\frac{7 \sqrt{2}}{2}$
C. $\frac{11}{2}$
D. $5 \sqrt{2}$
E. another value
Answer: E
Problem: <image>Question: 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?
<image1>
Choices:
A. $\pi$
B. $3 \pi$
C. $\frac{\pi}{2}$
D. $2 \pi$
E. $4 \pi$
Answer: D
Problem: <image>Question: Numbers are to be placed into the square grid shown, so that each of the numbers $1,2,3,4$ and 5 appears exactly once in each row and in each column. Furthermore sthe sum of all numbers in the three black-bordered sections should always be the same. Which number has to be written into the top right cell?
<image1>
Answer: 3
Problem: <image>Question: An ant walked $6 \mathrm{~m}$ every day to go from point $A$ to point $B$ in a straight line. One day Johnny put a straight cylinder of one meter high in that way. Now the ant walks on the same straight line or above it, having to go up and down the cylinder, as shown in the picture. How much does she have to walk now to go from $A$ to $B$?
<image1>
Choices:
A. $8 \mathrm{~m}$
B. $9 \mathrm{~m}$
C. $6+\pi \mathrm{~m}$
D. $12-\pi \mathrm{~m}$
E. $10 \mathrm{~m}$
Answer: A
Problem: <image>Question: 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?
<image1>
Choices:
A. $6 \%$
B. $11 \%$
C. $12 \%$
D. $13 \%$
E. $18 \%$
Answer: D
Problem: <image>Question: In the addition on the right, different letters represent different numbers. Assuming the account is correct, what is the highest possible value for the sum $\mathrm{C}+\mathrm{A}+\mathrm{N}$?
<image1>
Answer: 21
Problem: <image>Question: A gray square with an area of $36 \mathrm{~cm}^{2}$ and a black square with an area of $25 \mathrm{~cm}^{2}$ are superimposed, as shown beside. What is the perimeter of the overlapping region, represented by the white quadrilateral, which has a vertex on the side of the gray square?
<image1>
Choices:
A. It is not determined.
B. $11 \mathrm{~cm}$
C. $16 \mathrm{~cm}$
D. $18 \mathrm{~cm}$
E. $20 \mathrm{~cm}$
Answer: B
Problem: <image>Question: Zilda will use six equal cubes and two different rectangular blocks to form the structure beside with eight faces. Before gluing the pieces, she will paint each one entirely and calculated that she will need 18 liters of paint (the color does not matter). How many liters of paint would she use if she painted the whole structure only after gluing the parts?
<image1>
Answer: 11.5
Problem: <image>Question: The last two digits of a 2020 number are 9 and 9. At most, how many digits does the square of that number have?
<image1>
Answer: 4040
Problem: <image>Question: Matias wrote 15 numbers on the wheel represented beside. Only one of them is visible, the 10 on top of the wheel. The sum of the numbers in any seven consecutive positions, such as the gray positions in the figure, does not vary. When seven numbers in consecutive positions are summed up, which of the following results is possible?
<image1>
Choices:
A. 49
B. 70
C. 75
D. 105
E. 150
Answer: B
Problem: <image>Question: A large square touches another two squares, as shown in the picture. The numbers inside the smaller squares indicate their areas. What is the area of the largest square?
<image1>
Answer: 13
Problem: <image>Question: A circle is tangent to one side of a rectangle and passes through two of its vertices, as shown beside. A square of $20 \mathrm{~cm}^{2}$ area has one side over the side of the rectangle and two vertices over the circle, as shown in the figure. What is the area of the rectangle?
<image1>
Choices:
A. $40 \mathrm{~cm}^{2}$
B. $45 \mathrm{~cm}^{2}$
C. $50 \mathrm{~cm}^{2}$
D. $55 \mathrm{~cm}^{2}$
E. $60 \mathrm{~cm}^{2}$
Answer: C
Problem: <image>Question: Two rectangular blocks and a cube are joined to form a larger rectangular block, which volume is $280 \mathrm{~cm}^{3}$. The cube, in dark gray in the picture, has volume equal to $125 \mathrm{~cm}^{3}$ and the smaller rectangular block has volume equal to $75 \mathrm{~cm}^{3}$. What is the area of the face marked with the question mark?
<image1>
Choices:
A. $16 \mathrm{~cm}^{2}$
B. $18 \mathrm{~cm}^{2}$
C. $20 \mathrm{~cm}^{2}$
D. $24 \mathrm{~cm}^{2}$
E. $56 \mathrm{~cm}^{2}$
Answer: A
Problem: <image>Question: The figure shows the lines $r$ and $s$, which equations are, respectively, $y=a x
+b$ e $y=c x+d$. Which of the following statements is true?
<image1>
Choices:
A. $a b+c d<0$
B. $a+b+c+d<0$
C. $a c+b d \geq 0$
D. $a+b+c+d>0$
E. $a b c d>0$
Answer: A
Problem: <image>Question: A little kangaroo draws a line passing through point $P$ of the grid and then paints three triangles in black as shown in the picture. The areas of these triangles are proportional to which numbers?
<image1>
Choices:
A. $1: 4: 9$
B. $1: 2: 9$
C. $1: 3: 9$
D. $1: 2: 3$
E. $2: 3: 4$
Answer: A
Problem: <image>Question: A rectangular garden was $50 \mathrm{~m}$ long and $40 \mathrm{~m}$ wide. An artificial lake was built next to it, so that the whole set forms a $60 \mathrm{~m}$ square. Then a fence was stretched, separating both the garden and the lake in two parts with equal areas, as shown in the picture. How long is this fence?
<image1>
Choices:
A. $60 \mathrm{~m}$
B. $30 \sqrt{5} \mathrm{~m}$
C. $60 \sqrt{2} \mathrm{~m}$
D. $85 \mathrm{~m}$
E. $60 \sqrt{3} \mathrm{~m}$
Answer: B
Problem: <image>Question: Vilma took a sheet of paper measuring $10 \mathrm{~cm} \times 20 \mathrm{~cm}$ and made two folds, taking the two smaller sides of the sheet to a diagonal of it. She gets a parallelogram, as shown in the picture. What is the area of this quadrilateral, in $\mathrm{cm}^{2}$?
<image1>
Choices:
A. $\frac{100 \sqrt{5}}{3}$
B. $50 \sqrt{5}$
C. $100(\sqrt{5}-1)$
D. $50(5-\sqrt{5})$
E. $50(5+\sqrt{5})$
Answer: D
Problem: <image>Question: There are $n$ different prime numbers $p_{1}, p_{2}, \ldots, p_{n}$ written from left to right on the last line below the table shown beside. The product of two neighboring numbers in the same line is written in the upper two boxes. The number $K=p_{1}^{\alpha_{1}} \cdot p_{2}^{\alpha_{2}} \ldots p_{n}^{\alpha_{n}}$ is written in the last house above. In a table like this, in which $\propto_{2}=9$, how many numbers are divisible by number $p_{4}$?
<image1>
Answer: 28
Problem: <image>Question: Adam and Bruna try to find out which is Carla's favorite figure, amongst the figures beside. Adam knows that Carla told Bruna what the shape of the figure was. Bruna knows that Carla told Adam what color the figure was. The following conversation takes place. Adam: "I don't know what Carla's favorite figure is and I know that Bruna doesn't know either". Bruna: "At first I didn't know what Carla's favorite figure was, but now I know". Adam: "Now I know too". What is Carla's favorite figure?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: Paula's weather app shows a diagram of the predicted weather and maximum temperatures for the next seven days, as shown. Which of the following represents the corresponding graph of maximum temperatures?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>Question: A large square is divided into smaller squares, as shown. A shaded circle is inscribed inside each of the smaller squares. What proportion of the area of the large square is shaded?
<image1>
Choices:
A. $\frac{8 \pi}{9}$
B. $\frac{13 \pi}{16}$
C. $\frac{3}{\pi}$
D. $\frac{3}{4}$
E. $\frac{\pi}{4}$
Answer: E
Problem: <image>Question: After the storm last night, the flagpole on our school building is leaning over. Looking from northwest, its tip is to the right of its bottom point. Looking from the east, its tip is also to the right of its bottom point. In which direction could the flagpole be leaning over?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>Question: 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?
<image1>
Choices:
A. $y=b x+c$
B. $y=c x+b$
C. $y=a x+b$
D. $y=a x+c$
E. $y=c x+a$
Answer: D
Problem: <image>Question: A large triangle is divided into smaller triangles as shown. The number inside each small triangle indicates its perimeter. What is the perimeter of the large
triangle?
<image1>
Answer: 34
Problem: <image>Question: In the $5 \times 5$ square shown the sum of the numbers in each row and in each column is the same. There is a number in every cell, but some of the numbers are not shown. What is the number in the cell marked with a question mark?
<image1>
Answer: 10