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stringlengths 1
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| question
stringlengths 31
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| options
listlengths 6
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| image_path
stringlengths 12
15
| image
imagewidth (px) 56
2.52k
| answer
stringclasses 5
values | solution
stringclasses 259
values | level
int64 1
5
| subject
stringclasses 16
values | Answer(Option)
stringclasses 5
values |
|---|---|---|---|---|---|---|---|---|---|
327
|
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>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/327.jpg
|
C
| null | 3
|
solid geometry
|
C
|
|
328
|
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>
|
[
"$160 \\mathrm{~m}^{3}$",
"$180 \\mathrm{~m}^{3}$",
"$200 \\mathrm{~m}^{3}$",
"$220 \\mathrm{~m}^{3}$",
"$240 \\mathrm{~m}^{3}$",
"I don't know"
] |
images/328.jpg
|
E
| null | 3
|
solid geometry
|
E
|
|
330
|
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>
|
[
"$\\sqrt{a b}$",
"$\\frac{1}{2} a^{2}$",
"$\\frac{1}{2} b^{2}$",
"$\\frac{1}{4}\\left(a^{2}+b^{2}\\right)$",
"$\\frac{1}{2}\\left(a^{2}+b^{2}\\right)$",
"I don't know"
] |
images/330.jpg
|
B
| null | 5
|
metric geometry - area
|
B
|
|
332
|
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>
|
[
"$3 \\sqrt{2}$",
"$\\frac{7 \\sqrt{2}}{2}$",
"$\\frac{11}{2}$",
"$5 \\sqrt{2}$",
"another value",
"I don't know"
] |
images/332.jpg
|
E
| null | 5
|
metric geometry - length
|
E
|
|
333
|
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>
|
[
"$\\pi$",
"$3 \\pi$",
"$\\frac{\\pi}{2}$",
"$2 \\pi$",
"$4 \\pi$",
"I don't know"
] |
images/333.jpg
|
D
| null | 5
|
metric geometry - area
|
D
|
|
335
|
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>
|
[
"$8 \\mathrm{~m}$",
"$9 \\mathrm{~m}$",
"$6+\\pi \\mathrm{~m}$",
"$12-\\pi \\mathrm{~m}$",
"$10 \\mathrm{~m}$",
"I don't know"
] |
images/335.jpg
|
A
| null | 3
|
solid geometry
|
A
|
|
336
|
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>
|
[
"$6 \\%$",
"$11 \\%$",
"$12 \\%$",
"$13 \\%$",
"$18 \\%$",
"I don't know"
] |
images/336.jpg
|
D
| null | 3
|
statistics
|
D
|
|
338
|
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>
|
[
"It is not determined.",
"$11 \\mathrm{~cm}$",
"$16 \\mathrm{~cm}$",
"$18 \\mathrm{~cm}$",
"$20 \\mathrm{~cm}$",
"I don't know"
] |
images/338.jpg
|
B
| null | 5
|
metric geometry - length
|
B
|
|
341
|
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>
|
[
"49",
"70",
"75",
"105",
"150",
"I don't know"
] |
images/341.jpg
|
B
| null | 1
|
logic
|
B
|
|
343
|
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>
|
[
"$40 \\mathrm{~cm}^{2}$",
"$45 \\mathrm{~cm}^{2}$",
"$50 \\mathrm{~cm}^{2}$",
"$55 \\mathrm{~cm}^{2}$",
"$60 \\mathrm{~cm}^{2}$",
"I don't know"
] |
images/343.jpg
|
C
| null | 5
|
metric geometry - area
|
C
|
|
344
|
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>
|
[
"$16 \\mathrm{~cm}^{2}$",
"$18 \\mathrm{~cm}^{2}$",
"$20 \\mathrm{~cm}^{2}$",
"$24 \\mathrm{~cm}^{2}$",
"$56 \\mathrm{~cm}^{2}$",
"I don't know"
] |
images/344.jpg
|
A
| null | 3
|
solid geometry
|
A
|
|
345
|
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>
|
[
"$a b+c d<0$",
"$a+b+c+d<0$",
"$a c+b d \\geq 0$",
"$a+b+c+d>0$",
"$a b c d>0$",
"I don't know"
] |
images/345.jpg
|
A
| null | 4
|
analytic geometry
|
A
|
|
346
|
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>
|
[
"$1: 4: 9$",
"$1: 2: 9$",
"$1: 3: 9$",
"$1: 2: 3$",
"$2: 3: 4$",
"I don't know"
] |
images/346.jpg
|
A
| null | 4
|
analytic geometry
|
A
|
|
347
|
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>
|
[
"$60 \\mathrm{~m}$",
"$30 \\sqrt{5} \\mathrm{~m}$",
"$60 \\sqrt{2} \\mathrm{~m}$",
"$85 \\mathrm{~m}$",
"$60 \\sqrt{3} \\mathrm{~m}$",
"I don't know"
] |
images/347.jpg
|
B
| null | 5
|
metric geometry - length
|
B
|
|
348
|
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>
|
[
"$\\frac{100 \\sqrt{5}}{3}$",
"$50 \\sqrt{5}$",
"$100(\\sqrt{5}-1)$",
"$50(5-\\sqrt{5})$",
"$50(5+\\sqrt{5})$",
"I don't know"
] |
images/348.jpg
|
D
| null | 5
|
transformation geometry
|
D
|
|
350
|
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>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/350.jpg
|
E
| null | 1
|
logic
|
E
|
|
351
|
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>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/351.jpg
|
E
| null | 3
|
statistics
|
E
|
|
352
|
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>
|
[
"$\\frac{8 \\pi}{9}$",
"$\\frac{13 \\pi}{16}$",
"$\\frac{3}{\\pi}$",
"$\\frac{3}{4}$",
"$\\frac{\\pi}{4}$",
"I don't know"
] |
images/352.jpg
|
E
| null | 5
|
metric geometry - area
|
E
|
|
353
|
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>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/353.jpg
|
A
| null | 1
|
descriptive geometry
|
A
|
|
354
|
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>
|
[
"$y=b x+c$",
"$y=c x+b$",
"$y=a x+b$",
"$y=a x+c$",
"$y=c x+a$",
"I don't know"
] |
images/354.jpg
|
D
| null | 4
|
analytic geometry
|
D
|
|
357
|
A piece of string is lying on the table. It is partially covered by three coins as seen in the figure. Under each coin the string is equally likely to pass over itself like this: <image1>
or like this: <image2>. What is the probability that the string is knotted after its ends are pulled?
<image3>
|
[
"$\\frac{1}{2}$",
"$\\frac{1}{4}$",
"$\\frac{1}{8}$",
"$\\frac{3}{4}$",
"$\\frac{3}{8}$",
"I don't know"
] |
images/357.jpg
|
B
| null | 1
|
topology
|
B
|
|
358
|
A naughty pup grabs the end of a roll of toilet paper and walks away at a constant speed. Which of the functions below best describes the thickness $y$ of the roll as a function of the unrolled part $x$?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/358.jpg
|
E
| null | 4
|
analytic geometry
|
E
|
|
361
|
Five kangaroos named A, B, C, D and E have one child each, named a, b, c, d and e, not necessarily in that order. In the first group photo shown exactly 2 of the children are standing next to their mothers. In the second group photo exactly 3 of the children are standing next to their mothers. Whose child is a?
<image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/361.jpg
|
D
| null | 1
|
logic
|
D
|
|
365
|
Two plane mirrors $O P$ and $O Q$ are inclined at an acute angle (diagram is not to scale). A ray of light $X Y$ parallel to $O Q$ strikes mirror $O P$ at $Y$. The ray is reflected and hits mirror $O Q$, is reflected again and hits mirror $O P$ and is reflected for a third time and strikes mirror $O Q$ at right angles at $R$ as shown. If $O R=5 \mathrm{~cm}$, what is the distance $d$ of the ray $X Y$ from the mirror $O Q$?
<image1>
|
[
"$4 \\mathrm{~cm}$",
"$4.5 \\mathrm{~cm}$",
"$5 \\mathrm{~cm}$",
"$5.5 \\mathrm{~cm}$",
"$6 \\mathrm{~cm}$",
"I don't know"
] |
images/365.jpg
|
C
| null | 5
|
metric geometry - length
|
C
|
|
366
|
Martin's smartphone displays the diagram on the right. It shows how long he has worked with four different apps in the previous week. The apps are sorted from top to bottom according to the amount of time they have been used. This week he has spent only half the amount of time using two of the apps and the same amount of time as last week using the other two apps. Which of the following pictures cannot be the diagram for the current week?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/366.jpg
|
E
| null | 3
|
statistics
|
E
|
|
367
|
Four circles with radius 1 intersect each other as seen in the diagram. What is the perimeter of the grey area?
<image1>
|
[
"$\\pi$",
"$\\frac{3 \\pi}{2}$",
"a number between $\\frac{3 \\pi}{2}$ and $2 \\pi$",
"$2 \\pi$",
"$\\pi^{2}$",
"I don't know"
] |
images/367.jpg
|
D
| null | 5
|
metric geometry - length
|
D
|
|
368
|
The points $A, B, C$ and $D$ are marked on a straight line in this order as shown in the diagram. We know that $A$ is $12 \mathrm{~cm}$ from $C$ and that $B$ is $18 \mathrm{~cm}$ from $D$. How far apart from each other are the midpoints of the line segments $A B$ and $C D$?
<image1>
|
[
"$6 \\mathrm{~cm}$",
"$9 \\mathrm{~cm}$",
"$12 \\mathrm{~cm}$",
"$13 \\mathrm{~cm}$",
"$15 \\mathrm{~cm}$",
"I don't know"
] |
images/368.jpg
|
E
| null | 5
|
metric geometry - length
|
E
|
|
369
|
Four straight lines that intersect in one single point form eight equal angles (see diagram). Which one of the black arcs has the same length as the circumference of the little (grey) circle?
<image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/369.jpg
|
D
| null | 5
|
metric geometry - length
|
D
|
|
370
|
We check the water meter and see that all digits on the display are different. What is the minimum amount of water that has to be used before this happens again?
<image1>
|
[
"$0.006 \\mathrm{~m}^{3}$",
"$0.034 \\mathrm{~m}^{3}$",
"$0.086 \\mathrm{~m}^{3}$",
"$0.137 \\mathrm{~m}^{3}$",
"$1.048 \\mathrm{~m}^{3}$",
"I don't know"
] |
images/370.jpg
|
D
| null | 1
|
arithmetic
|
D
|
|
373
|
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?
<image1>
|
[
"$X$",
"$2 X$",
"$3 X$",
"$4 X$",
"It depends on the position of the planes.",
"I don't know"
] |
images/373.jpg
|
C
| null | 3
|
solid geometry
|
C
|
|
375
|
Which two building blocks can be joined together so that the object shown is created?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/375.jpg
|
A
| null | 5
|
combinatorial geometry
|
A
|
|
377
|
Two rectangles are inscribed into a triangle as shown in the diagram. The dimensions of the rectangles are $1 \times 5$ and $2 \times 3$ respectively. How big is the height of the triangle in $A$?
<image1>
|
[
"3",
"$\\frac{7}{2}$",
"$\\frac{8}{3}$",
"$\\frac{6}{5}$",
"another number",
"I don't know"
] |
images/377.jpg
|
B
| null | 5
|
metric geometry - length
|
B
|
|
378
|
The numbers 1 to 10 were written into the ten circles in the pattern shown in the picture. The sum of the four numbers in the left and the right column is 24 each and the sum of the three numbers in the bottom row is 25. Which number is in the circle with the question mark?
<image1>
|
[
"2",
"4",
"5",
"6",
"another number",
"I don't know"
] |
images/378.jpg
|
E
| null | 5
|
algebra
|
E
|
|
379
|
A square is placed in a co-ordinate system as shown. Each point $(x \mid y)$ of the square is deleted and replaced by the point $\left(\frac{1}{x} \mid \frac{1}{y}\right)$. Which diagram shows the resulting shape?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/379.jpg
|
C
| null | 4
|
analytic geometry
|
C
|
|
381
|
A cylindrical tin is $15 \mathrm{~cm}$ high. The circumference of the base circle is $30 \mathrm{~cm}$. An ant walks from point $A$ at the base to point $B$ at the top. Its path is partly vertically upwards and partly along horizontal circular arcs. Its path is drawn in bold on the diagram (with a solid line on the front and a dashed line at the back). How long is the total distance covered by the ant? <image1>
|
[
"$45 \\mathrm{~cm}$",
"$55 \\mathrm{~cm}$",
"$60 \\mathrm{~cm}$",
"$65 \\mathrm{~cm}$",
"$75 \\mathrm{~cm}$",
"I don't know"
] |
images/381.jpg
|
E
| null | 3
|
solid geometry
|
E
|
|
388
|
Leon has drawn a closed path on the surface of a cuboid. Which net can represent his path?
<image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/388.jpg
|
D
| null | 1
|
descriptive geometry
|
D
|
|
390
|
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? <image1>
|
[
"$625 \\uparrow 626 \\uparrow 627$",
"$625 \\uparrow 626 \\rightarrow$",
"$625 \\rightarrow 626 \\rightarrow 627$",
"$625 \\rightarrow 626 \\uparrow 627$",
"$625 \\downarrow 626 \\downarrow 627$",
"I don't know"
] |
images/390.jpg
|
B
| null | 5
|
algebra
|
B
|
|
391
|
A game marker in the shape of a regular tetrahedron has one marked area. That side is placed on the triangle marked START. The marker is then moved within the diagram always to the next adjacent triangle by rolling it around an edge. On which triangle is the marker when it is on the marked side again for the first time? <image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/391.jpg
|
E
| null | 3
|
solid geometry
|
E
|
|
392
|
A part of a polynomial of degree five is illegible due to an ink stain. It is known that all zeros of the polynomial are integers. What is the highest power of $x-1$ that divides this polynomial? <image1>
|
[
"$(x-1)^{1}$",
"$(x-1)^{2}$",
"$(x-1)^{3}$",
"$(x-1)^{4}$",
"$(x-1)^{5}$",
"I don't know"
] |
images/392.jpg
|
D
| null | 5
|
algebra
|
D
|
|
393
|
The big square shown is split into four small squares. The circle touches the right side of the square in its midpoint. How big is the side length of the big square? (Hint: The diagram is not drawn to scale.) <image1>
|
[
"$18 \\mathrm{~cm}$",
"$20 \\mathrm{~cm}$",
"$24 \\mathrm{~cm}$",
"$28 \\mathrm{~cm}$",
"$30 \\mathrm{~cm}$",
"I don't know"
] |
images/393.jpg
|
A
| null | 5
|
metric geometry - length
|
A
|
|
395
|
Two identical cylindrical glasses contain the same amount of water. The left glass is upright, while the right one rests against the other one at a slant. The water level in both glasses is at the same height. The water level in the leaning glass touches its bottom in exactly one point (see diagram). The bases of both glasses have an area of $3 \pi \mathrm{cm}^{2}$. How much water is in each glass? <image1>
|
[
"$9 \\pi \\mathrm{cm}^{3}$",
"$6 \\pi \\mathrm{cm}^{3}$",
"$3 \\sqrt{3} \\pi \\mathrm{cm}^{3}$",
"$\\frac{3 \\pi}{4} \\mathrm{~cm}^{3}$",
"It cannot be uniquely determined from this information.",
"I don't know"
] |
images/395.jpg
|
A
| null | 5
|
metric geometry - area
|
A
|
|
402
|
I surrounded the wooden circle (see picture) using $a \mathrm{~cm}$ of thread. After that I surrounded by thread the wooden square –– $b \mathrm{~cm}$ of thread was enough for that. How much thread (in $\mathrm{cm}$ ) would be enough to surround the three wooden circles without moving them?
<image1>
|
[
"3a",
"2a+b",
"a+2b",
"3b",
"a+b",
"I don't know"
] |
images/402.jpg
|
E
| null | 3
|
metric geometry - length
|
E
|
|
403
|
The picture on the right has been drawn on paper and cut out to make a house. Which of the houses does it make?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/403.jpg
|
A
| null | 5
|
descriptive geometry
|
A
|
|
406
|
Which numbers are written in the area that belongs to the rectangle and to the circle but doesn't belong to the triangle?
<image1>
|
[
"5 and 11",
"1 and 10",
"13",
"3 and 9",
"6, 7, and 4",
"I don't know"
] |
images/406.jpg
|
B
| null | 2
|
combinatorial geometry
|
B
|
|
408
|
Which of the rectangles $\mathbf{A}$ to $\mathbf{E}$ can be covered by the pattern on the right-hand side in such a way that the result is a totally black rectangle?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/408.jpg
|
D
| null | 5
|
descriptive geometry
|
D
|
|
409
|
In this picture there is what I saw on four different clocks at the same time. Only one of them had the right time. One was 20 minutes fast. Another 20 minutes slow. One had stopped some time ago.
<image1>
What was the right time?
|
[
"4:45",
"5:05",
"5:25",
"5:40",
"12:00",
"I don't know"
] |
images/409.jpg
|
B
| null | 2
|
logic
|
B
|
|
410
|
A cube (on the right) is colored in three colors so that each face has exactly one color and the opposite face has the same color. Which of the following developments is the development of this cube?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/410.jpg
|
E
| null | 5
|
solid geometry
|
E
|
|
412
|
There are five houses on Color Street: a blue, a red, a yellow, a pink, and a green one. The houses are numbered from 1 to 5 (see picture). The red house is the neighbor of the blue house only. The blue house stands between the green and red houses.
<image1>
Which color is the house with number 3?
|
[
"Blue",
"Red",
"Yellow",
"Pink",
"Green",
"I don't know"
] |
images/412.jpg
|
E
| null | 2
|
logic
|
E
|
|
414
|
This is a multiplication table. Which two letters represent the same number?
<image1>
|
[
"$L$ and $M$",
"$P$ and $N$",
"$R$ and $S$",
"$K$ and $R$",
"$M$ and $T$",
"I don't know"
] |
images/414.jpg
|
E
| null | 2
|
algebra
|
E
|
|
416
|
At noon the minute hand of a clock is in the position shown on the left and after the quarter of an hour -- in the position shown on the right. Which position the minute hand will take after seventeen quarters from the noon?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/416.jpg
|
A
| null | 3
|
arithmetic
|
A
|
|
419
|
A square piece of paper has been cut in three pieces. Two of them are in the picture on the right. What is the third one?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/419.jpg
|
B
| null | 2
|
combinatorial geometry
|
B
|
|
422
|
Two traffic signs mark the bridge in my village. These marks indicate the maximum width and the maximum possible weight. Which one of the following trucks is allowed to cross that bridge?
<image1>
|
[
"The one $315 \\mathrm{~cm}$ wide and weighing $4307 \\mathrm{~kg}$",
"The one $330 \\mathrm{~cm}$ wide and weighing $4250 \\mathrm{~kg}$",
"The one $325 \\mathrm{~cm}$ wide and weighing $4400 \\mathrm{~kg}$",
"The one $322 \\mathrm{~cm}$ wide and weighing $4298 \\mathrm{~kg}$",
"No one of these",
"I don't know"
] |
images/422.jpg
|
D
| null | 2
|
algebra
|
D
|
|
425
|
Which of the following cubes has been folded out of the plan on the right?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/425.jpg
|
E
| null | 5
|
descriptive geometry
|
E
|
|
426
|
Betty keeps drawing three different figures in the same order. Which figure should be the next?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/426.jpg
|
D
| null | 1
|
transformation geometry
|
D
|
|
428
|
A kangaroo enters a building. He only passes through triangular rooms. Where does he leave the building?
<image1>
|
[
"a",
"b",
"c",
"d",
"e",
"I don't know"
] |
images/428.jpg
|
E
| null | 2
|
graph theory
|
E
|
|
429
|
From which rectangular can you cut the figure shown on the right side out?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/429.jpg
|
E
| null | 2
|
combinatorial geometry
|
E
|
|
432
|
Between two points four routes are drawn. Which route is the shortest?
<image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/432.jpg
|
E
| null | 2
|
combinatorial geometry
|
E
|
|
439
|
Zita walks from left to right and puts the numbers into her basket. Which of the following numbers can be in her basket?
<image1>
|
[
"1, 2 and 4",
"2, 3 and 4",
"2, 3 and 5",
"1, 5 and 6",
"1, 2 and 5",
"I don't know"
] |
images/439.jpg
|
C
| null | 2
|
graph theory
|
C
|
|
440
|
In which figure can you find the largest number of small squares?
<image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/440.jpg
|
C
| null | 2
|
counting
|
C
|
|
441
|
What is the piece that fits completely to the given one to form a rectangle?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/441.jpg
|
B
| null | 2
|
combinatorial geometry
|
B
|
|
446
|
A square piece of paper is folded twice so that the result is a square again. In this square one of the corners is cut off. Then the paper is folded out. Which sample below cannot be obtained in this way?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/446.jpg
|
E
| null | 1
|
transformation geometry
|
E
|
|
451
|
Carol is playing with two equilateral triangular cards shown. She puts one card beside or on the top of a part of the other and both on a sheet of paper. Then she draws on the paper around them, following the contour. She cannot get only one of the shapes. Which one is it?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/451.jpg
|
E
| null | 2
|
combinatorial geometry
|
E
|
|
452
|
Anna made the figure on the right out of five cubes. Which of the following figures (when seen from any direction) cannot she get from the figure on the right side if she is allowed to move exactly one cube?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/452.jpg
|
D
| null | 2
|
combinatorial geometry
|
D
|
|
453
|
Which of the figures is shown most often in the sequence?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/453.jpg
|
D
| null | 2
|
counting
|
D
|
|
456
|
A garden of a square shape is divided into a pool (P), a flowerbed (F), a lawn (L) and a sandpit (S) (see the picture). The lawn and the flowerbed are of a square shape. The perimeter of the lawn is $20 \mathrm{~m}$, the perimeter of the flowerbed is $12 \mathrm{~m}$. What is the perimeter of the pool?
<image1>
|
[
"$10 \\mathrm{~m}$",
"$12 \\mathrm{~m}$",
"$14 \\mathrm{~m}$",
"$16 \\mathrm{~m}$",
"$18 \\mathrm{~m}$",
"I don't know"
] |
images/456.jpg
|
D
| null | 3
|
metric geometry - length
|
D
|
|
457
|
One of the cube faces is cut along its diagonals (see the fig.). Which two of the following nets are impossible?
<image1>
<image2>
|
[
"1 and 3",
"1 and 5",
"3 and 4",
"3 and 5",
"2 and 4",
"I don't know"
] |
images/457.jpg
|
D
| null | 5
|
descriptive geometry
|
D
|
|
458
|
Where is the Kangaroo?
<image1>
|
[
"In the circle and in the triangle but not in the square.",
"In the circle and in the square but not in the triangle.",
"In the triangle and in the square but not in the circle.",
"In the circle but in neither the square or the triangle.",
"In the square but in neither the circle or the triangle.",
"I don't know"
] |
images/458.jpg
|
B
| null | 2
|
combinatorial geometry
|
B
|
|
460
|
In his garden Tony made a pathway using 10 paving stones. Each paver was $4 \mathrm{dm}$ wide and 6 dm long. He then drew a black line connecting the middle points of each paving stone. How long is the black line?
<image1>
|
[
"$24 \\mathrm{dm}$",
"$40 \\mathrm{dm}$",
"$46 \\mathrm{dm}$",
"$50 \\mathrm{dm}$",
"$56 \\mathrm{dm}$",
"I don't know"
] |
images/460.jpg
|
C
| null | 2
|
combinatorial geometry
|
C
|
|
462
|
Picture $X$ is paired with picture $Y$. Which of the following pictures is paired with picture $G$ ?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/462.jpg
|
E
| null | 2
|
combinatorial geometry
|
E
|
|
464
|
Which of the following diagrams is impossible to make with the two dominos?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/464.jpg
|
E
| null | 2
|
combinatorial geometry
|
E
|
|
466
|
Sylvia draws shapes made up of straight lines which are each $1 \mathrm{~cm}$ long. At the end of each line she continues in a right angle either to the left or right. At every turn she notes down either a $\vee$ or a $\wedge$ on a piece of paper. The same symbol always indicates a turn in the same direction. Today her notes show $\vee \wedge \wedge \wedge \vee \vee$. Which of the following shapes could she have drawn today if $A$ indicates her starting point?
<image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/466.jpg
|
E
| null | 2
|
algebra
|
E
|
|
467
|
In the picture on the right you see a map. In the middle a piece is missing. The cat should be able to reach the milk, and the mouse the cheese, but the cat and the mouse must not meet each other. What should the piece in the middle look like?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/467.jpg
|
E
| null | 2
|
graph theory
|
E
|
|
468
|
Which square contains 3 quadrilaterals, 3 circles and 4 hearts?
<image1>
|
[
"A)",
"B)",
"C)",
"D)",
"E)",
"I don't know"
] |
images/468.jpg
|
D
| null | 2
|
counting
|
D
|
|
470
|
I have tiles that look like this...
<image1>
Which pattern can I not create with them?
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/470.jpg
|
B
| null | 2
|
combinatorial geometry
|
B
|
|
473
|
Kamilla wrote down all of the numbers from 1-100 one after the other in a table with 5 columns. A part of the table is shown. Her brother cut out a piece of the table and erased some of the numbers. Which of the following could this piece have been?
<image1>
<image2>
|
[
"A)",
"B)",
"C)",
"D)",
"E)",
"I don't know"
] |
images/473.jpg
|
C
| null | 2
|
algebra
|
C
|
|
475
|
Which stone should Mr Flintstone place on the right side of the scales, so that both sides weigh the same?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/475.jpg
|
C
| null | 3
|
arithmetic
|
C
|
|
476
|
A game is played on a board as shown in the picture. I move the counter from square to square according to the following rules. First, one square to the right, then one square up, then one square left, then one square down, and then once again one square right. Which picture shows where the counter can then be found?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/476.jpg
|
B
| null | 1
|
analytic geometry
|
B
|
|
477
|
Maria describes one of these five shapes in the following way: "It is not a square. It is grey. It is either round or three sided." Which shape did she describe?
<image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/477.jpg
|
B
| null | 2
|
logic
|
B
|
|
478
|
Which shape has the biggest area?
<image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/478.jpg
|
C
| null | 2
|
counting
|
C
|
|
479
|
A page is folded along the thick line as shown. Which letter will not be covered by a grey square?
<image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/479.jpg
|
E
| null | 1
|
transformation geometry
|
E
|
|
481
|
How often in a day does a digital clock display four identical digits? The picture shows a digital clock that is displaying exactly two different digits.
<image1>
|
[
"1 time",
"24 times",
"3 times",
"5 times",
"12 times",
"I don't know"
] |
images/481.jpg
|
C
| null | 2
|
counting
|
C
|
|
482
|
Four identical dice were put together to make a tower as shown. The sum of the numbers on opposite faces of each dice is always 7. What would the tower look like from behind?
<image1>
<image2>
|
[
"A)",
"B)",
"C)",
"D)",
"E)",
"I don't know"
] |
images/482.jpg
|
C
| null | 5
|
descriptive geometry
|
C
|
|
484
|
Andrea made the pattern in the picture out of several identical tiles. None of the tiles overlap each other. Which of the following tiles could she definitely not have used?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/484.jpg
|
D
| null | 2
|
combinatorial geometry
|
D
|
|
488
|
In which of the five pictures is the white area bigger than the grey area?
<image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/488.jpg
|
D
| null | 2
|
combinatorial geometry
|
D
|
|
490
|
Oli coloured in the following 8 fields in the grid: A2, B1, B2, B3, B4, C3, D3 and D4. Which is his grid?
<image1>
<image2>
|
[
"(A)",
"(B)",
"(C)",
"(D)",
"(E)",
"I don't know"
] |
images/490.jpg
|
C
| null | 1
|
analytic geometry
|
C
|
|
491
|
Mike and Jake play darts. Each of them throws three darts. Who won, and by how many points?
Mike: <image1>
Jake: <image2>
|
[
"Mike won. He had 3 points more.",
"Jake won. He had 4 points more.",
"Mike won. He had 2 points more.",
"Jake won. He had 2 points more.",
"Mike won. He had 4 points more.",
"I don't know"
] |
images/491.jpg
|
E
| null | 3
|
arithmetic
|
E
|
|
494
|
You need 3 pieces to build this shape. Each piece is made out of 4 , equally sized cubes of the same colour. What is the shape of the white piece?
<image1>
<image2>
|
[
"(A)",
"(B)",
"(C)",
"(D)",
"(E)",
"I don't know"
] |
images/494.jpg
|
D
| null | 5
|
descriptive geometry
|
D
|
|
497
|
Grandma's watch has an hour, minute and second hand. We don't know which hand does which job, but we know that the watch tells the correct time. At 12:55:30 hours the watch looked as pictured. How will the watch look at 8:11:00 hours?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/497.jpg
|
E
| null | 2
|
algebra
|
E
|
|
499
|
In which picture are there more black Kangaroos than white ones?
<image1>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/499.jpg
|
D
| null | 2
|
counting
|
D
|
|
500
|
Anna has <image1>.
Barbara gave Eva <image2>.
Josef has a <image3>.
Bob has <image4>.
Who is Barbara?
<image5>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/500.jpg
|
D
| null | 2
|
logic
|
D
|
|
501
|
Anna starts in the direction of the arrow. At each crossing she turns either right or left. At the first crossing she turns right, at the next left, then left again, then right, then left and left again. What will she find at the next crossing that she comes to?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/501.jpg
|
A
| null | 2
|
graph theory
|
A
|
|
503
|
The rectangular mirror has broken. Which piece is missing?
<image1>
<image2>
|
[
"(A)",
"(B)",
"(C)",
"(D)",
"(E)",
"I don't know"
] |
images/503.jpg
|
B
| null | 2
|
combinatorial geometry
|
B
|
|
505
|
Which of the following pieces can be joined to the one pictured so that a rectangle is formed?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/505.jpg
|
B
| null | 2
|
combinatorial geometry
|
B
|
|
510
|
Luisa draws a star. She cuts a piece out of the middle of the drawing. What does this piece look like?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/510.jpg
|
D
| null | 2
|
counting
|
D
|
|
511
|
For which houses, were exactly the same building blocks used?
<image1>
|
[
"House 1 and 4",
"House 3 and 4",
"House 1, 4 and 5",
"House 3, 4 and 5",
"House 1, 2, 4 and 5",
"I don't know"
] |
images/511.jpg
|
A
| null | 2
|
combinatorial geometry
|
A
|
|
512
|
Christopher solved the sums next to the dots that you can see on the right, and got the answers 0 to 5 . He joined the dots in order. He started with the dot that had the answer 0 and finished with the dot that had the answer 5 . Which shape was he left with?
<image1>
<image2>
|
[
"(A)",
"(B)",
"(C)",
"(D)",
"(E)",
"I don't know"
] |
images/512.jpg
|
A
| null | 3
|
arithmetic
|
A
|
|
513
|
Mr Hofer has drawn a picture of flowers on the inside of a display window (large picture). What do these flowers look like when you look at the picture from the outside?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/513.jpg
|
E
| null | 5
|
descriptive geometry
|
E
|
|
514
|
With which square do you have to swap the question mark, so that the white area and the black area are the same size?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/514.jpg
|
B
| null | 2
|
combinatorial geometry
|
B
|
|
515
|
The solid in the diagram is made out of 8 identical cubes. What does the solid look like when viewed from above?
<image1>
<image2>
|
[
"A",
"B",
"C",
"D",
"E",
"I don't know"
] |
images/515.jpg
|
C
| null | 5
|
descriptive geometry
|
C
|
|
517
|
Katja throws darts at the target pictured on the right. If she does not hit the target she gets no points. She throws twice and adds her points. What can her total not be?
<image1>
|
[
"60",
"70",
"80",
"90",
"100",
"I don't know"
] |
images/517.jpg
|
D
| null | 3
|
arithmetic
|
D
|
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