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910 | spatial | MathVision/test_000910.png | Each of the nets of a cube has a line drawn on. For which net does the line form a closed loop when the net is folded up to make a cube?
<image1>
Select only from the following 4 options:
A
C
D
E | D | descriptive geometry | A
C
D
E |
914 | spatial | MathVision/test_000914.png | The cardboard is folded up into a $2 \times 1 \times 1$ box. Which of the pictures does not show the box?
<image1>
<image2>
Select only from the following 4 options:
A
B
D
E | B | descriptive geometry | A
B
D
E |
919 | algorithmic | MathVision/test_000919.png | Bia has five coins as shown beside. She went to the grocery store to buy a fruit, using only three coins, without having to receive change. Among the prices of the following fruits, which one can she NOT buy?
<image1>
Select only from the following 4 options:
A. 1,30
B. 1,35
C. 1,40
E. 1,75 | C | combinatorics | A. 1,30
B. 1,35
C. 1,40
E. 1,75 |
923 | Quantitative Reasoning | MathVision/test_000923.png | When the bat Elisa left its cave at night, the digital clock showed <image1>. When she came back in the morning and hung herself upside down, she looked at her watch and saw <image1>. How long did she stay out of the cave?
Select only from the following 4 options:
A. 2h 48m
B. 2h 59m
C. 3h 39m
D. 3h 41m | D | arithmetic | A. 2h 48m
B. 2h 59m
C. 3h 39m
D. 3h 41m |
925 | Quantitative Reasoning | MathVision/test_000925.png | The following figures show five paths, indicated by the thickest lines, between the $X$ and $Y$ points. Which of these paths is the longest?
<image1>
Select only from the following 4 options:
A
B
D
E | A | counting | A
B
D
E |
934 | deductive | MathVision/test_000934.png | Ten people order an ice cream for each one. They ask for four vanilla ice creams, three chocolate ice creams, two lemon ice creams and one mango ice cream. As a topping, they ask for four umbrellas, three cherries, two wafers and a chocolate gum, one topping for each ice cream. Since they don't want two ice creams the same, which of the following combinations is possible?
<image1>
Select only from the following 4 options:
A. Chocolat and chocolate gum.
B. Mango and cherry.
C. Lemmon and wafer.
D. Mango and wafer. | E | logic | A. Chocolat and chocolate gum.
B. Mango and cherry.
C. Lemmon and wafer.
D. Mango and wafer. |
937 | algorithmic | MathVision/test_000937.png | The figure shows a map with some islands and how they are connected by bridges. A navigator wants to pass through each of the islands exactly once. He started at Cang Island and wants to finish at Uru Island. He has just arrived at the black island in the center of the map. In which direction must he go now to be able to complete his route?
<image1>
Select only from the following 4 options:
A. North.
C. South.
D. West.
E. There is more than one possible choice | C | graph theory | A. North.
C. South.
D. West.
E. There is more than one possible choice |
941 | deductive | MathVision/test_000941.png | Sofie wants to write the word KENGU by using letters from the boxes. She can only take one letter from each box. What letter must Sofie take from box 4?
<image1>
Select only from the following 4 options:
A. K
C. N
D. G
E. U | D | logic | A. K
C. N
D. G
E. U |
947 | algorithmic | MathVision/test_000947.png | The map shows three bus stations at points $A, B$ and $C$. A tour from station $A$ to the Zoo and the Port and back to $A$ is $10 \mathrm{~km}$ long. $A$ tour from station $B$ to the Park and the Zoo and back to B is $12 \mathrm{~km}$ long. A tour from station C to the Port and the Park and back to $C$ is $13 \mathrm{~km}$ long. Also, A tour from the Zoo to the Park and the Port and back to the Zoo is $15 \mathrm{~km}$ long. How long is the shortest tour from A to B to $C$ and back to $A$?
<image1>
Select only from the following 4 options:
A. $18 \mathrm{~km}$
C. $25 \mathrm{~km}$
D. $35 \mathrm{~km}$
E. $50 \mathrm{~km}$ | B | graph theory | A. $18 \mathrm{~km}$
C. $25 \mathrm{~km}$
D. $35 \mathrm{~km}$
E. $50 \mathrm{~km}$ |
951 | spatial | MathVision/test_000951.png | A triangular pyramid is built with 10 identical balls, like this <image1>. Each ball has one of the letters A, $B, C, D$ and $E$ on it. There are 2 balls marked with each letter. The picture shows 3 side views of the pyramid. What is the letter on the ball with the question mark?
<image2>
Select only from the following 4 options:
A
B
C
E | A | descriptive geometry | A
B
C
E |
952 | algorithmic | MathVision/test_000952.png | Ronja had four white tokens and Wanja had four grey tokens. They played a game in which they took turns to place one of their tokens to create two piles. Ronja placed her first token first. Which pair of piles could they not create?
<image1>
Select only from the following 4 options:
B
C
D
E | E | combinatorics | B
C
D
E |
959 | deductive | MathVision/test_000959.png | There are rectangular cards divided into 4 equal cells with different shapes <image1> drawn in each cell. Cards can be placed side by side only if the same shapes appear in adjacent cells on their common side. 9 cards are used to form a rectangle as shown in the figure. Which of the following cards was definitely NOT used to form this rectangle?
<image2>
<image3>
Select only from the following 4 options:
A
B
D
E | E | logic | A
B
D
E |
965 | Quantitative Reasoning | MathVision/test_000965.png | How much does this Ferris wheel need to turn so that a white gondola is on top for
the first time?
<image1>
Select only from the following 4 options:
A. $\frac{1}{2}$ turn
C. $\frac{1}{6}$ turn
D. $\frac{1}{12}$ turn
E. $\frac{5}{6}$ turn | D | arithmetic | A. $\frac{1}{2}$ turn
C. $\frac{1}{6}$ turn
D. $\frac{1}{12}$ turn
E. $\frac{5}{6}$ turn |
966 | Quantitative Reasoning | MathVision/test_000966.png | The sides of the square $A B C D$ are $10 \mathrm{~cm}$ long. What is the total area of the shaded part?
<image1>
Select only from the following 4 options:
B. $45 \mathrm{~cm}^{2}$
C. $50 \mathrm{~cm}^{2}$
D. $55 \mathrm{~cm}^{2}$
E. $60 \mathrm{~cm}^{2}$ | C | arithmetic | B. $45 \mathrm{~cm}^{2}$
C. $50 \mathrm{~cm}^{2}$
D. $55 \mathrm{~cm}^{2}$
E. $60 \mathrm{~cm}^{2}$ |
967 | algorithmic | MathVision/test_000967.png | Five big and four small elephants are marching along a path. Since the path is narrow the elephants cannot change their order. At the fork in the path each elephant either goes to the right or to the left. Which of the following situations cannot happen?
<image1>
<image2>
Select only from the following 4 options:
A
B
C
D | C | combinatorics | A
B
C
D |
973 | spatial | MathVision/test_000973.png | Anna has glued together several cubes of the same size to form a solid (see picture). Which of the following pictures shows a different view of this solid?
<image1>
<image2>
Select only from the following 4 options:
B
C
D
E | C | descriptive geometry | B
C
D
E |
982 | spatial | MathVision/test_000982.png | Four ribbons $\mathrm{M}, \mathrm{N}, \mathrm{P}$ and $\mathrm{Q}$ are wrapped around a box. <image1> In which order were they wrapped around the box?
Select only from the following 4 options:
B. N, M, P, Q
C. N, Q, M, P
D. N, M, Q, P
E. $Q, N, M, P$ | D | descriptive geometry | B. N, M, P, Q
C. N, Q, M, P
D. N, M, Q, P
E. $Q, N, M, P$ |
995 | algorithmic | MathVision/test_000995.png | Martin has three cards that are labelled on both sides with a number. Martin places the three cards on the table without paying attention to back or front. He adds the three numbers that he can then see. How many different sums can Martin get that way?
<image1>
Select only from the following 4 options:
B. 5
C. 6
D. 9
E. A different amount. | E | combinatorics | B. 5
C. 6
D. 9
E. A different amount. |
997 | algorithmic | MathVision/test_000997.png | Monika wants to find a path through the labyrinth from 'Start' to 'Ziel'. She has to stick to the following rules: She is only allowed to move horizontally and vertically respectively. She has to enter every white circle exactly once but is not allowed to enter a black circle. In which direction does Monika have to move forwards when she reaches the circle marked with $x$ ? <image1>
Select only from the following 4 options:
B. $\uparrow$
C. $\rightarrow$
D. $\leftarrow$
E. there are several possibilities | A | graph theory | B. $\uparrow$
C. $\rightarrow$
D. $\leftarrow$
E. there are several possibilities |
1003 | spatial | MathVision/test_001003.png | A rectangular parallelepiped was composed of 3 pieces, each consisting of 4 little cubes. Then one piece was removed (see picture). Which one?
<image1>
<image2>
Select only from the following 4 options:
B
C
D
E | D | descriptive geometry | B
C
D
E |
1011 | spatial | MathVision/test_001011.png | The section of a cube by a plane generates a plane figure. I have plotted this section in the development of the cube (see the picture). Can you find out what figure it is?
<image1>
Select only from the following 4 options:
B. A rectangle, but not a square
C. A right triangle
D. A square
E. A hexagon | A | descriptive geometry | B. A rectangle, but not a square
C. A right triangle
D. A square
E. A hexagon |
1023 | spatial | MathVision/test_001023.png | Which of the following nets has a cube in the right picture?
<image1>
<image2>
Select only from the following 4 options:
B
C
D
E | E | descriptive geometry | B
C
D
E |
1048 | Quantitative Reasoning | MathVision/test_001048.png | In the picture the large square has an area of 1. What is the area of the small black square?
<image1>
Select only from the following 4 options:
A. $\frac{1}{100}$
B. $\frac{1}{300}$
C. $\frac{1}{600}$
D. $\frac{1}{900}$ | D | arithmetic | A. $\frac{1}{100}$
B. $\frac{1}{300}$
C. $\frac{1}{600}$
D. $\frac{1}{900}$ |
1054 | algorithmic | MathVision/test_001054.png | We want to paint each square in the grid with the colours P, Q, R and S, so that neighbouring squares always have different colours. (Squares which share the same corner point also count as neighbouring.) Some of the squares are already painted. In which colour(s) could the grey square be painted?
<image1>
Select only from the following 4 options:
A. only Q
C. only S
D. either R or S
E. it is not possible. | D | graph theory | A. only Q
C. only S
D. either R or S
E. it is not possible. |
1075 | deductive | MathVision/test_001075.png | Each area in the picture on the right should be coloured using one of the colours, red (R), green (G), blue (B) or orange (O). Areas which touch must be different colours. Which colour is the area marked $X$?
<image1>
Select only from the following 4 options:
B. blue
C. green
D. orange
E. The colour cannot definitely be determined. | A | logic | B. blue
C. green
D. orange
E. The colour cannot definitely be determined. |
1077 | spatial | MathVision/test_001077.png | The dark line halves the surface area of the dice shown on the right. Which drawing could represent the net of the die?
<image1>
<image2>
Select only from the following 4 options:
A
C
D
E | A | descriptive geometry | A
C
D
E |
1078 | spatial | MathVision/test_001078.png | Lina has placed two tiles on a square game board. Which one of the 5 counters shown, can she add, so that none of the remaining four counters can be placed anymore?
<image1>
<image2>
Select only from the following 4 options:
B
C
D
E | D | descriptive geometry | B
C
D
E |
1098 | spatial | MathVision/test_001098.png | The five shapes pictured were cut out of paper. Four of them can be folded to form a cube. For which shape is this not possible.
<image1>
Select only from the following 4 options:
B. Shape 2
C. Shape 3
D. Shape 4
E. Shape 5 | C | descriptive geometry | B. Shape 2
C. Shape 3
D. Shape 4
E. Shape 5 |
1100 | spatial | MathVision/test_001100.png | Johann stacked $1 \times 1$ cubes on the squares of a $4 \times 4$ grid. The diagram on the right shows the number of cubes that were stacked on top of each other above each square. What will Johann see if he looks from the back (hinten) at the tower?
<image1>
<image2>
Select only from the following 4 options:
A
C
D
E | C | descriptive geometry | A
C
D
E |
1116 | spatial | MathVision/test_001116.png | Four identical cubes (see diagram) were fitted together. If the resulting shape is viewed from the front you see a black circle (picture on the right). What will you see on the back of the shape?
<image1>
<image2>
Select only from the following 4 options:
A
B
D
E | A | descriptive geometry | A
B
D
E |
1119 | spatial | MathVision/test_001119.png | The word KANGAROO is written on the top of my umbrella. Which of the following pictures shows my umbrella?
<image1>
<image2>
Select only from the following 4 options:
A
C
D
E | E | descriptive geometry | A
C
D
E |
1120 | spatial | MathVision/test_001120.png | The diagram shows the net of a cube whose faces are numbered. Sascha adds the numbers that are on opposite faces of the cube. Which three results does he get?
<image1>
Select only from the following 4 options:
B. $4,5,12$
C. $5,6,10$
D. $5,7,9$
E. $5,8,8$ | A | descriptive geometry | B. $4,5,12$
C. $5,6,10$
D. $5,7,9$
E. $5,8,8$ |
1121 | spatial | MathVision/test_001121.png | The diagram shows the net of a three-sided prism. Which line of the diagram forms an edge of the prism together with line UV when the net is folded up?
<image1>
Select only from the following 4 options:
A. WV
B. XW
C. XY
E. RS | C | descriptive geometry | A. WV
B. XW
C. XY
E. RS |
1126 | deductive | MathVision/test_001126.png | Each side of each triangle in the diagram is painted either blue, green or red. Four of the sides are already painted. Which colour can the line marked "x" have, if each triangle must have all sides in different colours?
<image1>
Select only from the following 4 options:
A. only green
B. only red
C. only blue
D. either red or blue | A | logic | A. only green
B. only red
C. only blue
D. either red or blue |
1149 | Quantitative Reasoning | MathVision/test_001149.png | 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>
Select only from the following 4 options:
A. $\frac{3}{8}$
B. $\frac{1}{12}$
C. $\frac{5}{7}$
E. $\frac{7}{12}$ | D | arithmetic | A. $\frac{3}{8}$
B. $\frac{1}{12}$
C. $\frac{5}{7}$
E. $\frac{7}{12}$ |
1160 | spatial | MathVision/test_001160.png | 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>
Select only from the following 4 options:
A
B
C
D | C | descriptive geometry | A
B
C
D |
1177 | Quantitative Reasoning | MathVision/test_001177.png | Which cloud contains even numbers only?
<image1>
Select only from the following 4 options:
A
B
C
E | E | arithmetic | A
B
C
E |
1179 | spatial | MathVision/test_001179.png | 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>
Select only from the following 4 options:
B
C
D
E | D | descriptive geometry | B
C
D
E |
1180 | algorithmic | MathVision/test_001180.png | 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>
Select only from the following 4 options:
A
C
D
E | D | graph theory | A
C
D
E |
1191 | algorithmic | MathVision/test_001191.png | 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>
Select only from the following 4 options:
A. 5 and 8
B. 1 and 6
C. 2 and 7
E. 3 and 6 | A | graph theory | A. 5 and 8
B. 1 and 6
C. 2 and 7
E. 3 and 6 |
1197 | deductive | MathVision/test_001197.png | 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>
Select only from the following 4 options:
B. $21 \mathrm{~km}$
C. $29 \mathrm{~km}$
D. $41 \mathrm{~km}$
E. $52 \mathrm{~km}$ | D | logic | B. $21 \mathrm{~km}$
C. $29 \mathrm{~km}$
D. $41 \mathrm{~km}$
E. $52 \mathrm{~km}$ |
1198 | spatial | MathVision/test_001198.png | Which of the pictures below shows what you will see if you look from above the piece represented on the right?
<image1>
<image2>
Select only from the following 4 options:
A
B
C
E | C | descriptive geometry | A
B
C
E |
1201 | Quantitative Reasoning | MathVision/test_001201.png | 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>
Select only from the following 4 options:
A. $25 \mathrm{~cm}^{2}$
C. $36 \mathrm{~cm}^{2}$
D. $47 \mathrm{~cm}^{2}$
E. $49 \mathrm{~cm}^{2}$ | D | arithmetic | A. $25 \mathrm{~cm}^{2}$
C. $36 \mathrm{~cm}^{2}$
D. $47 \mathrm{~cm}^{2}$
E. $49 \mathrm{~cm}^{2}$ |
1210 | spatial | MathVision/test_001210.png | 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>
Select only from the following 4 options:
A
B
D
E | E | descriptive geometry | A
B
D
E |
1217 | deductive | MathVision/test_001217.png | 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>
Select only from the following 4 options:
A
B
C
E | E | logic | A
B
C
E |
1229 | deductive | MathVision/test_001229.png | There are 5 trees and 3 paths in a park as shown on the map. Another tree is planted so that there is an equal number of trees on both sides of each path. In
which section of the park will the new tree be planted?
<image1>
Select only from the following 4 options:
A
B
C
D | B | logic | A
B
C
D |
1273 | Quantitative Reasoning | MathVision/test_001273.png | In a square $2003 \times 2003$, the squares $1 \times 1$ on the diagonals are colored (like in the picture, where the square is $7 \times 7$). How many white squares are there?
<image1>
Select only from the following 4 options:
A. $2002^{2}$
C. $2001^{2}$
D. $2003 \times 2002$
E. $2003^{2}-2004$ | A | arithmetic | A. $2002^{2}$
C. $2001^{2}$
D. $2003 \times 2002$
E. $2003^{2}-2004$ |
1292 | Quantitative Reasoning | MathVision/test_001292.png | A flag consists of three stripes of equal width, which are divided into two, three and four equal parts, respectively. What fraction of the area of the flag is coloured grey?
<image1>
Select only from the following 4 options:
B. $\frac{2}{3}$
C. $\frac{3}{5}$
D. $\frac{4}{7}$
E. $\frac{5}{9}$ | E | arithmetic | B. $\frac{2}{3}$
C. $\frac{3}{5}$
D. $\frac{4}{7}$
E. $\frac{5}{9}$ |
1302 | deductive | MathVision/test_001302.png | 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>
Select only from the following 4 options:
A. GRGR
B. RGRG
C. GRRG
D. RGGR | A | logic | A. GRGR
B. RGRG
C. GRRG
D. RGGR |
1367 | Quantitative Reasoning | MathVision/test_001367.png | 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>
Select only from the following 4 options:
A. $0.80 €$
C. $2.80 €$
D. $3.20 €$
E. $80 €$ | C | arithmetic | A. $0.80 €$
C. $2.80 €$
D. $3.20 €$
E. $80 €$ |
1369 | spatial | MathVision/test_001369.png | 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>
Select only from the following 4 options:
A
C
D
E | E | descriptive geometry | A
C
D
E |
1412 | algorithmic | MathVision/test_001412.png | Three weights are randomly placed on each tray of a beam balance. The balance dips to the right hand side as shown on the picture. The masses of the weights are 101, 102, 103, 104, 105 and 106 grams. For how many percent of the possible distributions is the 106grams-weight on the right (heavier) side?
<image1>
Select only from the following 4 options:
A. $75 \%$
B. $80 \%$
D. $95 \%$
E. $100 \%$ | B | combinatorics | A. $75 \%$
B. $80 \%$
D. $95 \%$
E. $100 \%$ |
1423 | spatial | MathVision/test_001423.png | Seven little dice were removed from a $3 \times 3 \times 3$ die, as can be seen in the diagram. The remaining (completely symmetrical) figure is cut along a plane through the centre and perpendicular to one of the four space diagonals. What does the cross-section look like?
<image1>
<image2>
Select only from the following 4 options:
A
B
D
E | A | descriptive geometry | A
B
D
E |
1426 | Inductive Reasoning | MathVision/test_001426.png | Five identical measuring jugs are filled with water. Four of them contain exactly the same amount of water. Which measuring jug contains a different amount?
<image1>
Select only from the following 4 options:
A
B
C
D | B | statistics | A
B
C
D |
1446 | algorithmic | MathVision/test_001446.png | Julia puts the nine chips on the right in a box. She then takes one chip at a time, without looking, and notes down its digit, obtaining, at the end, a number of nine different digits. What is the probability that the number written by Julia is divisible by 45?
<image1>
Select only from the following 4 options:
A. $\frac{1}{9}$
B. $\frac{2}{9}$
C. $\frac{1}{3}$
D. $\frac{4}{9}$ | A | combinatorics | A. $\frac{1}{9}$
B. $\frac{2}{9}$
C. $\frac{1}{3}$
D. $\frac{4}{9}$ |
1451 | Inductive Reasoning | MathVision/test_001451.png | Jenny looks at her weather app that shows the predicted weather and maximum temperatures for the next five days. Which of the following represents the corresponding graph of maximum temperatures?
<image1>
<image2>
Select only from the following 4 options:
A
B
C
D | B | statistics | A
B
C
D |
1469 | Inductive Reasoning | MathVision/test_001469.png | Sonja's smartphone displays the diagram on the right. It shows how long she has worked with four different apps in the previous week. 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 could be the diagram for the current week?
<image1>
<image2>
Select only from the following 4 options:
B
C
D
E | C | statistics | B
C
D
E |
1498 | spatial | MathVision/test_001498.png | Leon has drawn a closed loop on the surface of a cuboid.
Which net cannot show his loop? <image1>
Select only from the following 4 options:
A
B
C
E | C | descriptive geometry | A
B
C
E |
1503 | spatial | MathVision/test_001503.png | The net on the right can be cut out and folded to make a cube. Which face will then be opposite the face marked $\mathbf{x}$ ? <image1>
Select only from the following 4 options:
A. a
C. c
D. d
E. e | E | descriptive geometry | A. a
C. c
D. d
E. e |
1515 | spatial | MathVision/test_001515.png | The diagram shows a net of a cube, with three dotted lines added. If you folded the net into a cube and then cut along the dotted lines you would have a hole in the cube. What would be the shape of the hole? <image1>
Select only from the following 4 options:
B. a rectangle, but not a square
C. a right-angled triangle
D. a square
E. a hexagon | A | descriptive geometry | B. a rectangle, but not a square
C. a right-angled triangle
D. a square
E. a hexagon |
1518 | Quantitative Reasoning | MathVision/test_001518.png | Alfonso the Ostrich has been training for the Head in the Sand Competition in the Animolympiad. He buried his head in the sand last week and pulled it out at 8.15 am on Monday to find he had reached a new personal record - he had been underground for 98 hours and 56 minutes. When did Alfonso bury his head in the sand? <image1>
Select only from the following 4 options:
A. On Thursday at 5.19 am
B. On Thursday at $5.41 \mathrm{am}$
D. On Friday at 5.19 am
E. On Friday at 11.11 am | A | arithmetic | A. On Thursday at 5.19 am
B. On Thursday at $5.41 \mathrm{am}$
D. On Friday at 5.19 am
E. On Friday at 11.11 am |
1526 | spatial | MathVision/test_001526.png | Which of the following cubes can be folded from the net on the right?
<image1>
<image2>
Select only from the following 4 options:
A
B
C
E | E | descriptive geometry | A
B
C
E |
1535 | deductive | MathVision/test_001535.png | If all the statements in the box are true, which of $\mathrm{A}, \mathrm{B}, \mathrm{C}$, $\mathrm{D}$ or $\mathrm{E}$ can be deduced? <image1>
Select only from the following 4 options:
A. It's red
B. It's a blue square
C. It's red and round
E. It's blue and round | E | logic | A. It's red
B. It's a blue square
C. It's red and round
E. It's blue and round |
1547 | spatial | MathVision/test_001547.png | Each object shown is made up of 7 cubes. Which of $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$ can be obtained by rotating $\mathrm{T}$ ?
<image1>
Select only from the following 4 options:
A. P and R
B. Q and S
C. only R
D. none of them | A | descriptive geometry | A. P and R
B. Q and S
C. only R
D. none of them |
1564 | deductive | MathVision/test_001564.png | In each of the squares in the grid, one of the letters $P, Q, R$ and $S$ must be entered in such a way that adjacent squares (whether connected by an edge or just a corner) do not contain the same letter. Some of the letters have already been entered as shown.
What are the possibilities for the letter in the shaded square?
<image1>
Select only from the following 4 options:
B. only $R$
C. only $S$
D. either $R$ or $S$, but no others
E. it is impossible to complete the grid | D | logic | B. only $R$
C. only $S$
D. either $R$ or $S$, but no others
E. it is impossible to complete the grid |
1582 | deductive | MathVision/test_001582.png | Each region in the figure is to be coloured with one of four colours: red $(\mathrm{R})$, green $(\mathrm{G})$, orange $(\mathrm{O})$ or yellow $(\mathrm{Y})$. The colours of only three regions are shown. Any two regions that touch must have different colours. <image1> The colour of the region $\mathrm{X}$ is:
Select only from the following 4 options:
B. orange
C. green
D. yellow
E. impossible to determine | A | logic | B. orange
C. green
D. yellow
E. impossible to determine |
1587 | algorithmic | MathVision/test_001587.png | Each of the nine paths in a park is $100 \mathrm{~m}$ long. Ann wants to go from $X$ to $Y$ without going along any path more than once. What is the length of the longest route she can choose? <image1>
Select only from the following 4 options:
A. $900 \mathrm{~m}$
B. $800 \mathrm{~m}$
C. $700 \mathrm{~m}$
D. $600 \mathrm{~m}$ | C | graph theory | A. $900 \mathrm{~m}$
B. $800 \mathrm{~m}$
C. $700 \mathrm{~m}$
D. $600 \mathrm{~m}$ |
1603 | spatial | MathVision/test_001603.png | John has made a building of unit cubes standing on a $4 \times 4$ grid. The diagram shows the number of cubes standing on each cell. When John looks horizontally at the building from behind, what does he see? <image1>
<image2>
Select only from the following 4 options:
A
C
D
E | C | descriptive geometry | A
C
D
E |
1618 | spatial | MathVision/test_001618.png | My umbrella has KANGAROO written on top as shown in the diagram. Which one of the following pictures also shows my umbrella?
<image1>
<image2>
Select only from the following 4 options:
B
C
D
E | E | descriptive geometry | B
C
D
E |
1623 | deductive | MathVision/test_001623.png | Luis wants to make a pattern by colouring the sides of the triangles shown in the diagram. He wants each triangle to have one red side, one green side and one blue side. Luis has already coloured some of the sides as shown. What colour can he use for the side marked $x$ ? <image1>
Select only from the following 4 options:
A. only green
B. only blue
D. either blue or red
E. The task is impossible | A | logic | A. only green
B. only blue
D. either blue or red
E. The task is impossible |
1638 | spatial | MathVision/test_001638.png | A $3 \times 3 \times 3$ cube is built from 15 black cubes and 12 white cubes. Five faces of the larger cube are shown.
<image1>
Which of the following is the sixth face of the larger cube?
<image2>
Select only from the following 4 options:
A
B
D
E | A | descriptive geometry | A
B
D
E |
1641 | Quantitative Reasoning | MathVision/test_001641.png | Adam the Ant started at the left-hand end of a pole and crawled $\frac{2}{3}$ of its length. Benny the Beetle started at the right-hand end of the same pole and crawled $\frac{3}{4}$ of its length. What fraction of the length of the pole are Adam and Benny now apart?
<image1>
Select only from the following 4 options:
B. $\frac{1}{12}$
C. $\frac{5}{7}$
D. $\frac{1}{2}$
E. $\frac{5}{12}$ | E | arithmetic | B. $\frac{1}{12}$
C. $\frac{5}{7}$
D. $\frac{1}{2}$
E. $\frac{5}{12}$ |
1663 | algorithmic | MathVision/test_001663.png | Which of the diagrams below cannot be drawn without lifting your pencil off the page and without drawing along the same line twice?
<image1>
Select only from the following 4 options:
A
C
D
E | D | graph theory | A
C
D
E |
1672 | algorithmic | MathVision/test_001672.png | Prab painted each of the eight circles in the diagram red, yellow or blue such that no two circles that are joined directly were painted the same colour. Which two circles must have been painted the same colour? <image1>
Select only from the following 4 options:
A. 5 and 8
B. 1 and 6
C. 2 and 7
E. 3 and 6 | A | graph theory | A. 5 and 8
B. 1 and 6
C. 2 and 7
E. 3 and 6 |
1696 | deductive | MathVision/test_001696.png | There are five big trees and three paths in a park. It has been decided to plant a sixth tree so that there are the same number of trees on either side of each path. In which region of the park should the sixth tree be planted? <image1>
Select only from the following 4 options:
A
B
C
E | B | logic | A
B
C
E |
1718 | algorithmic | MathVision/test_001718.png | In the diagram, five rectangles of the same size are shown with each side labelled with a number.
<image1>
These rectangles are placed in the positions I to $\mathrm{V}$ as shown so that the numbers on the sides that touch each other are equal.
<image2>
Which of the rectangles should be placed in position I?
Select only from the following 4 options:
B
C
D
E | C | combinatorics | B
C
D
E |
1754 | deductive | MathVision/test_001754.png | The diagram below shows five rectangles, each containing some of the letters $\mathrm{P}, \mathrm{R}, \mathrm{I}, \mathrm{S}$ and $\mathrm{M}$.
<image1>
Harry wants to cross out letters so that each rectangle contains only one letter and each rectangle contains a different letter. Which letter does he not cross out in rectangle 2?
Select only from the following 4 options:
A. P
B. R
C. I
D. S | B | logic | A. P
B. R
C. I
D. S |
1771 | algorithmic | MathVision/test_001771.png | Sid is colouring the cells in the grid using the four colours red, blue, yellow and green in such a way that any two cells that share a vertex are coloured differently. He has already coloured some of the cells as shown.
What colour will he use for the cell marked $X$ ?
<image1>
Select only from the following 4 options:
A. Red
B. Blue
D. Green
E. You can't be certain | A | graph theory | A. Red
B. Blue
D. Green
E. You can't be certain |
1773 | algorithmic | MathVision/test_001773.png | Andrew wants to write the letters of the word KANGAROO in the cells of a $2 \times 4$ grid such that each cell contains exactly one letter. He can write the first letter in any cell he chooses but each subsequent letter can only be written in a cell with at least one common vertex with the cell in which the previous letter was written. Which of the following arrangements of letters could he not produce in this way?
<image1>
Select only from the following 4 options:
A
B
D
E | D | combinatorics | A
B
D
E |
1780 | deductive | MathVision/test_001780.png | Claudette has eight dice, each with one of the letters $P, Q, R$ and $S$ written on all six faces. She builds the block shown in the diagram so that dice with faces which touch have different letters written on them.
What letter is written on the faces of the one dice which is not shown on the picture? <image1>
Select only from the following 4 options:
A. P
B. Q
C. R
D. S | B | logic | A. P
B. Q
C. R
D. S |
1786 | algorithmic | MathVision/test_001786.png | Joseph writes the numbers 1 to 12 in the circles so that the numbers in adjacent circles differ by either 1 or 2 . Which pair of numbers does he write in adjacent circles? <image1>
Select only from the following 4 options:
A. 3 and 4
C. 6 and 7
D. 8 and 9
E. 8 and 10 | E | combinatorics | A. 3 and 4
C. 6 and 7
D. 8 and 9
E. 8 and 10 |
1787 | deductive | MathVision/test_001787.png | Patricia painted some of the cells of a $4 \times 4$ grid. Carl counted how many red cells there were in each row and in each column and created a table to show his answers.
Which of the following tables could Carl have created?
<image1>
Select only from the following 4 options:
B
C
D
E | D | logic | B
C
D
E |
1795 | spatial | MathVision/test_001795.png | Christopher has made a building out of blocks. The grid on the right shows the number of blocks in each part of the building, when viewed from above. Which of the following gives the view you see when you look at Christopher's building from the front?
\begin{tabular}{|l|l|l|l|}
\hline 4 & 2 & 3 & 2 \\
\hline 3 & 3 & 1 & 2 \\
\hline 2 & 1 & 3 & 1 \\
\hline 1 & 2 & 1 & 2 \\
\hline \multicolumn{4}{|c|}{ front }
\end{tabular}
<image1>
Select only from the following 4 options:
B
C
D
E | E | descriptive geometry | B
C
D
E |
1826 | Quantitative Reasoning | MathVision/test_001826.png | The flag shown in the diagram consists of three stripes, each of equal height, which are divided into two, three and four equal parts, respectively. What fraction of the area of the flag is shaded? <image1>
Select only from the following 4 options:
A. $\frac{1}{2}$
B. $\frac{2}{3}$
D. $\frac{4}{7}$
E. $\frac{5}{9}$ | D | arithmetic | A. $\frac{1}{2}$
B. $\frac{2}{3}$
D. $\frac{4}{7}$
E. $\frac{5}{9}$ |
1834 | deductive | MathVision/test_001834.png | To complete the table, each cell must contain either 0 or 1 , and the total of each row and column must be 2 . What are the values of the entries $X$ and $Y$ ? <image1>
Select only from the following 4 options:
A. $X=0, Y=0$
C. $X=1, Y=0$
D. $X=1, Y=1$
E. It is impossible to complete. | A | logic | A. $X=0, Y=0$
C. $X=1, Y=0$
D. $X=1, Y=1$
E. It is impossible to complete. |
1841 | algorithmic | MathVision/test_001841.png | Five boxes contain cards as shown. Simon removes cards so that each box contains exactly one card, and the five cards remaining in the boxes can be used to spell his name. Which card remains in box 2 ?
<image1>
Select only from the following 4 options:
A. S
B. I
C. M
D. O | D | combinatorics | A. S
B. I
C. M
D. O |
1926 | algorithmic | MathVision/test_001926.png | On a balance scale, three different masses were put at random on each pan and the result is shown in the picture. The masses are of 101, 102, 103, 104, 105 and 106 grams. What is the probability that the 106 gram mass stands on the heavier pan?
<image1>
Select only from the following 4 options:
B. $80 \%$
C. $90 \%$
D. $95 \%$
E. $100 \%$ | B | combinatorics | B. $80 \%$
C. $90 \%$
D. $95 \%$
E. $100 \%$ |
1969 | Inductive Reasoning | MathVision/test_001969.png | On Nadya's smartphone, the diagram shows how much time she spent last week on four of her apps. This week she halved the time spent on two of these apps, but spent the same amount of time as the previous week on the other two apps.
<image1>
Which of the following could be the diagram for this week?
<image2>
Select only from the following 4 options:
A
B
D
E | E | statistics | A
B
D
E |
1977 | algorithmic | MathVision/test_001977.png | Cuthbert is going to make a cube with each face divided into four squares. Each square must have one shape drawn on it; either a cross, a triangle or a circle. Squares that share an edge must have different shapes on them. One possible cube is shown in the diagram. Which of the following combinations of crosses and triangles is possible on such a cube (with the other shapes being circles)?
<image1>
Select only from the following 4 options:
A. 6 crosses, 8 triangles
B. 7 crosses, 8 triangles
D. 7 crosses, 7 triangles
E. none of these are possible | E | combinatorics | A. 6 crosses, 8 triangles
B. 7 crosses, 8 triangles
D. 7 crosses, 7 triangles
E. none of these are possible |
1992 | algorithmic | MathVision/test_001992.png | Vumos wants to write the integers 1 to 9 in the nine boxes shown so that the sum of the integers in any three adjacent boxes is a multiple of 3 . In how many ways can he do this? <image1>
Select only from the following 4 options:
B. $6 \times 6 \times 6$
C. $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
D. $6 \times 5 \times 4 \times 3 \times 2 \times 1$
E. $9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$ | A | combinatorics | B. $6 \times 6 \times 6$
C. $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
D. $6 \times 5 \times 4 \times 3 \times 2 \times 1$
E. $9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$ |
2111 | algorithmic | MathVision/test_002111.png | There are $5$ yellow pegs, $4$ red pegs, $3$ green pegs, $2$ blue pegs, and $1$ orange peg on a triangular peg board. In how many ways can the pegs be placed so that no (horizontal) row or (vertical) column contains two pegs of the same color?
<image1>
Select only from the following 4 options:
A. $0$
B. $1$
D. $\frac{15!}{5!\cdot4!\cdot3!\cdot2!\cdot1!}$
E. $15!$ | B | combinatorics | A. $0$
B. $1$
D. $\frac{15!}{5!\cdot4!\cdot3!\cdot2!\cdot1!}$
E. $15!$ |
2131 | algorithmic | MathVision/test_002131.png | A set of three points is randomly chosen from the grid shown. Each three point set has the same probability of being chosen. What is the probability that the points lie on the same straight line?
<image1>
Select only from the following 4 options:
A. $\frac{1}{21}$
C. $\frac{2}{21}$
D. $\frac{1}{7}$
E. $\frac{2}{7}$ | C | combinatorics | A. $\frac{1}{21}$
C. $\frac{2}{21}$
D. $\frac{1}{7}$
E. $\frac{2}{7}$ |
2243 | algorithmic | MathVision/test_002243.png | Arjun and Beth play a game in which they take turns removing one brick or two adjacent bricks from one "wall" among a set of several walls of bricks, with gaps possibly creating new walls. The walls are one brick tall. For example, a set of walls of sizes $4$ and $2$ can be changed into any of the following by one move: $(3,2),(2,1,2),(4),(4,1),(2,2),$ or $(1,1,2)$.
<image1>
Arjun plays first, and the player who removes the last brick wins. For which starting configuration is there a strategy that guarantees a win for Beth?
Select only from the following 4 options:
A. (6,1,1)
B. (6,2,1)
C. (6,2,2)
E. (6,3,2) | B | combinatorics | A. (6,1,1)
B. (6,2,1)
C. (6,2,2)
E. (6,3,2) |
2295 | algorithmic | MathVision/test_002295.png | <image1>
Pascal's triangle is an array of positive integers(See figure), in which the first row is $1$, the second row is two $1$'s, each row begins and ends with $1$, and the $k^\text{th}$ number in any row when it is not $1$, is the sum of the $k^\text{th}$ and $(k-1)^\text{th}$ numbers in the immediately preceding row. The quotient of the number of numbers in the first $n$ rows which are not $1$'s and the number of $1$'s is
Select only from the following 4 options:
A. $\frac{n^2-n}{2n-1}$
B. $\frac{n^2-n}{4n-2}$
D. $\frac{n^2-3n+2}{4n-2}$
E. $\text{None of these}$ | D | combinatorics | A. $\frac{n^2-n}{2n-1}$
B. $\frac{n^2-n}{4n-2}$
D. $\frac{n^2-3n+2}{4n-2}$
E. $\text{None of these}$ |
2344 | algorithmic | MathVision/test_002344.png | The adjacent map is part of a city: the small rectangles are rocks, and the paths in between are streets. Each morning, a student walks from intersection A to intersection B, always walking along streets shown, and always going east or south. For variety, at each intersection where he has a choice, he chooses with probability $\frac{1}{2}$ whether to go east or south. Find the probability that through any given morning, he goes through $C$.
<image1>
Select only from the following 4 options:
B. $\frac{1}{2}$
C. $\frac{4}{7}$
D. $\frac{21}{32}$
E. $\frac{3}{4}$ | D | combinatorics | B. $\frac{1}{2}$
C. $\frac{4}{7}$
D. $\frac{21}{32}$
E. $\frac{3}{4}$ |
2374 | Inductive Reasoning | MathVision/test_002374.png | On each horizontal line in the figure below, the five large dots indicate the populations of cities $A$, $B$, $C$, $D$ and $E$ in the year indicated. Which city had the greatest percentage increase in population from 1970 to 1980?
<image1>
Select only from the following 4 options:
A
B
C
E | C | statistics | A
B
C
E |
2405 | algorithmic | MathVision/test_002405.png | Let $S$ be the set of points on the rays forming the sides of a $120^{\circ}$ angle, and let $P$ be a fixed point inside the angle on the angle bisector. Consider all distinct equilateral triangles $PQR$ with $Q$ and $R$ in $S$. (Points $Q$ and $R$ may be on the same ray, and switching the names of $Q$ and $R$ does not create a distinct triangle.) There are
<image1>
Select only from the following 4 options:
A. $\text{exactly 2 such triangles} \$
B. $\text{exactly 3 such triangles} \$
C. $\text{exactly 7 such triangles} \$
E. $\text{more than 15 such triangles}$ | E | combinatorics | A. $\text{exactly 2 such triangles} \$
B. $\text{exactly 3 such triangles} \$
C. $\text{exactly 7 such triangles} \$
E. $\text{more than 15 such triangles}$ |
2473 | spatial | MathVision/test_002473.png | There are 5 coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?
<image1>
Select only from the following 4 options:
A. $(C, A, E, D, B)$
B. $(C, A, D, E, B)$
D. $(C, E, A, D, B)$
E. $(C, E, D, A, B)$ | E | descriptive geometry | A. $(C, A, E, D, B)$
B. $(C, A, D, E, B)$
D. $(C, E, A, D, B)$
E. $(C, E, D, A, B)$ |
2505 | Inductive Reasoning | MathVision/test_002505.png | <image1>
The bar graph shows the grades in a mathematics class for the last grading period. If A, B, C, and D are satisfactory grades, what fraction of the grades shown in the graph are satisfactory?
Select only from the following 4 options:
B. $\frac{2}{3}$
C. $\frac{3}{4}$
D. $\frac{4}{5}$
E. $\frac{9}{10}$ | C | statistics | B. $\frac{2}{3}$
C. $\frac{3}{4}$
D. $\frac{4}{5}$
E. $\frac{9}{10}$ |
2509 | deductive | MathVision/test_002509.png | <image1>
Five cards are lying on a table as shown. Each card has a letter on one side and a whole number on the other side. Jane said, "If a vowel is on one side of any card, then an even number is on the other side." Mary showed Jane was wrong by turning over one card. Which card did Mary turn over?
Select only from the following 4 options:
A. $3$
C. $6$
D. $\text{P}$
E. $\text{Q}$ | A | logic | A. $3$
C. $6$
D. $\text{P}$
E. $\text{Q}$ |