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1449
[{"role": "user", "question": "A large rectangular plot is divided into two lots that are separated from each other by an $A B C D$ fence, as shown in the picture beside. The $A B, B C$ and $C D$ parts of this fence are parallel to the sides of the rectangle and have lengths of $30 \\mathrm{~m}$, $24 \\mathrm{~m}$ and ...
C
mcq
4
metric geometry - length
145
[{"role": "user", "question": "The kangaroo wants to visit the koala. On its way it is not allowed to jump through a square with water. Each arrow shows one jump on to a neighbouring field.\n<image1>\nWhich path is the kangaroo allowed to take?\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D",...
C
mcq
1
combinatorial geometry
1450
[{"role": "user", "question": "On the $8 \\times 8$ board beside, in how many ways can you place two chips, one green and one red, in different colored cells, so that the chips are not in the same row or in the same column of the board?\n<image1>", "hint": "", "options": {}, "choices": []}]
1536
numeric
4
combinatorics
1451
[{"role": "user", "question": "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?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E...
B
mcq
1
statistics
1452
[{"role": "user", "question": "A park is shaped like an equilateral triangle. A cat wants to walk along one of the three indicated paths (thicker lines) from the upper corner to the lower right corner. The lengths of the paths are $P, Q$ and $R$, as shown. Which of the following statements about the lengths of the path...
B
mcq
4
metric geometry - length
1453
[{"role": "user", "question": "Six rectangles are arranged as shown. The top left-hand rectangle has height $6 \\mathrm{~cm}$. The numbers within the rectangles indicate their areas in $\\mathrm{cm}^{2}$. What is the height of the bottom right-hand rectangle?\n<image1>", "hint": "", "options": {"A": "$4 \\mathrm{~cm}$"...
B
mcq
4
metric geometry - length
1454
[{"role": "user", "question": "Six congruent rhombuses, each of area $5 \\mathrm{~cm}^{2}$, form a star. The tips of the star are joined to draw a regular hexagon, as shown. What is the area of the hexagon?\n<image1>", "hint": "", "options": {"A": "$36 \\mathrm{~cm}^{2}$", "B": "$40 \\mathrm{~cm}^{2}$", "C": "$45 \\mat...
C
mcq
4
metric geometry - area
1455
[{"role": "user", "question": "A rectangle with perimeter $30 \\mathrm{~cm}$ is divided into four parts by a vertical line and a horizontal line. One of the parts is a square of area $9 \\mathrm{~cm}^{2}$, as shown in the figure. What is the perimeter of rectangle $A B C D$?\n<image1>", "hint": "", "options": {"A": "$1...
C
mcq
4
metric geometry - length
1456
[{"role": "user", "question": "Ally drew 3 triangles on a grid. Exactly 2 of them have the same area, exactly 2 of them are isosceles, and exactly 2 are right-angled triangles. 2 of the triangles are shown. Which could be the third one?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D...
D
mcq
3
combinatorial geometry
1457
[{"role": "user", "question": "The numbers from 1 to 6 are placed in the circles at the intersections of 3 rings. The position of number 6 is shown. The sums of the numbers on each ring are the same. What number is placed in the circle with the question mark?\n<image1>", "hint": "", "options": {}, "choices": []}]
1
numeric
5
logic
1458
[{"role": "user", "question": "The figure shows a semicircle with center $O$. Two of the angles are given. What is the size, in degrees, of the angle $\\alpha$?\n<image1>", "hint": "", "options": {"A": "$9^{\\circ}$", "B": "$11^{\\circ}$", "C": "$16^{\\circ}$", "D": "$17.5^{\\circ}$", "E": "$18^{\\circ}$"}, "choices": ...
A
mcq
2
metric geometry - angle
1459
[{"role": "user", "question": "Five cars participated in a race, starting in the order shown.\n<image1>. Whenever a car overtook another car, a point was awarded. The cars reached the finish line in the following order: <image2>. What is the smallest number of points in total that could have been awarded?", "hint": "",...
6
numeric
4
graph theory
146
[{"role": "user", "question": "Carl writes down a five-digit number.\nHe then places a shape on each of the five digits (see picture).\nHe places different shapes on different digits.\nHe places the same shape on the same digits.\nWhich number did Carl hide?\n<image1>", "hint": "", "options": {}, "choices": []}]
34426
numeric
3
logic
1460
[{"role": "user", "question": "A $3 \\times 3$ square initially has the number 0 in each of its cells. In one step all four numbers in one $2 \\times 2$ sub-square such as the shaded one, for example, are then increased by 1. This operation is repeated several times to obtain the arrangement on the right. Unfortunately...
16
numeric
5
logic
1461
[{"role": "user", "question": "What is the sum of the six marked angles in the picture?\n<image1>", "hint": "", "options": {"A": "$360^{\\circ}$", "B": "$900^{\\circ}$", "C": "$1080^{\\circ}$", "D": "$1120^{\\circ}$", "E": "$1440^{\\circ}$"}, "choices": []}]
C
mcq
2
metric geometry - angle
1462
[{"role": "user", "question": "There are eight boxes in the strip shown. Numbers in adjacent boxes have suma or $a+1$ as shown. The numbers in the first box and the eighth box are both 2021. What is the value of $a$?\n<image1>", "hint": "", "options": {}, "choices": []}]
4045
numeric
3
algebra
1463
[{"role": "user", "question": "An ant climbs from $C$ to $A$ on path $C A$ and descends from $A$ to $B$ on the stairs, as shown in the diagram. What is the ratio of the lengths of the ascending and descending paths?\n<image1>", "hint": "", "options": {"A": "1", "B": "$\\frac{1}{2}$", "C": "$\\frac{1}{3}$", "D": "$\\fra...
E
mcq
4
metric geometry - length
1464
[{"role": "user", "question": "In the $4 \\times 4$ table some cells must be painted black. The numbers next to and below the table show how many cells in that row or column must be black. In how many ways can this table be painted?\n<image1>", "hint": "", "options": {}, "choices": []}]
5
numeric
5
logic
1465
[{"role": "user", "question": "Karo has a box of matches with 30 matches. Using some of the matches she forms the number 2022. She has already formed the first two digits (see picture). How many matches will be left in the box when she has finished the number?\n<image1>", "hint": "", "options": {}, "choices": []}]
9
numeric
4
arithmetic
1466
[{"role": "user", "question": "Various symbols are drawn on a piece of paper (see picture). The teacher folds the left side along the vertical line to the right. How many symbols of the left side are now congruent on top of a symbol on the right side?\n<image1>", "hint": "", "options": {}, "choices": []}]
3
numeric
4
transformation geometry
1467
[{"role": "user", "question": "Karin places tables of size $2 \\times 1$ according to the number of participants in a meeting. The diagram shows the table arrangements from above for a small, a medium and a large meeting. How many tables are used in a large meeting?\n<image1>", "hint": "", "options": {}, "choices": []}...
12
numeric
3
algebra
1468
[{"role": "user", "question": "The midpoints of both longer sides of a rectangle are connected with the vertices (see diagram). Which fraction of the rectangle is shaded?\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{5}$", "B": "$\\frac{1}{4}$", "C": "$\\frac{2}{7}$", "D": "$\\frac{1}{3}$", "E": "$\\frac{2}{5}$"...
B
mcq
4
metric geometry - area
1469
[{"role": "user", "question": "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 f...
C
mcq
1
statistics
147
[{"role": "user", "question": "Katrin forms a path around each square. For that she uses stones like this\n<image1>\nHow many such stones does she need for a path around the square with side length 5?", "hint": "", "options": {}, "choices": []}]
12
numeric
1
combinatorial geometry
1470
[{"role": "user", "question": "In the multiplication grid displayed, each white cell should show the product of the numbers in the grey cells that are in the same row and column respectively. One number is already entered. The integer $x$ is bigger than the positive integer $y$. What is the value of $y$?\n<image1>", "h...
6
numeric
3
algebra
1471
[{"role": "user", "question": "Five squares and two right-angled triangles are placed as shown in the diagram. The numbers 3, 8 and 22 in the squares state the size of the area in $\\mathrm{m}^{2}$. How big is the area (in $\\mathrm{m}^{2}$ ) of the square with the question mark?\n<image1>", "hint": "", "options": {}, ...
17
numeric
4
metric geometry - area
1472
[{"role": "user", "question": "The diagram shows three big circles of equal size and four small circles. Each small circle touches two big circles and has radius 1. How big is the shaded area?\n<image1>", "hint": "", "options": {"A": "$\\pi$", "B": "$2 \\pi$", "C": "$3 \\pi$", "D": "$4 \\pi$", "E": "$6 \\pi$"}, "choice...
B
mcq
4
metric geometry - area
1473
[{"role": "user", "question": "A bee called Maja wants to hike from honeycomb $X$ to honeycomb $Y$. She can only move from one honeycomb to the neighbouring honeycomb if they share an edge. How many, different ways are there for Maja to go from $X$ to $Y$ if she has to step onto every one of the seven honeycombs exactl...
5
numeric
4
graph theory
1474
[{"role": "user", "question": "The rectangle $A B C D$ is made up of 12 congruent rectangles (see diagram). How big is the ratio $\\frac{A D}{D C}$?\n<image1>", "hint": "", "options": {"A": "$\\frac{8}{9}$", "B": "$\\frac{5}{6}$", "C": "$\\frac{7}{8}$", "D": "$\\frac{2}{3}$", "E": "$\\frac{9}{8}$"}, "choices": []}]
A
mcq
3
combinatorial geometry
1475
[{"role": "user", "question": "There are three paths running through our park in the city (see diagram). A tree is situated in the centre of the park. What is the minimum number of trees that have to be planted additionally so that there are the same number of trees on either side of each path?\n<image1>", "hint": "", ...
3
numeric
5
logic
1476
[{"role": "user", "question": "The diagram shows a square $P Q R S$ with side length 1. The point $U$ is the midpoint of the side $R S$ and the point $W$ is the midpoint of the square. The three line segments, $T W, U W$ and $V W$ split the square into three equally big areas. How long is the line segment $S V$?\n<imag...
E
mcq
4
metric geometry - length
1477
[{"role": "user", "question": "Veronika wears five rings as shown. How many, different ways are there for her to take off the rings one by one?\n<image1>", "hint": "", "options": {}, "choices": []}]
20
numeric
4
combinatorics
1478
[{"role": "user", "question": "One square is drawn inside each of the two congruent isosceles right-angled triangles. The area of square $P$ is 45 units. How many units is the area of square R?\n<image1>", "hint": "", "options": {}, "choices": []}]
40
numeric
4
metric geometry - area
1479
[{"role": "user", "question": "Twelve weights have integer masses of $1 \\mathrm{~g}, 2 \\mathrm{~g}, 3 \\mathrm{~g}, \\ldots, 11 \\mathrm{~g}$ and $12 \\mathrm{~g}$ respectively. A vendor divides those weights up into 3 groups of 4 weights each. The total mass of the first group is $41 \\mathrm{~g}$, the mass of the s...
C
mcq
3
algebra
148
[{"role": "user", "question": "Below you see five pieces of lawn. Which one has the smallest area of grass?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}]
A
mcq
1
combinatorial geometry
1480
[{"role": "user", "question": "The diagonals of the squares $A B C D$ and $E F G B$ are $7 \\mathrm{~cm}$ and $10 \\mathrm{~cm}$ long respectively (see diagram). The point $P$ is the point of intersection of the two diagonals of the square $A B C D$. How big is the area of the triangle $F P D$ (in $\\mathrm{cm}^{2}$)?\...
17.5
numeric
4
metric geometry - area
1481
[{"role": "user", "question": "Consider the five circles with midpoints $A, B, C, D$ and $E$ respectively, which touch each other as displayed in the diagram. The line segments, drawn in, connect the midpoints of adjacent circles. The distances between the midpoints are $A B=16, B C=14, C D=17, D E=13$ and $A E=14$ Whi...
A
mcq
4
metric geometry - length
1482
[{"role": "user", "question": "A hemispheric hole is carved into each face of a wooden cube with sides of length 2. All holes are equally sized, and their midpoints are in the centre of the faces of the cube. The holes are as big as possible so that each hemisphere touches each adjacent hemisphere in exactly one point....
C
mcq
2
solid geometry
1483
[{"role": "user", "question": "A dark disc with two holes is placed on the dial of a watch as shown in the diagram. The dark disc is now rotated so that the number 10 can be seen through one of the two holes. Which of the numbers could one see through the other hole now? <image1>", "hint": "", "options": {"A": "2 and 6...
A
mcq
4
transformation geometry
1484
[{"role": "user", "question": "On her way to school Maria first had to run to the underground, she exited from that after two stops and subsequently walked the rest of the way by foot all the way to school. Which of the following speed-time-diagrams best describes her journey to school?\n<image1>", "hint": "", "options...
D
mcq
5
analytic geometry
1485
[{"role": "user", "question": "A small square with side length $4 \\mathrm{~cm}$ is drawn within a big square with side length $10 \\mathrm{~cm}$; their sides are parallel to each other (see diagram). What percentage of the figure is shaded? <image1>", "hint": "", "options": {"A": "$25 \\%$", "B": "$30 \\%$", "C": "$40...
D
mcq
4
metric geometry - area
1486
[{"role": "user", "question": "The big rectangle shown is divided into 30 equally big squares. The perimeter of the area shaded in grey is $240 \\mathrm{~cm}$. How big is the area of the big rectangle? <image1>", "hint": "", "options": {"A": "$480 \\mathrm{~cm}^{2}$", "B": "$750 \\mathrm{~cm}^{2}$", "C": "$1080 \\mathr...
D
mcq
3
combinatorial geometry
1487
[{"role": "user", "question": "A straight wooden fence is made up of vertical beams stuck in the ground which are each connected to the next beam by 4 horizontal beams. The fence begins and ends with a vertical beam. Out of how many beams could such a fence be made? <image1>", "hint": "", "options": {"A": "95", "B": "9...
B
mcq
3
algebra
1488
[{"role": "user", "question": "The diagram shows three adjacent squares with side lengths $3 \\mathrm{~cm}, 5 \\mathrm{~cm}$ and $8 \\mathrm{~cm}$. How big is the area of the shaded in trapezium? <image1>", "hint": "", "options": {"A": "$13 \\mathrm{~cm}^{2}$", "B": "$\\frac{55}{4} \\mathrm{~cm}^{2}$", "C": "$\\frac{61...
B
mcq
4
metric geometry - area
1489
[{"role": "user", "question": "The points $M$ and $N$ are the midpoints of two sides of the big rectangle (see diagram). Which part of the area of the big rectangle is shaded? <image1>", "hint": "", "options": {"A": "$\\frac{1}{6}$", "B": "$\\frac{1}{5}$", "C": "$\\frac{1}{4}$", "D": "$\\frac{1}{3}$", "E": "$\\frac{1}{...
C
mcq
4
metric geometry - area
149
[{"role": "user", "question": "The numbers in the five circles around each house add up to 20 . Some numbers are missing.\n<image1>\nWhich number does the question mark stand for?", "hint": "", "options": {}, "choices": []}]
9
numeric
1
algebra
1490
[{"role": "user", "question": "The pentagon $A B C D E$ is split into four triangles that all have the same perimeter (see diagram). Triangle $A B C$ is equilateral and the triangles $A E F, D F E$ and $C D F$ are congruent isosceles triangles. How big is the ratio of the perimeter of the pentagon $A B C D E$ to the pe...
D
mcq
4
metric geometry - length
1491
[{"role": "user", "question": "A tower consists of blocks that are labelled from bottom to top with the numbers from 1 to 90 . Bob uses these blocks to build a new tower. For each step he takes the top three blocks from the old tower and places them on the new tower without changing their order (see diagram). How many ...
4
numeric
3
algebra
1492
[{"role": "user", "question": "A staircase has 2023 steps. Every third step is coloured in black. The first seven steps of this staircase can be fully seen in the diagram. Anita walks up the staircase and steps on each step exactly once. She can start with either the right or the left foot and then steps down alternate...
337
numeric
3
algebra
1493
[{"role": "user", "question": "A square with side length $30 \\mathrm{~cm}$ is split into 9 squares. The big square contains three circles with radii $5 \\mathrm{~cm}$ (bottom right), $4 \\mathrm{~cm}$ (top left) as well as $3 \\mathrm{~cm}$ (top right) as seen in the diagram. How many $\\mathrm{cm}^{2}$ are shaded in ...
500
numeric
4
metric geometry - area
1494
[{"role": "user", "question": "The numbers from 1 to 9 should be distributed among the 9 squares in the diagram according to the following rules: <image1> There should be one number in each square. The sum of three adjacent numbers is always a multiple of 3 . The numbers 3 and 1 are already placed. How many ways are th...
24
numeric
4
combinatorics
1495
[{"role": "user", "question": "How many different ways are there to read the word BANANA in the following table if we can only cross to a field that shares an edge with the current field and we can use fields several times? <image1>", "hint": "", "options": {}, "choices": []}]
128
numeric
4
graph theory
1496
[{"role": "user", "question": "Seven pairwise different single-digit numbers are distributed among the circles shown so that the product of the three numbers that are connected by a straight line is the same in all three cases. Which number is written in the circle with the question mark? <image1>", "hint": "", "option...
2
numeric
5
logic
1497
[{"role": "user", "question": "Consider the two touching semicircles with radius 1 and their diameters $A B$ and $C D$ respectively that are parallel to each other. The extensions of the two diameters are also tangents to the respective other semicircle (see diagram). How big is the square of the length $A D$ ? <image1...
B
mcq
4
metric geometry - length
1498
[{"role": "user", "question": "Leon has drawn a closed loop on the surface of a cuboid.\nWhich net cannot show his loop? <image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}]
C
mcq
3
descriptive geometry
1499
[{"role": "user", "question": "The diagram shows the map of a big park. The park is split into several sections and the number in each section states its perimeter in $\\mathrm{km}$. How big is the perimeter of the entire park in $\\mathrm{km}$ ? <image1>", "hint": "", "options": {}, "choices": []}]
26
numeric
4
metric geometry - length
15
[{"role": "user", "question": "Emily celebrated her birthday on Thursday, and her sister Liepa 8 days earlier. Which weekday was that?\n<image1>", "hint": "", "options": {"A": "Wednesday", "B": "Thursday", "C": "Friday", "D": "Tuesday", "E": "Sunday"}, "choices": []}]
A
mcq
2
arithmetic
150
[{"role": "user", "question": "Dino walks from the entrance to the exit. He is only allowed to go through each room once. The rooms have numbers (see diagram). Dino adds up all the numbers of the rooms he walks through.\n<image1>\nWhat is the biggest result he can get this way?", "hint": "", "options": {}, "choices": [...
34
numeric
2
arithmetic
1500
[{"role": "user", "question": "This piece of paper was folded in half twice, and then had two equilateral triangles cut out of it. Which diagram shows how the paper will look when it is unfolded again? <image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}]
C
mcq
3
transformation geometry
1501
[{"role": "user", "question": "For a hexagon (with six sides like these) the greatest possible number of interior right-angles is:\n<image1>", "hint": "", "options": {}, "choices": []}]
5
numeric
4
combinatorial geometry
1502
[{"role": "user", "question": "There used to be 5 parrots in my cage. Their average value was $€ 6000$. One day while I was cleaning out the cage the most beautiful parrot flew away. The average value of the remaining four parrots was $€ 5000$. What was the value of the parrot that escaped? <image1>", "hint": "", "opti...
E
mcq
4
algebra
1503
[{"role": "user", "question": "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>", "hint": "", "options": {"A": "a", "B": "b", "C": "c", "D": "d", "E": "e"}, "choices": []}]
E
mcq
4
descriptive geometry
1504
[{"role": "user", "question": "A transparent square sheet of film lies on a table. The letter $\\mathbf{Y}$ is drawn (like this) on the sheet. We turn the sheet clockwise through $90^{\\circ}$, then turn it over what is now the left edge of the sheet, and then turn it through $180^{\\circ}$. Which figure can we now see...
A
mcq
3
transformation geometry
1505
[{"role": "user", "question": "Jeffrey fires three arrows at each of four archery targets. He scores 29 points on the first target, 43 on the second and 47 on the third. How many points does Jeffrey score on the fourth target? <image1>", "hint": "", "options": {}, "choices": []}]
36
numeric
4
algebra
1506
[{"role": "user", "question": "Two squares of the same size, and with their edges parallel, cover a circle with a radius of $3 \\mathrm{~cm}$, as shown. In square centimetres, what is the total shaded area? <image1>", "hint": "", "options": {"A": "$8(\\pi-1)$", "B": "$6(2 \\pi-1)$", "C": "$(9 \\pi-25)$", "D": "$9(\\pi-...
D
mcq
3
metric geometry - area
1507
[{"role": "user", "question": "A cuboid has been built using 3 shapes (not necessarily different) each made from 4 little cubes as shown. The shape shaded black is completely visible, but both of the others are only partially visible. Which of the following shapes is the unshaded one? <image1>\n<image2>", "hint": "", "...
A
mcq
4
combinatorial geometry
1508
[{"role": "user", "question": "In a rectangle $A B C D$, the points $P, Q, R$ and $S$ are the midpoints of sides $A B, B C, C D$ and $A D$ respectively, and $T$ is the midpoint of the line $R S$. What fraction of the area of $A B C D$ is the triangle $P Q T$ ? <image1>", "hint": "", "options": {"A": "$\\frac{5}{16}$", ...
B
mcq
3
metric geometry - area
1509
[{"role": "user", "question": "Carl tries to divide the large shape of squares into smaller pieces using only copies of the T-piece and the F-piece shown on the right. (Pieces may be turned over or around.) What is the smallest possible number of the T-pieces that he can achieve? <image1>", "hint": "", "options": {}, "...
2
numeric
4
combinatorial geometry
151
[{"role": "user", "question": "Out of how many circles is the beaver made of?\n<image1>", "hint": "", "options": {}, "choices": []}]
8
numeric
1
counting
1510
[{"role": "user", "question": "In the diagram the large square is divided into 25 smaller squares. Adding up the sizes of the five angles $X P Y, X Q Y, X R Y, X S Y$ and $X T Y$, what total is obtained? <image1>", "hint": "", "options": {"A": "$30^{\\circ}$", "B": "$45^{\\circ}$", "C": "$60^{\\circ}$", "D": "$75^{\\ci...
B
mcq
4
combinatorial geometry
1511
[{"role": "user", "question": "The diagram shows a spiral of isosceles triangles. The largest angle in each of the triangles is $100^{\\circ}$. The grey triangle is number 0 . Each of the following triangles (numbered 1, 2, 3, ...) join by one edge to the previous one, as shown. As you can see triangle 3 only partially...
18
numeric
3
transformation geometry
1512
[{"role": "user", "question": "In triangle $ABC, AB=AC, AE=AD$ and angle $BAD=30^{\\circ}$. What is the size of angle $CDE$ ? <image1>", "hint": "", "options": {"A": "$10^{\\circ}$", "B": "$15^{\\circ}$", "C": "$20^{\\circ}$", "D": "$25^{\\circ}$", "E": "$30^{\\circ}$"}, "choices": []}]
B
mcq
5
metric geometry - angle
1513
[{"role": "user", "question": "In order to get 50 in the last box of the following chain, what positive number do you have to start with?\n<image1>", "hint": "", "options": {}, "choices": []}]
42
numeric
4
algebra
1514
[{"role": "user", "question": "Roo has 16 cards: 4 spades ( $(\\boldsymbol{*}), 4$ clubs ( $*$ ), 4 diamonds ( $\\bullet$ ) and 4 hearts $(\\boldsymbol{v})$. He wants to place them in the square shown, so that every row and every column has exactly one card of each suit. The diagram shows how Roo started. How many of t...
2
numeric
4
logic
1515
[{"role": "user", "question": "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>", "hint": "", "options": {"A": "an equilateral triangle", "B": "a rectan...
A
mcq
4
descriptive geometry
1516
[{"role": "user", "question": "A chain is made from circular links, with external radius $3 \\mathrm{~cm}$ and internal radius $2 \\mathrm{~cm}$, as shown in the diagram. The length of the chain is $1.7 \\mathrm{~m}$.\n<image1>\nHow many rings are used?", "hint": "", "options": {}, "choices": []}]
42
numeric
5
arithmetic
1517
[{"role": "user", "question": "The diagram shows a square $A B C D$ and two semicircles with diameters $A B$ and $A D$.\n<image1>\nIf $A B=2$, what is the area of the shaded region?", "hint": "", "options": {}, "choices": []}]
2
numeric
3
metric geometry - area
1518
[{"role": "user", "question": "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 Alfo...
A
mcq
5
arithmetic
1519
[{"role": "user", "question": "Boris has a big box of building bricks. Each brick is $1 \\mathrm{~cm}$ long, $2 \\mathrm{~cm}$ wide and $3 \\mathrm{~cm}$ high. What is the smallest number of bricks he would need to build a cube? <image1>", "hint": "", "options": {}, "choices": []}]
36
numeric
4
combinatorial geometry
152
[{"role": "user", "question": "The picture shows 5 cubes from the front. What do they look like from above?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}]
B
mcq
2
descriptive geometry
1520
[{"role": "user", "question": "In a square with sides of length $6 \\mathrm{~cm}$ the points $A$ and $B$ are on one of the axes of symmetry, as shown. The shaded area is equal to each of the two unshaded areas.\n<image1>\nWhat is the length of $A B$ ?", "hint": "", "options": {"A": "$3.6 \\mathrm{~cm}$", "B": "$3.8 \\m...
C
mcq
2
metric geometry - length
1521
[{"role": "user", "question": "Consecutive numbers have been entered diagonally criss-crossing the square on the right. Which of the following numbers could $x$ not be? <image1>", "hint": "", "options": {"A": "128", "B": "256", "C": "81", "D": "121", "E": "400"}, "choices": []}]
A
mcq
4
algebra
1522
[{"role": "user", "question": "In the diagram on the right, the triangle is equilateral.\n<image1>\nWhat is the area of the large circle divided by the area of the small circle?", "hint": "", "options": {}, "choices": []}]
16
numeric
3
metric geometry - area
1523
[{"role": "user", "question": "In the diagram, $A B C D$ is a parallelogram. If $A A_{1}=4 \\mathrm{~cm}, D D_{1}=5 \\mathrm{~cm}$ and $C C_{1}=7 \\mathrm{~cm}$, what is the length of $B B_{1}$ ? <image1>", "hint": "", "options": {"A": "$9 \\mathrm{~cm}$", "B": "$11 \\mathrm{~cm}$", "C": "$12 \\mathrm{~cm}$", "D": "$16...
D
mcq
2
metric geometry - length
1524
[{"role": "user", "question": "The diagram shows a cube with edges of length $12 \\mathrm{~cm}$. An ant crawls from the point $P$ to the point $Q$ along the route shown. What is the length of the ant's path? <image1>", "hint": "", "options": {"A": "$40 \\mathrm{~cm}$", "B": "$48 \\mathrm{~cm}$", "C": "$50 \\mathrm{~cm}...
D
mcq
4
solid geometry
1525
[{"role": "user", "question": "The diagram shows the ground plan of a room. Adjoining walls are perpendicular to each other. The letters $a$ and $b$ on the plan show the lengths of some of the walls. What is the area of the room? <image1>", "hint": "", "options": {"A": "$3 a b+a^{2}$", "B": "$8 a+2 b$", "C": "$3 a b-a^...
E
mcq
3
metric geometry - area
1526
[{"role": "user", "question": "Which of the following cubes can be folded from the net on the right?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}]
E
mcq
4
descriptive geometry
1527
[{"role": "user", "question": "The diagram shows an equilateral triangle and a regular pentagon. What is the value of $x$ ? <image1>", "hint": "", "options": {}, "choices": []}]
132
numeric
5
metric geometry - angle
1528
[{"role": "user", "question": "The diagram shows a length of string wound over and under $n$ equal circles. The sum of the diameters of the circles is $d \\mathrm{~cm}$. What is the length of the string in $\\mathrm{cm}$ ?\n<image1>", "hint": "", "options": {"A": "$\\frac{1}{2} \\pi d$", "B": "$\\pi d n$", "C": "$2 \\p...
A
mcq
2
metric geometry - length
1529
[{"role": "user", "question": "Two rectangles $A B C D$ and $D B E F$ are shown in the diagram. What is the area of the rectangle $D B E F$ ? <image1>", "hint": "", "options": {"A": "$10 \\mathrm{~cm}^{2}$", "B": "$12 \\mathrm{~cm}^{2}$", "C": "$13 \\mathrm{~cm}^{2}$", "D": "$14 \\mathrm{~cm}^{2}$", "E": "$16 \\mathrm{...
B
mcq
3
metric geometry - area
153
[{"role": "user", "question": "Each bowl has 4 balls. Add up the numbers on the balls. In which bowl is the result biggest?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}]
A
mcq
2
arithmetic
1530
[{"role": "user", "question": "Five straight lines intersect at a common point and five triangles are constructed as shown. What is the total of the 10 angles marked on the diagram? <image1>", "hint": "", "options": {"A": "$300^{\\circ}$", "B": "$450^{\\circ}$", "C": "$360^{\\circ}$", "D": "$600^{\\circ}$", "E": "$720^...
E
mcq
5
metric geometry - angle
1531
[{"role": "user", "question": "Gregor's computer is tracing out a path in the first quadrant as shown in the diagram. In the first second the computer draws the line from the origin to $(1,0)$ and after that it continues to follow the directions indicated in the diagram at a speed of 1 unit length per second.\nWhich po...
A
mcq
4
algebra
1532
[{"role": "user", "question": "Let $a$ and $b$ be the lengths of the two shorter sides of the right-angled triangle shown in the diagram. The longest side, $D$, is the diameter of the large circle and $d$ is the diameter of the small circle, which touches all three sides of the triangle.\nWhich one of the following exp...
A
mcq
2
metric geometry - length
1533
[{"role": "user", "question": "Which of the following is a net for the cube with two holes shown alongside?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}]
C
mcq
4
solid geometry
1534
[{"role": "user", "question": "The solid shown on the right is made from two cubes. The small cube with edges $1 \\mathrm{~cm}$ long sits on top of a bigger cube with edges $3 \\mathrm{~cm}$ long. What is the surface area of the whole solid? <image1>", "hint": "", "options": {"A": "$56 \\mathrm{~cm}^{2}$", "B": "$58 \\...
B
mcq
4
solid geometry
1535
[{"role": "user", "question": "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>", "hint": "", "options": {"A": "It's red", "B": "It's a blue square", "C": "It's red and round", "D": "It's yellow and round", "E": "It's bl...
E
mcq
4
logic
1536
[{"role": "user", "question": "The rectangle shown in the diagram on the right is divided into 7 squares. The sides of the grey squares on the right are all $8 \\mathrm{~cm}$ long. What is the length in $\\mathrm{cm}$ of the side of the black square? <image1>", "hint": "", "options": {}, "choices": []}]
18
numeric
2
metric geometry - length
1537
[{"role": "user", "question": "Max and Moritz have drawn out a $5 \\times 5$ grid on the playground, together with three obstacles. They want to walk from $P$ to $Q$ using the shortest route, avoiding the obstacles and always crossing a common edge to go from the centre of one square to the centre of the next. How many...
12
numeric
3
graph theory
1538
[{"role": "user", "question": "Belinda is making patterns using identical matchsticks. The $1 \\times 1,2 \\times 2$ and $3 \\times 3$ patterns are shown on the right. How many matchsticks should Belinda add to the $30 \\times 30$ pattern in order to make the $31 \\times 31$ pattern? <image1>", "hint": "", "options": {...
124
numeric
4
algebra