id stringlengths 1 4 | media images listlengths 1 1 | messages stringlengths 84 1.58k | answer stringclasses 371
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|---|---|---|---|---|---|---|
1629 | [{"role": "user", "question": "What is the total area in $\\mathrm{cm}^{2}$ of the shaded region? <image1>", "hint": "", "options": {}, "choices": []}] | 100 | numeric | 3 | metric geometry - area | |
163 | [{"role": "user", "question": "Maria has a total of 19 apples in 3 bags. She takes the same amount of apples from each bag. Then there are 3, 4 and 6 apples in the bags.\n<image1>\nHow many apples did Maria take from each bag?", "hint": "", "options": {}, "choices": []}] | 2 | numeric | 1 | algebra | |
1630 | [{"role": "user", "question": "Four towns $P, Q, R$ and $S$ are connected by roads, as shown. A race uses each road exactly once. The race starts at $S$ and finishes at $Q$. How many possible routes are there for the race? <image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 2 | combinatorics | |
1631 | [{"role": "user", "question": "Three equilateral triangles are cut from the corners of a large equilateral triangle to form an irregular hexagon, as shown in the diagram.\nThe perimeter of the large equilateral triangle is $60 \\mathrm{~cm}$. The perimeter of the irregular hexagon is $40 \\mathrm{~cm}$. What is the sum... | A | mcq | 2 | metric geometry - length | |
1632 | [{"role": "user", "question": "A $3 \\mathrm{~cm}$ wide strip is grey on one side and white on the other. Maria folds the strip, so that it fits inside a rectangle of length $27 \\mathrm{~cm}$, as shown. The grey trapeziums are identical. What is the length of the original strip?\n<image1>", "hint": "", "options": {"A"... | D | mcq | 3 | transformation geometry | |
1633 | [{"role": "user", "question": "Seven standard dice are glued together to make the solid shown. The pairs of faces of the dice that are glued together have the same number of dots on them. How many dots are on the surface of the solid? <image1>", "hint": "", "options": {}, "choices": []}] | 105 | numeric | 4 | solid geometry | |
1634 | [{"role": "user", "question": "Inside a square of area $36 \\mathrm{~cm}^{2}$, there are shaded regions as shown. The total shaded area is $27 \\mathrm{~cm}^{2}$. What is the value of $p+q+r+s$ ? <image1>", "hint": "", "options": {"A": "$4 \\mathrm{~cm}$", "B": "$6 \\mathrm{~cm}$", "C": "$8 \\mathrm{~cm}$", "D": "$9 \\... | D | mcq | 2 | metric geometry - length | |
1635 | [{"role": "user", "question": "The cube shown is divided into 64 small cubes. Exactly one of the cubes is grey, as shown in the diagram. Two cubes are said to be 'neighbours' if they have a common face.\nOn the first day, the white neighbours of the grey cube are changed to grey. On the second day, the white neighbours... | 17 | numeric | 4 | solid geometry | |
1636 | [{"role": "user", "question": "The diagram shows a pentagon. The lengths of the sides of the pentagon are given in the diagram.\nSepideh draws five circles with centres $A, B, C, D$ and $E$ such that the two circles with centres at the ends of a side of the pentagon touch on that side. Which point is the centre of the ... | A | mcq | 2 | metric geometry - length | |
1637 | [{"role": "user", "question": "Katie writes a different positive integer on the top face of each of the fourteen cubes in the pyramid shown.\nThe sum of the nine integers written on the cubes in the bottom layer is 50. The integer written on each of the cubes in the middle and top layers of the pyramid is equal to the ... | 118 | numeric | 4 | algebra | |
1638 | [{"role": "user", "question": "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.\n<image1>\nWhich of the following is the sixth face of the larger cube?\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices"... | A | mcq | 4 | descriptive geometry | |
1639 | [{"role": "user", "question": "The diagram shows two rectangles whose corresponding sides are parallel as shown. What is the difference between the lengths of the perimeters of the two rectangles? <image1>", "hint": "", "options": {"A": "$12 \\mathrm{~m}$", "B": "$16 \\mathrm{~m}$", "C": "$20 \\mathrm{~m}$", "D": "$22 ... | E | mcq | 2 | metric geometry - length | |
164 | [{"role": "user", "question": "According to the rule given in the left picture below, we construct a numerical triangle with an integer number greater than 1 in each cell. Which of the numbers given in the answers cannot appear in the shaded cell?\n<image1>", "hint": "", "options": {"A": "154", "B": "100", "C": "90", "... | A | mcq | 5 | algebra | |
1640 | [{"role": "user", "question": "The diagram shows four overlapping hearts. The areas of the hearts are $1 \\mathrm{~cm}^{2}, 4 \\mathrm{~cm}^{2}, 9 \\mathrm{~cm}^{2}$ and $16 \\mathrm{~cm}^{2}$. What is the total shaded area? <image1>", "hint": "", "options": {"A": "$9 \\mathrm{~cm}^{2}$", "B": "$10 \\mathrm{~cm}^{2}$",... | B | mcq | 3 | metric geometry - area | |
1641 | [{"role": "user", "question": "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?\n<image1>", "hint":... | E | mcq | 5 | arithmetic | |
1642 | [{"role": "user", "question": "Ellie wants to write a number in each box of the diagram shown. She has already written in two of the numbers. She wants the sum of all the numbers to be 35, the sum of the numbers in the first three boxes to be 22, and the sum of the numbers in the last three boxes to be 25. <image1> Wha... | 63 | numeric | 4 | algebra | |
1643 | [{"role": "user", "question": "Two segments, each $1 \\mathrm{~cm}$ long, are marked on opposite sides of a square of side $8 \\mathrm{~cm}$. The ends of the segments are joined as shown in the diagram. What is the total shaded area? <image1>", "hint": "", "options": {"A": "$2 \\mathrm{~cm}^{2}$", "B": "$4 \\mathrm{~cm... | B | mcq | 3 | metric geometry - area | |
1644 | [{"role": "user", "question": "Ella wants to write a number into each cell of a $3 \\times 3$ grid so that the sum of the numbers in any two cells that share an edge is the same. She has already written two numbers, as shown in the diagram.\nWhen Ella has completed the grid, what will be the sum of all the\n<image1>\nn... | 22 | numeric | 4 | logic | |
1645 | [{"role": "user", "question": "Ten kangaroos stood in a line as shown in the diagram.\n<image1>\nAt a particular moment, two kangaroos standing nose-to-nose exchanged places by jumping past each other. Each of the two kangaroos involved in an exchange continued to face the same way as it did before the exchange. This w... | 18 | numeric | 3 | counting | |
1646 | [{"role": "user", "question": "Anastasia's tablecloth has a regular pattern, as shown in the diagram. What percentage of her tablecloth is black? <image1>", "hint": "", "options": {}, "choices": []}] | 32 | numeric | 3 | metric geometry - area | |
1647 | [{"role": "user", "question": "Stan had 125 small cubes. He glued some of them together to form a large cube with nine tunnels, each perpendicular to two opposite faces and passing through the cube, as shown in the diagram.\nHow many of the small cubes did he not use? <image1>", "hint": "", "options": {}, "choices": []... | 39 | numeric | 4 | solid geometry | |
1648 | [{"role": "user", "question": "Ellen wants to colour some of the cells of a $4 \\times 4$ grid. She wants to do this so that each coloured cell shares at least one side with an uncoloured cell and each uncoloured cell shares at least one side with a coloured cell.\nWhat is the largest number of cells she can colour?\n<... | 12 | numeric | 3 | graph theory | |
1649 | [{"role": "user", "question": "The diagram shows a parallelogram $W X Y Z$ with area $S$. The diagonals of the parallelogram meet at the point $O$. The point $M$ is on the edge $Z Y$. The lines $W M$ and $Z X$ meet at $N$. The lines $M X$ and $W Y$ meet at $P$. The sum of the areas of triangles $W N Z$ and $X Y P$ is $... | D | mcq | 3 | metric geometry - area | |
165 | [{"role": "user", "question": "Let $A B C$ be a triangle with area 30. Let $D$ be any point in its interior and let $e, f$ and $g$ denote the distances from $D$ to the sides of the triangle. What is the value of the expression $5 e+12 f+13 g$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 60 | numeric | 5 | metric geometry - length | |
1650 | [{"role": "user", "question": "The faces of a cube are painted black, white or grey. Each face is only painted one colour and opposite faces are painted the same colour. Which of the following is a possible net for the cube?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices... | B | mcq | 4 | solid geometry | |
1651 | [{"role": "user", "question": "The large rectangle shown is made up of nine identical rectangles whose longest sides are $10 \\mathrm{~cm}$ long. What is the perimeter of the large rectangle? <image1>", "hint": "", "options": {"A": "$40 \\mathrm{~cm}$", "B": "$48 \\mathrm{~cm}$", "C": "$76 \\mathrm{~cm}$", "D": "$81 \\... | C | mcq | 4 | combinatorial geometry | |
1652 | [{"role": "user", "question": "The diagram shows a rectangle of size $7 \\mathrm{~cm} \\times 11 \\mathrm{~cm}$ containing two circles that each touch three of the sides of the rectangle. What is the distance between the centres of the two circles?\n<image1>", "hint": "", "options": {"A": "$2 \\mathrm{~cm}$", "B": "$2.... | E | mcq | 2 | metric geometry - length | |
1653 | [{"role": "user", "question": "Square $A B C D$ has sides of length $3 \\mathrm{~cm}$. The points $M$ and $N$ lie on $A D$ and $A B$ so that $C M$ and $C N$ split the square into three pieces of the same area. What is the length of $D M$ ? <image1>", "hint": "", "options": {"A": "$0.5 \\mathrm{~cm}$", "B": "$1 \\mathrm... | D | mcq | 2 | metric geometry - length | |
1654 | [{"role": "user", "question": "Martha multiplied two 2-digit numbers correctly on a piece of paper. Then she scribbled out three digits as shown.\nWhat is the sum of the three digits she scribbled out?\n<image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 4 | algebra | |
1655 | [{"role": "user", "question": "Valeriu draws a zig-zag line inside a rectangle, creating angles of $10^{\\circ}, 14^{\\circ}, 33^{\\circ}$ and $26^{\\circ}$ as shown. What is the size of the angle marked $\\theta$ ? <image1>", "hint": "", "options": {"A": "$11^{\\circ}$", "B": "$12^{\\circ}$", "C": "$16^{\\circ}$", "D"... | A | mcq | 5 | metric geometry - angle | |
1656 | [{"role": "user", "question": "James wrote a different integer from 1 to 9 in each cell of a table. He then calculated the sum of the integers in each of the rows and in each of the columns of the table. Five of his answers were 12, 13, 15, 16 and 17, in some order. What was his sixth answer? <image1>", "hint": "", "op... | 17 | numeric | 4 | logic | |
1657 | [{"role": "user", "question": "The diagram shows a net of an unfolded rectangular box. What is the volume of the box (in $\\mathrm{cm}^{3}$ )? <image1>", "hint": "", "options": {}, "choices": []}] | 80 | numeric | 4 | solid geometry | |
1658 | [{"role": "user", "question": "Ruth and Sarah decide to have a race. Ruth runs around the perimeter of the pool shown in the diagram while Sarah swims lengths of the pool.\nRuth runs three times as fast as Sarah swims. Sarah swims six lengths of the pool in the same time Ruth runs around the pool five times. How wide i... | B | mcq | 2 | metric geometry - length | |
1659 | [{"role": "user", "question": "Freda's flying club designed a flag of a flying dove on a square grid as shown.\nThe area of the dove is $192 \\mathrm{~cm}^{2}$. All parts of the perimeter of the dove are either quarter-circles or straight lines. What are the dimensions of the flag?\n<image1>", "hint": "", "options": {"... | D | mcq | 4 | combinatorial geometry | |
166 | [{"role": "user", "question": "The diagram shows two squares: one has a side with a length of 2 and the other (abut on the first square) has a side with a length of 1. What is the area of the shaded zone?\n<image1>", "hint": "", "options": {}, "choices": []}] | 1 | numeric | 5 | metric geometry - area | |
1660 | [{"role": "user", "question": "Dominoes are said to be arranged correctly if, for each pair of adjacent dominoes, the numbers of spots on the adjacent ends are equal. Paul laid six dominoes in a line as shown in the diagram.\n<image1>\nHe can make a move either by swapping the position of any two dominoes (without rota... | 3 | numeric | 2 | combinatorics | |
1661 | [{"role": "user", "question": "Wendy wants to write a number in every cell on the border of a table.\nIn each cell, the number she writes is equal to the sum of the two numbers in the cells with which this cell shares an edge. Two of the numbers are given in the diagram.\nWhat number should she write in the cell marked... | 7 | numeric | 4 | algebra | |
1662 | [{"role": "user", "question": "In the isosceles triangle $A B C$, points $K$ and $L$ are marked on the equal sides $A B$ and $B C$ respectively so that $A K=K L=L B$ and $K B=A C$.\n<image1>\nWhat is the size of angle $A B C$ ?", "hint": "", "options": {"A": "$36^{\\circ}$", "B": "$38^{\\circ}$", "C": "$40^{\\circ}$", ... | A | mcq | 5 | metric geometry - angle | |
1663 | [{"role": "user", "question": "Which of the diagrams below cannot be drawn without lifting your pencil off the page and without drawing along the same line twice?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | D | mcq | 3 | graph theory | |
1664 | [{"role": "user", "question": "A large square is divided into smaller squares, as shown. What fraction of the large square is shaded grey? <image1>", "hint": "", "options": {"A": "$\\frac{2}{3}$", "B": "$\\frac{2}{5}$", "C": "$\\frac{4}{7}$", "D": "$\\frac{4}{9}$", "E": "$\\frac{5}{12}$"}, "choices": []}] | D | mcq | 4 | combinatorial geometry | |
1665 | [{"role": "user", "question": "A four-digit integer is written on each of three pieces of paper and the pieces of paper are arranged so that three of the digits are covered, as shown. The sum of the three four-digit integers is 10126 . What are the covered digits? <image1>", "hint": "", "options": {"A": "5,6 and 7", "B... | A | mcq | 4 | algebra | |
1666 | [{"role": "user", "question": "In the diagram, $P Q=P R=Q S$ and $\\angle Q P R=20^{\\circ}$. What is $\\angle R Q S$ ? <image1>", "hint": "", "options": {"A": "$50^{\\circ}$", "B": "$60^{\\circ}$", "C": "$65^{\\circ}$", "D": "$70^{\\circ}$", "E": "$75^{\\circ}$"}, "choices": []}] | B | mcq | 5 | metric geometry - angle | |
1667 | [{"role": "user", "question": "Which of the following $4 \\times 4$ tiles cannot be formed by combining the two given pieces?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | E | mcq | 4 | combinatorial geometry | |
1668 | [{"role": "user", "question": "Cathie folded a square sheet of paper in half twice and then cut it through the middle twice, as shown in the diagram, before unfolding it all. How many of the pieces that she obtained were squares? <image1>", "hint": "", "options": {}, "choices": []}] | 5 | numeric | 3 | transformation geometry | |
1669 | [{"role": "user", "question": "Some identical rectangles are drawn on the floor. A triangle of base $10 \\mathrm{~cm}$ and height $6 \\mathrm{~cm}$ is drawn over them, as shown, and the region inside the rectangles and outside the triangle is shaded. What is the area of the shaded region? <image1>", "hint": "", "option... | B | mcq | 4 | combinatorial geometry | |
167 | [{"role": "user", "question": "We first draw an equilateral triangle, then draw the circumcircle of this triangle, then circumscribe a square to this circle. After drawing another circumcircle, we circumscribe a regular pentagon to this circle, and so on. We repeat this construction with new circles and new regular pol... | 248 | numeric | 5 | algebra | |
1670 | [{"role": "user", "question": "Natasha has many sticks of length 1 . Each stick is coloured blue, red, yellow or green. She wants to make a $3 \\times 3$ grid, as shown, so that each $1 \\times 1$ square in the grid has four sides of different colours. What is the smallest number of green sticks that she could use? <im... | 5 | numeric | 3 | graph theory | |
1671 | [{"role": "user", "question": "The integers from 1 to $n$, inclusive, are equally spaced in order round a circle. The diameter through the position of the integer 7 also goes through the position of 23 , as shown. What is the value of $n$ ? <image1>", "hint": "", "options": {}, "choices": []}] | 32 | numeric | 4 | algebra | |
1672 | [{"role": "user", "question": "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>", "hint": "", "options": {"A": "5 and 8", "B": "1 and 6", "C": "2 an... | A | mcq | 3 | graph theory | |
1673 | [{"role": "user", "question": "The diagram shows the square $W X Y Z$. The points $P, Q$ and $R$ are the midpoints of the sides $Z W, X Y$ and $Y Z$ respectively. What fraction of the square $W X Y Z$ is shaded? <image1>", "hint": "", "options": {"A": "$\\frac{3}{4}$", "B": "$\\frac{5}{8}$", "C": "$\\frac{1}{2}$", "D":... | E | mcq | 3 | metric geometry - area | |
1674 | [{"role": "user", "question": "A large square is divided into smaller squares. In one of the smaller squares a diagonal is also drawn, as shown. What fraction of the large square is shaded? <image1>", "hint": "", "options": {"A": "$\\frac{4}{5}$", "B": "$\\frac{3}{8}$", "C": "$\\frac{4}{9}$", "D": "$\\frac{1}{3}$", "E"... | E | mcq | 3 | metric geometry - area | |
1675 | [{"role": "user", "question": "The diagram shows a shape made up of 36 identical small equilateral triangles. What is the smallest number of small triangles identical to these that could be added to the shape to turn it into a hexagon? <image1>", "hint": "", "options": {}, "choices": []}] | 18 | numeric | 4 | combinatorial geometry | |
1676 | [{"role": "user", "question": "Each cell of a $3 \\times 3$ square has a number written in it. Unfortunately the numbers are not visible because they are covered in ink. However, the sum of the numbers in each row and the sum of the numbers in two of the columns are all known, as shown by the arrows on the diagram. Wha... | 43 | numeric | 4 | algebra | |
1677 | [{"role": "user", "question": "The shortest path from Atown to Cetown runs through Betown. The two signposts shown are set up at different places along this path. What distance is written on the broken sign? <image1>", "hint": "", "options": {"A": "$1 \\mathrm{~km}$", "B": "$3 \\mathrm{~km}$", "C": "$4 \\mathrm{~km}$",... | A | mcq | 2 | metric geometry - length | |
1678 | [{"role": "user", "question": "Sacha's garden has the shape shown. All the sides are either parallel or perpendicular to each other. Some of the dimensions are shown in the diagram. What is the length of the perimeter of Sacha's garden? <image1>", "hint": "", "options": {}, "choices": []}] | 24 | numeric | 2 | metric geometry - length | |
1679 | [{"role": "user", "question": "The pattern on a large square tile consists of eight congruent right-angled triangles and a small square. The area of the tile is $49 \\mathrm{~cm}^{2}$ and the length of the hypotenuse $P Q$ of one of the triangles is $5 \\mathrm{~cm}$. What is the area of the small square? <image1>", "h... | A | mcq | 3 | metric geometry - area | |
168 | [{"role": "user", "question": "In the picture $A B C D$ is a rectangle with $A B=16, B C=12$. Let $E$ be such a point that $A C \\perp C E, C E=15$. If $F$ is the point of intersection of segments $A E$ and $C D$, then the area of the triangle $A C F$ is equal to\n<image1>", "hint": "", "options": {}, "choices": []}] | 75 | numeric | 5 | metric geometry - area | |
1680 | [{"role": "user", "question": "Aisha has a strip of paper with the numbers $1,2,3,4$ and 5 written in five cells as shown. She folds the strip so that the cells overlap, forming 5 layers. Which of the following configurations, from top layer to bottom layer, is it not possible to obtain? <image1>", "hint": "", "options... | E | mcq | 3 | topology | |
1681 | [{"role": "user", "question": "Bella took a square piece of paper and folded two of its sides to lie along the diagonal, as shown, to obtain a quadrilateral. What is the largest size of an angle in that quadrilateral? <image1>", "hint": "", "options": {"A": "$112.5^{\\circ}$", "B": "$120^{\\circ}$", "C": "$125^{\\circ}... | A | mcq | 3 | transformation geometry | |
1682 | [{"role": "user", "question": "In the final of a dancing competition, each of the three members of the jury gives each of the five competitors 0 points, 1 point, 2 points, 3 points or 4 points. No two competitors get the same mark from any individual judge. Adam knows all the sums of the marks and a few single marks, a... | 1 | numeric | 2 | statistics | |
1683 | [{"role": "user", "question": "Cleo builds a pyramid with identical metal spheres. Its square base is a $4 \\times 4$ array of spheres, as shown in the diagram. The upper layers are a $3 \\times 3$ array of spheres, a $2 \\times 2$ array of spheres and a single sphere at the top. At each point of contact between two sp... | 96 | numeric | 4 | solid geometry | |
1684 | [{"role": "user", "question": "The statements on the right give clues to the identity of a four-digit number.\n<image1>\nWhat is the last digit of the four-digit number?", "hint": "", "options": {}, "choices": []}] | 3 | numeric | 4 | logic | |
1685 | [{"role": "user", "question": "When the five pieces shown are fitted together correctly, the result is a rectangle with a calculation written on it. What is the answer to this calculation? <image1>", "hint": "", "options": {}, "choices": []}] | -100 | numeric | 5 | arithmetic | |
1686 | [{"role": "user", "question": "A student correctly added the two two-digit numbers on the left of the board and got the answer 137. What answer will she obtain if she adds the two four-digit numbers on the right of the board?\n<image1>", "hint": "", "options": {}, "choices": []}] | 13837 | numeric | 4 | algebra | |
1687 | [{"role": "user", "question": "In the diagram, the area of the large square is $16 \\mathrm{~cm}^{2}$ and the area of each small corner square is $1 \\mathrm{~cm}^{2}$. What is the shaded area? <image1>", "hint": "", "options": {"A": "$3 \\mathrm{~cm}^{2}$", "B": "$\\frac{7}{2} \\mathrm{~cm}^{2}$", "C": "$4 \\mathrm{~c... | C | mcq | 3 | metric geometry - area | |
1688 | [{"role": "user", "question": "Costa is building a new fence in his garden. He uses 25 planks of wood, each of which is $30 \\mathrm{~cm}$ long. He arranges these planks so that there is the same slight overlap between any two adjacent planks, as shown in the diagram. The total length of Costa's new fence is 6.9 metres... | 2.5 | numeric | 2 | metric geometry - length | |
1689 | [{"role": "user", "question": "A rectangular strip of paper of dimensions $4 \\times 13$ is folded as shown in the diagram. Two rectangle s are formed with areas $P$ and $Q$ where $P=2 Q$. What is the value of $x$ ? <image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 3 | transformation geometry | |
169 | [{"role": "user", "question": "In a square of side $s$, where $s$ is an odd integer, the squares of side 1 on the diagonals are colored (like in the picture, where the square is of side 7). How many white squares are there?\n<image1>", "hint": "", "options": {"A": "$s^{2}+1-2 s$", "B": "$s^{2}+4-4 s$", "C": "$2 s^{2}+1... | A | mcq | 5 | combinatorial geometry | |
1690 | [{"role": "user", "question": "Three villages are connected by paths as shown. From Downend to Uphill, the detour via Middleton is $1 \\mathrm{~km}$ longer than the direct path. From Downend to Middleton, the detour via Uphill is $5 \\mathrm{~km}$ longer than the direct path. From Uphill to Middleton, the detour via Do... | C | mcq | 2 | metric geometry - length | |
1691 | [{"role": "user", "question": "A triangular pyramid is built with 20 cannonballs, as shown. Each cannonball is labelled with one of A, B, C, D or E. There are four cannonballs with each type of label.\n<image1>\nThe diagrams show the labels on the cannonballs on three of the faces of the pyramid. What is the label on t... | D | mcq | 4 | solid geometry | |
1692 | [{"role": "user", "question": "A ball is made of white hexagons and black pentagons, as seen in the picture. There are 12 pentagons in total. How many hexagons are there? <image1>", "hint": "", "options": {}, "choices": []}] | 20 | numeric | 4 | solid geometry | |
1693 | [{"role": "user", "question": "The diagram shows a $3 \\times 4 \\times 5$ cuboid consisting of 60 identical small cubes. A termite eats its way along the diagonal from $P$ to $Q$. This diagonal does not intersect the edges of any small cube inside the cuboid. How many of the small cubes does it pass through on its jou... | 10 | numeric | 4 | solid geometry | |
1694 | [{"role": "user", "question": "In a tournament each of the six teams plays one match against every other team. In each round of matches, three take place simultaneously. A TV station has already decided which match it will broadcast for each round, as shown in the diagram. In which round will team $\\mathrm{S}$ play ag... | 1 | numeric | 2 | combinatorics | |
1695 | [{"role": "user", "question": "Kanga likes jumping on the number line. She always makes two large jumps of length 3 , followed by three small jumps of length 1 , as shown, and then repeats this over and over again. She starts jumping at 0 .\n<image1>\nWhich of these numbers will Kanga land on?", "hint": "", "options": ... | C | mcq | 4 | algebra | |
1696 | [{"role": "user", "question": "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>", "hint": "", "options": {"A": "A", "B": "B", "C": "... | B | mcq | 4 | logic | |
1697 | [{"role": "user", "question": "On a standard dice, the sum of the numbers of pips on opposite faces is always 7. Four standard dice are glued together as shown. What is the minimum number of pips that could lie on the whole surface? <image1>", "hint": "", "options": {}, "choices": []}] | 58 | numeric | 2 | combinatorics | |
1698 | [{"role": "user", "question": "Tony the gardener planted tulips $\\mathbb{P}$ and daisies in a square flowerbed of side-length $12 \\mathrm{~m}$, arranged as shown\nWhat is the total area, in $\\mathrm{m}^{2}$, of the regions in which he planted daisies? <image1>", "hint": "", "options": {}, "choices": []}] | 48 | numeric | 3 | metric geometry - area | |
1699 | [{"role": "user", "question": "The numbers 1 to 8 are to be placed, one per circle, in the circles shown. The number next to each arrow shows what the product of the numbers in the circles on that straight line should be.\nWhat will be the sum of the numbers in the three circles at the bottom of the diagram?\n<image1>"... | 17 | numeric | 4 | algebra | |
17 | [{"role": "user", "question": "A jump of a little kangaroo is three times shorter than its mother's. How many jumps should the little kangaroo make to cover the distance equal to 7 jumps of its mother?\n<image1>", "hint": "", "options": {}, "choices": []}] | 21 | numeric | 2 | arithmetic | |
170 | [{"role": "user", "question": "On the circumference of radius $r$ three points $X, Y$ and $A$ are marked such that $X Y=r, X Y \\perp A Y$ (see the figure). How many degrees has the angle $X A Y$?\n<image1>", "hint": "", "options": {}, "choices": []}] | 30 | numeric | 4 | metric geometry - angle | |
1700 | [{"role": "user", "question": "The area of the intersection of a triangle and a circle is $45 \\%$ of the total area of the diagram. The area of the triangle outside the circle is $40 \\%$ of the total area of the diagram. What percentage of the circle lies outside the triangle? <image1>", "hint": "", "options": {"A": ... | B | mcq | 3 | metric geometry - area | |
1701 | [{"role": "user", "question": "Jenny decided to enter numbers into the cells of a $3 \\times 3$ table so that the sum of the numbers in all four possible $2 \\times 2$ cells will be the same. The numbers in three of the corner cells have already been written, as shown.\nWhich number should she write in the fourth corne... | 1 | numeric | 4 | algebra | |
1702 | [{"role": "user", "question": "The large rectangle $W X Y Z$ is divided into seven identical rectangles, as shown. What is the ratio $W X: X Y$ ? <image1>", "hint": "", "options": {"A": "$3: 2$", "B": "$4: 3$", "C": "$8: 5$", "D": "$12: 7$", "E": "$7: 3$"}, "choices": []}] | D | mcq | 2 | metric geometry - length | |
1703 | [{"role": "user", "question": "A builder has two identical bricks. She places them side by side in three different ways, as shown. The surface areas of the three shapes obtained are 72, 96 and 102 .\nWhat is the surface area of the original brick?\n<image1>", "hint": "", "options": {}, "choices": []}] | 54 | numeric | 4 | solid geometry | |
1704 | [{"role": "user", "question": "What is the smallest number of cells that need to be coloured in a $5 \\times 5$ square grid so that every $1 \\times 4$ or $4 \\times 1$ rectangle in the grid has at least one coloured cell? <image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 3 | graph theory | |
1705 | [{"role": "user", "question": "An isosceles triangle $P Q R$, in which $P Q=P R$, is split into three separate isosceles triangles, as shown, so that $P S=S Q, R T=R S$ and $Q T=R T$.\nWhat is the size, in degrees, of angle $Q P R$ ? <image1>", "hint": "", "options": {}, "choices": []}] | 36 | numeric | 5 | metric geometry - angle | |
1706 | [{"role": "user", "question": "Which of the shapes below cannot be divided into two trapeziums by a single straight line?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | A | mcq | 4 | combinatorial geometry | |
1707 | [{"role": "user", "question": "Werner wants to write a number at each vertex and on each edge of the rhombus shown. He wants the sum of the numbers at the two vertices at the ends of each edge to be equal to the number written on that edge. What number should he write on the edge marked with the question mark? <image1>... | 12 | numeric | 4 | algebra | |
1708 | [{"role": "user", "question": "Kristina has a piece of transparent paper with some lines marked on it. She folds it along the central dashed line, as indicated. What can she now see? <image1>", "hint": "", "options": {"A": "$2: 6: 9$", "B": "$2: 6: 6$", "C": "$5: 6: 9$", "D": "$2: 8: 6$", "E": "$5: 8: 9$"}, "choices": ... | C | mcq | 3 | transformation geometry | |
1709 | [{"role": "user", "question": "Evita wants to write the numbers 1 to 8 in the boxes of the grid shown, so that the sums of the numbers in the boxes in each row are equal and the sums of the numbers in the boxes in each column are equal. She has already written numbers 3,4 and 8 , as shown. What number should she write ... | 7 | numeric | 2 | combinatorics | |
171 | [{"role": "user", "question": "The set of all pairs $(x, y)$ which satisfy conditions $x y \\leqslant 0$ and $x^{2}+y^{2}=4$ is on the graph:\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}] | C | mcq | 4 | analytic geometry | |
1710 | [{"role": "user", "question": "Matchsticks can be used to write digits, as shown in the diagram. How many different positive integers can be written using exactly six matchsticks in this way? <image1>", "hint": "", "options": {}, "choices": []}] | 6 | numeric | 2 | combinatorics | |
1711 | [{"role": "user", "question": "In the diagram shown, sides $P Q$ and $P R$ are equal. Also $\\angle Q P R=40^{\\circ}$ and $\\angle T Q P=\\angle S R Q$. What is the size of $\\angle T U R$ ? <image1>", "hint": "", "options": {"A": "$55^{\\circ}$", "B": "$60^{\\circ}$", "C": "$65^{\\circ}$", "D": "$70^{\\circ}$", "E": ... | D | mcq | 5 | metric geometry - angle | |
1712 | [{"role": "user", "question": "Tom, John and Lily each shot six arrows at a target. Arrows hitting anywhere within the same ring scored the same number of points. Tom scored 46 points and John scored 34 points, as shown. How many points did Lily score? <image1>", "hint": "", "options": {}, "choices": []}] | 40 | numeric | 4 | algebra | |
1713 | [{"role": "user", "question": "The diagram shows a smaller rectangle made from three squares, each of area $25 \\mathrm{~cm}^{2}$, inside a larger rectangle. Two of the vertices of the smaller rectangle lie on the mid-points of the shorter sides of the larger rectangle. The other two vertices of the smaller rectangle l... | 150 | numeric | 3 | metric geometry - area | |
1714 | [{"role": "user", "question": "Elizabetta wants to write the integers 1 to 9 in the regions of the shape shown, with one integer in each region. She wants the product of the integers in any two regions that have a common edge to be not more than 15 . In how many ways can she do this? <image1>", "hint": "", "options": {... | 16 | numeric | 2 | combinatorics | |
1715 | [{"role": "user", "question": "Some mice live in three neighbouring houses. Last night, every mouse left its house and moved to one of the other two houses, always taking the shortest route. The numbers in the diagram show the number of mice per house, yesterday and today. How many mice used the path at the bottom of t... | 11 | numeric | 3 | counting | |
1716 | [{"role": "user", "question": "Bart wrote the number 1015 as a sum of numbers using only the digit 7 . He used a 7 a total of 10 times, including using the number 77 three times, as shown. Now he wants to write the number 2023 as a sum of numbers using only the digit 7, using a 7 a total of 19 times. How many times wil... | 6 | numeric | 4 | algebra | |
1717 | [{"role": "user", "question": "The diagram on the right shows a cube of side $18 \\mathrm{~cm}$. A giant ant walks across the cube's surface from $\\mathrm{X}$ to $\\mathrm{Y}$ along the route shown. How far does it walk? <image1>", "hint": "", "options": {"A": "$54 \\mathrm{~cm}$", "B": "$72 \\mathrm{~cm}$", "C": "$80... | E | mcq | 5 | solid geometry | |
1718 | [{"role": "user", "question": "In the diagram, five rectangles of the same size are shown with each side labelled with a number.\n<image1>\nThese 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.\n<image2>\nWhich of the rectangles should... | C | mcq | 3 | combinatorics |
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