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16 values
1719
[{"role": "user", "question": "In the diagram on the right, the number in each circle is the sum of the numbers in the two circles below it. What is the value of $x$ ? <image1>", "hint": "", "options": {}, "choices": []}]
82
numeric
2
algebra
172
[{"role": "user", "question": "In the figure the two equilateral triangles $A B C$ and $E C D$ have sides of length 2 and 1 respectively. The area of the quadrilateral $A B C E$ is:\n<image1>", "hint": "", "options": {"A": "$\\frac{5 \\sqrt{3}}{3}$", "B": "$\\frac{4+5 \\sqrt{3}}{5}$", "C": "3", "D": "$\\frac{6+\\sqrt{3...
E
mcq
5
metric geometry - area
1720
[{"role": "user", "question": "The diagram on the right shows a large triangle divided up into squares and triangles. $S$ is the number of squares of any size in the diagram and $T$ is the number of triangles of any size in the diagram. What is the value of $S \\times T$ ?\n<image1>", "hint": "", "options": {}, "choice...
70
numeric
3
combinatorics
1721
[{"role": "user", "question": "In the diagram, the small equilateral triangles have area $4 \\mathrm{~cm}^{2}$. What is the area of the shaded region? <image1>", "hint": "", "options": {"A": "$80 \\mathrm{~cm}^{2}$", "B": "$90 \\mathrm{~cm}^{2}$", "C": "$100 \\mathrm{~cm}^{2}$", "D": "$110 \\mathrm{~cm}^{2}$", "E": "$1...
B
mcq
2
combinatorial geometry
1722
[{"role": "user", "question": "In the sum shown, different shapes represent different digits.\n<image1>\nWhat digit does the square represent?", "hint": "", "options": {}, "choices": []}]
6
numeric
2
algebra
1723
[{"role": "user", "question": "The diagram shows five circles of the same radius touching each other. A square is drawn so that its vertices are at the centres of the four outer circles.\n<image1>\nWhat is the ratio of the area of the shaded parts of the circles to the area of the unshaded parts of the circles?", "hint...
D
mcq
2
metric geometry - area
1724
[{"role": "user", "question": "A rectangular garden is surrounded by a path of constant width. The perimeter of the garden is $24 \\mathrm{~m}$ shorter than the distance along the outside edge of the path. What is the width of the path? <image1>", "hint": "", "options": {"A": "$1 \\mathrm{~m}$", "B": "$2 \\mathrm{~m}$"...
C
mcq
3
metric geometry - length
1725
[{"role": "user", "question": "The diagram below shows a sequence of shapes made up of black and white floor tiles where each shape after the first has two more rows and two more columns than the one before it.\n<image1>\nHow many black tiles would be required to create the 15th shape in the sequence?", "hint": "", "op...
421
numeric
2
algebra
1726
[{"role": "user", "question": "<image1>\nThe diagram above shows the front and right-hand views of a solid made up of cubes of side $3 \\mathrm{~cm}$. The maximum volume that the solid could have is $\\mathrm{V} \\mathrm{cm}^{3}$. What is the value of $\\mathrm{V}$ ?", "hint": "", "options": {}, "choices": []}]
540
numeric
5
descriptive geometry
1727
[{"role": "user", "question": "It takes 9 litres of paint to cover the surface of the cube on the left.\n<image1>\nHow much paint would it take to cover the surface of the shape on the right?", "hint": "", "options": {"A": "9 litres", "B": "8 litres", "C": "6 litres", "D": "4 litres", "E": "2 litres"}, "choices": []}]
A
mcq
5
solid geometry
1728
[{"role": "user", "question": "Which of the following nets can be used to build the partial cube shown in the diagram?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}]
C
mcq
5
solid geometry
1729
[{"role": "user", "question": "A piece of paper in the shape of a regular hexagon, as shown, is folded so that the three marked vertices meet at the centre $O$ of the hexagon. What is the shape of the figure that is formed? <image1>", "hint": "", "options": {"A": "Six-pointed star", "B": "Dodecagon", "C": "Hexagon", "D...
E
mcq
1
transformation geometry
173
[{"role": "user", "question": "A circle $K$ is inscribed in a quarter circle with radius 6 as shown in the figure. What is the radius of circle $K$?\n<image1>", "hint": "", "options": {"A": "$\\frac{6-\\sqrt{2}}{2}$", "B": "$\\frac{3 \\sqrt{2}}{2}$", "C": "2.5", "D": "3", "E": "$6(\\sqrt{2}-1)$"}, "choices": []}]
E
mcq
5
metric geometry - length
1730
[{"role": "user", "question": "Four circles of radius $5 \\mathrm{~cm}$ touch the sides of a square and each other, as shown in the diagram. On each side of the square, an equilateral triangle is drawn to form a four-pointed star.\n<image1>\nWhat is the perimeter of the star?", "hint": "", "options": {"A": "$40 \\mathr...
D
mcq
3
metric geometry - length
1731
[{"role": "user", "question": "The diagram shows a rectangle $A B C D$ in which $A B=1$ metre and $A D=4$ metres. The points $E$ and $G$ are the midpoints of $A D$ and $A B$ and the points $F$ and $H$ are the midpoints of $A E$ and $A G$.\n<image1>\nWhat is the area of the shaded rectangle?", "hint": "", "options": {"A...
C
mcq
2
metric geometry - area
1732
[{"role": "user", "question": "The diameter of the circle shown is $10 \\mathrm{~cm}$. The circle passes through the vertices of a large rectangle which is divided into 16 identical smaller rectangles.\n<image1>\nWhat is the perimeter of the shape drawn with a dark line?", "hint": "", "options": {"A": "$10 \\mathrm{~cm...
C
mcq
3
metric geometry - length
1733
[{"role": "user", "question": "The diagram shows part of a river which has two islands in it. There are six bridges linking the islands and the two banks as shown. Leonhard goes for a walk every day in which he walks over each bridge exactly once. He always starts at point $A$, goes first over bridge 1 and always finis...
6
numeric
2
graph theory
1734
[{"role": "user", "question": "The square $A B C D$ consists of four congruent rectangles arranged around a central square. The perimeter of each of the rectangles is $40 \\mathrm{~cm}$. What is the area of the square $A B C D$ ? <image1>", "hint": "", "options": {"A": "$400 \\mathrm{~cm}^{2}$", "B": "$200 \\mathrm{~cm...
A
mcq
2
metric geometry - area
1735
[{"role": "user", "question": "The diagram shows five congruent right-angled isosceles triangles. What is the total area of the triangles? <image1>", "hint": "", "options": {"A": "$25 \\mathrm{~cm}^{2}$", "B": "$30 \\mathrm{~cm}^{2}$", "C": "$35 \\mathrm{~cm}^{2}$", "D": "$45 \\mathrm{~cm}^{2}$", "E": "$60 \\mathrm{~cm...
D
mcq
2
metric geometry - area
1736
[{"role": "user", "question": "In the addition sum below, $a, b$ and $c$ stand for different digits.\n<image1>\nWhat is the value of $a+b+c$ ?", "hint": "", "options": {}, "choices": []}]
16
numeric
2
algebra
1737
[{"role": "user", "question": "Sophie wants to complete the grid shown so that each row and each column of the grid contains the digits 1, 2 and 3 exactly once. What is the sum of the digits she will write in the shaded cells? <image1>", "hint": "", "options": {}, "choices": []}]
4
numeric
3
combinatorics
1738
[{"role": "user", "question": "Beattie wants to walk from $P$ to $Q$ along the paths shown, always moving in the direction from $P$ to $Q$.\n<image1>\nShe will add the numbers on the paths she walks along. How many different totals could she obtain?", "hint": "", "options": {}, "choices": []}]
4
numeric
3
combinatorics
1739
[{"role": "user", "question": "A cube has diagonals drawn on three adjacent faces as shown in the diagram. Which of the following nets could Usman use to make the cube shown?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}]
D
mcq
5
solid geometry
174
[{"role": "user", "question": "A parallelogram is divided into 4 triangles as shown in the figure. Of the following possibilities for the areas of the triangles at most one can be true. Which one is it?\n<image1>", "hint": "", "options": {"A": "$4,5,8,9$", "B": "$3,5,6,7$", "C": "$5,6,7,12$", "D": "$10,11,12,19$", "E":...
A
mcq
5
metric geometry - area
1740
[{"role": "user", "question": "Maddie has a paper ribbon of length $36 \\mathrm{~cm}$. She divides it into four rectangles of different lengths. She draws two lines joining the centres of two adjacent rectangles as shown.\n<image1>\nWhat is the sum of the lengths of the lines that she draws?", "hint": "", "options": {"...
A
mcq
1
transformation geometry
1741
[{"role": "user", "question": "In trapezium $P Q R S, \\angle R S P=2 \\times \\angle S P Q$ and $\\angle S P Q=2 \\times \\angle P Q R$. Also $\\angle Q R S=k \\times \\angle P Q R$. What is the value of $k$ ? <image1>", "hint": "", "options": {}, "choices": []}]
5
numeric
3
metric geometry - angle
1742
[{"role": "user", "question": "In the diagram, $P R S V$ is a rectangle with $P R=20 \\mathrm{~cm}$ and $P V=12 \\mathrm{~cm}$. Jeffrey marks points $U$ and $T$ on $V S$ and $Q$ on $P R$ as shown. What is the shaded area? <image1>", "hint": "", "options": {"A": "More information needed", "B": "$60 \\mathrm{~cm}^{2}$", ...
E
mcq
2
metric geometry - area
1743
[{"role": "user", "question": "The line $P Q$ is divided into six parts by the points $V, W, X, Y$ and $Z$. Squares are drawn on $P V, V W, W X, X Y, Y Z$ and $Z Q$ as shown in the diagram. The length of line $P Q$ is $24 \\mathrm{~cm}$. What is the length of the path from $P$ to $Q$ indicated by the arrows?\n<image1>"...
D
mcq
3
metric geometry - length
1744
[{"role": "user", "question": "Henna has four hair ribbons of width $10 \\mathrm{~cm}$. When she measures them, she finds that each ribbon is $25 \\mathrm{~cm}$ longer than the next smallest ribbon. She then arranges the ribbons to form two different shapes as shown in the diagram. How much longer is the perimeter of t...
B
mcq
2
combinatorial geometry
1745
[{"role": "user", "question": "In the diagram, $P Q R S$ is a square of side $10 \\mathrm{~cm} . T$ is a point inside the square so that $\\angle S P T=75^{\\circ}$ and $\\angle T S P=30^{\\circ}$. What is the length of $T R$ ? <image1>", "hint": "", "options": {"A": "$8 \\mathrm{~cm}$", "B": "$8.5 \\mathrm{~cm}$", "C"...
E
mcq
3
metric geometry - length
1746
[{"role": "user", "question": "In the diagram, $P Q R S$ and $W X Y Z$ are congruent squares. The sides $P S$ and $W Z$ are parallel. The shaded area is equal to $1 \\mathrm{~cm}^{2}$. What is the area of square $P Q R S$ ? <image1>", "hint": "", "options": {"A": "$1 \\mathrm{~cm}^{2}$", "B": "$2 \\mathrm{~cm}^{2}$", "...
A
mcq
2
metric geometry - area
1747
[{"role": "user", "question": "Rory uses four identical standard dice to build the solid shown in the diagram.\nWhenever two dice touch, the numbers on the touching faces are the same. The numbers on some of the faces of the solid are shown. What number is written on the face marked with question mark?\n(On a standard ...
5
numeric
2
logic
1748
[{"role": "user", "question": "Three congruent isosceles trapeziums are assembled to form an equilateral triangle with a hole in the middle, as shown in the diagram.\n<image1>\nWhat is the perimeter of the hole?", "hint": "", "options": {"A": "$3 a+6 b$", "B": "$3 b-6 a$", "C": "$6 b-3 a$", "D": "$6 a+3 b$", "E": "$6 a...
E
mcq
2
combinatorial geometry
1749
[{"role": "user", "question": "Each of the designs shown is initially divided into squares. For how many of the designs is the total area of the shaded region equal to three-fifths of the area of the whole design?\n<image1>", "hint": "", "options": {}, "choices": []}]
2
numeric
2
combinatorial geometry
175
[{"role": "user", "question": "The figure shows graphs of functions $f$ and $g$ defined on real numbers. Each graph consists of two perpendicular halflines. Which equality is satisfied for every real number $x$?\n<image1>", "hint": "", "options": {"A": "$f(x)=-g(x)+2$", "B": "$f(x)=-g(x)-2$", "C": "$f(x)=-g(x+2)$", "D"...
C
mcq
4
analytic geometry
1750
[{"role": "user", "question": "Emily has two identical cards in the shape of equilateral triangles. She places them both onto a sheet of paper so that they touch or overlap and draws around the shape she creates. Which one of the following is it impossible for her to draw?\n<image1>", "hint": "", "options": {"A": "A", ...
E
mcq
2
combinatorial geometry
1751
[{"role": "user", "question": "In the triangle $P Q R$, the lengths of sides $P Q$ and $P R$ are the same. The point $S$ lies on $Q R$ so that $Q S=P S$ and $\\angle R P S=75^{\\circ}$. What is the size of $\\angle Q R P$ ? <image1>", "hint": "", "options": {"A": "$35^{\\circ}$", "B": "$30^{\\circ}$", "C": "$25^{\\circ...
A
mcq
3
metric geometry - angle
1752
[{"role": "user", "question": "William has four cards with different integers written on them. Three of these integers are 2, 3 and 4 . He puts one card in each cell of the $2 \\times 2$ grid shown. The sum of the two integers in the second row is 6 . The sum of the two integers in the second column is 10 . Which numbe...
3
numeric
3
combinatorics
1753
[{"role": "user", "question": "Tom throws two darts at the target shown in the diagram. Both his darts hit the target. For each dart, he scores the number of points shown in the region he hits. How many different totals could he score?\n<image1>", "hint": "", "options": {}, "choices": []}]
9
numeric
3
combinatorics
1754
[{"role": "user", "question": "The diagram below shows five rectangles, each containing some of the letters $\\mathrm{P}, \\mathrm{R}, \\mathrm{I}, \\mathrm{S}$ and $\\mathrm{M}$.\n<image1>\nHarry wants to cross out letters so that each rectangle contains only one letter and each rectangle contains a different letter. ...
B
mcq
2
logic
1755
[{"role": "user", "question": "The two diagrams show a side view and a plan view of a tower made with light and dark coloured blocks. In the tower, only dark coloured blocks are placed on top of dark coloured blocks and only light coloured blocks are placed on top of light\n<image1>\ncoloured blocks. How many blocks in...
20
numeric
5
solid geometry
1756
[{"role": "user", "question": "The diagram shows a triangle joined to a square to form an irregular pentagon. The triangle has the same perimeter as the square.\n<image1>\nWhat is the ratio of the perimeter of the pentagon to the perimeter of the square?", "hint": "", "options": {"A": "2: 1", "B": "3: 2", "C": "4: 3", ...
B
mcq
3
metric geometry - length
1757
[{"role": "user", "question": "My TV screen has sides in the ratio $16: 9$. My mother's TV screen has sides in the ratio $4: 3$. A picture which exactly fills the screen of my TV only fills the width of the screen of my mother's TV.\nWhat fraction of the screen on my mother's TV is not covered?\n<image1>", "hint": "", ...
C
mcq
2
metric geometry - area
1758
[{"role": "user", "question": "In triangle $P Q R$, the point $S$ is on $P Q$ so that the ratio of the length of $P S$ to the length of $S Q$ is $2: 3$. The point $T$ lies on $S R$ so that the area of triangle $P T R$ is 20 and the area of triangle $S Q T$ is 18 , as shown in the diagram.\n<image1>\nWhat is the area of...
80
numeric
2
metric geometry - area
1759
[{"role": "user", "question": "The diagram shows a plan of a town with various bus stops. There are four bus routes in the town.\nRoute 1 goes $\\mathrm{C}-\\mathrm{D}-\\mathrm{E}-\\mathrm{F}-\\mathrm{G}-\\mathrm{H}-\\mathrm{C}$ and is $17 \\mathrm{~km}$ long.\nRoute 2 goes $\\mathrm{A}-\\mathrm{B}-\\mathrm{C}-\\mathrm...
B
mcq
3
metric geometry - length
176
[{"role": "user", "question": "How many triangles can be drawn with vertices in the 18 points shown in the figure?\n<image1>", "hint": "", "options": {}, "choices": []}]
711
numeric
5
combinatorics
1760
[{"role": "user", "question": "In the sum each letter stands for a different digit.\nWhat is the answer to the subtraction $ RN - KG $ ? <image1>", "hint": "", "options": {}, "choices": []}]
11
numeric
2
algebra
1761
[{"role": "user", "question": "The diagram shows squares of three different sizes arranged into a rectangle. The length of each side of the smallest squares is $20 \\mathrm{~cm}$. Adam Ant walks along the path marked from $P$ to $Q$. How far does Adam walk? <image1>", "hint": "", "options": {"A": "$380 \\mathrm{~cm}$",...
C
mcq
2
combinatorial geometry
1762
[{"role": "user", "question": "Two rectangles of dimensions $8 \\mathrm{~cm}$ by $10 \\mathrm{~cm}$ and $9 \\mathrm{~cm}$ by $12 \\mathrm{~cm}$ overlap as shown in the diagram. The area of the black region is $37 \\mathrm{~cm}^{2}$. What is the area of the grey region? <image1>", "hint": "", "options": {"A": "$60 \\mat...
E
mcq
2
metric geometry - area
1763
[{"role": "user", "question": "In the quadrilateral $P Q R S$, the length of $P Q$ is $11 \\mathrm{~cm}$, the length of $Q R$ is $7 \\mathrm{~cm}$, the length of $R S$ is $9 \\mathrm{~cm}$ and the length of $S P$ is $3 \\mathrm{~cm}$. Both $\\angle Q R S$ and $\\angle S P Q$ are $90^{\\circ}$. What is the area of the q...
B
mcq
2
metric geometry - area
1764
[{"role": "user", "question": "Two of the following four facts about a positive integer $N$ are true and two are false. <image1>\nWhat is the value of $N$ ?", "hint": "", "options": {}, "choices": []}]
5
numeric
2
logic
1765
[{"role": "user", "question": "The shape in the diagram is made up of a rectangle, a square and an equilateral triangle, all of which have the same perimeter. The length of the side of the square is $9 \\mathrm{~cm}$. What is the length of the shorter sides of the rectangle? <image1>", "hint": "", "options": {"A": "$4 ...
C
mcq
3
metric geometry - length
1766
[{"role": "user", "question": "The diagram shows a square, an equilateral triangle and a regular pentagon. What is the size of $\\angle W U V$ ? <image1>", "hint": "", "options": {"A": "$21^{\\circ}$", "B": "$23^{\\circ}$", "C": "$25^{\\circ}$", "D": "$27^{\\circ}$", "E": "$29^{\\circ}$"}, "choices": []}]
A
mcq
3
metric geometry - angle
1767
[{"role": "user", "question": "In the diagram, each symbol represent a positive integer. The sums of the numbers in each row and in each column are as shown.\n<image1>\nWhat is the value of <image2>?", "hint": "", "options": {}, "choices": []}]
23
numeric
2
algebra
1768
[{"role": "user", "question": "In the diagram, $P Q R S$ is a square of side $10 \\mathrm{~cm}$. The distance $M N$ is $6 \\mathrm{~cm}$. The square is divided into four congruent isosceles triangles, four congruent squares and the shaded region.\n<image1>\nWhat is the area of the shaded region?", "hint": "", "options"...
C
mcq
2
metric geometry - area
1769
[{"role": "user", "question": "The diagram shows a $2 \\times 4$ table in which the numbers in each column except the first column are the sum and the difference of the numbers in the previous column.\n<image1>\nCarl completes a $2 \\times 7$ table in the same way and obtains the numbers 96 and 64 in the final column. ...
20
numeric
2
algebra
177
[{"role": "user", "question": "Let $A B C D$ be a convex quadrilateral with an area of 1 where $A B$ and $B D$ are the bases of two isosceles triangles $A D B$ and $B C D$ respectively (as shown). The product $A C \\cdot B D$ is equal to:\n<image1>", "hint": "", "options": {"A": "$\\frac{\\sqrt{3}}{3}$", "B": "$\\frac{...
D
mcq
5
metric geometry - length
1770
[{"role": "user", "question": "Ellis's Eel Emporium contains a large tank holding three different types of eel: electric eels, moray eels and freshwater eels. A notice on the tank reads as follows:\n<image1>\nHow many eels are in the tank?", "hint": "", "options": {}, "choices": []}]
21
numeric
2
algebra
1771
[{"role": "user", "question": "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.\nWhat colour will he use for the cell marked $X$ ?\n<image1>", "hint...
A
mcq
2
graph theory
1772
[{"role": "user", "question": "Lily pours 296 litres of water into the top of the pipework shown in the diagram. Each time a pipe forks, half the water flows to one side and half to the other. How many litres of water will reach container $\\mathrm{Y}$ ? <image1>", "hint": "", "options": {}, "choices": []}]
222
numeric
3
arithmetic
1773
[{"role": "user", "question": "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 t...
D
mcq
3
combinatorics
1774
[{"role": "user", "question": "The diagram shows four congruent right-angled triangles inside a rectangle. What is the total area, in $\\mathrm{cm}^{2}$, of the four triangles? <image1>", "hint": "", "options": {}, "choices": []}]
56
numeric
2
metric geometry - area
1775
[{"role": "user", "question": "The diagram shows three triangles which are formed by the five line segments $A C D F, B C G, G D E, A B$ and $E F$ so that $A C=B C=C D=G D=D F=E F$. Also $\\angle C A B=\\angle E F D$. What is the size, in degrees, of $\\angle C A B$ ? <image1>", "hint": "", "options": {}, "choices": []...
60
numeric
3
metric geometry - angle
1776
[{"role": "user", "question": "Each square in the grid shown is $1 \\mathrm{~cm}$ by $1 \\mathrm{~cm}$. What is the area of the shaded figure, in $\\mathrm{cm}^{2}$ ? <image1>", "hint": "", "options": {}, "choices": []}]
17
numeric
2
combinatorial geometry
1777
[{"role": "user", "question": "The diagram shows the eight vertices of an octagon connected by line segments. Jodhvir wants to write one of the integers 1,2,3 or 4 at each of the vertices so that the two integers at the ends of every line segment are different. He has already written three integers as shown.\n<image1>\...
4
numeric
2
graph theory
1778
[{"role": "user", "question": "In the diagram $P Q R S$ is a rhombus. Point $T$ is the mid-point of $P S$ and point $W$ is the mid-point of $S R$.\n<image1>\nWhat is the ratio of the unshaded area to the shaded area?", "hint": "", "options": {"A": "$1: 1$", "B": "$2: 3$", "C": "$3: 5$", "D": "$4: 7$", "E": "$5: 9$"}, "...
A
mcq
2
metric geometry - area
1779
[{"role": "user", "question": "Using only pieces like the one shown in the diagram, Zara wants to make a complete square without gaps or overlaps.\n<image1>\nWhat is the smallest number of pieces she can use?", "hint": "", "options": {}, "choices": []}]
20
numeric
2
combinatorial geometry
178
[{"role": "user", "question": "Five cards are lying on the table in the order 1,3,5,4,2. You must get the cards in the order $1,2,3,4,5$. Per move, any two cards may be interchanged. How many moves do you need at least?\n<image1>", "hint": "", "options": {}, "choices": []}]
2
numeric
5
algebra
1780
[{"role": "user", "question": "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.\nWhat letter is written on the faces of the one dice which is not shown ...
B
mcq
2
logic
1781
[{"role": "user", "question": "A map of Wonderland shows five cities. Each city is joined to every other city by a road. Alice's map, as shown, is incomplete. How many roads are missing? <image1>", "hint": "", "options": {}, "choices": []}]
3
numeric
2
graph theory
1782
[{"role": "user", "question": "Both of the shapes shown in the diagram are formed from the same five pieces, a $5 \\mathrm{~cm}$ by $10 \\mathrm{~cm}$ rectangle, two large quarter circles and two small quarter circles. What is the difference in $\\mathrm{cm}$ between their perimeters? <image1>", "hint": "", "options": ...
20
numeric
2
combinatorial geometry
1783
[{"role": "user", "question": "In the diagram, lines $Q T$ and $R S$ are parallel and $P Q$ and $Q T$ are equal. Angle $S T Q$ is $154^{\\circ}$. What is the size of angle $S R Q$ ? <image1>", "hint": "", "options": {"A": "$120^{\\circ}$", "B": "$122^{\\circ}$", "C": "$124^{\\circ}$", "D": "$126^{\\circ}$", "E": "$128^...
E
mcq
3
metric geometry - angle
1784
[{"role": "user", "question": "A regular octagon is folded exactly in half three times until a triangle is obtained. The bottom corner of the triangle is then cut off with a cut perpendicular to one side of the triangle as shown.\n<image1>\nWhich of the following will be seen when the triangle is unfolded?\n<image2>", ...
C
mcq
1
transformation geometry
1785
[{"role": "user", "question": "Rectangle $W X Y Z$ is cut into four smaller rectangles as shown. The lengths of the perimeters of three of the smaller rectangles are 11, 16 and 19 . The length of the perimeter of the fourth smaller rectangle lies between 11 and 19. What is the length of the perimeter of $W X Y Z$ ? <im...
30
numeric
3
metric geometry - length
1786
[{"role": "user", "question": "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>", "hint": "", "options": {"A": "3 and 4", "B": "5 and 6", "C": "6 and 7", "D": "8 and 9", "E": "8 and 10"}, ...
E
mcq
3
combinatorics
1787
[{"role": "user", "question": "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.\nWhich of the following tables could Carl have created?\n<image1>", "hint": "", "options": {"A": "A", "B": "B", "C...
D
mcq
2
logic
1788
[{"role": "user", "question": "Andrew wants to write the numbers $1,2,3,4,5,6$ and 7 in the circles in the diagram so that the sum of the three numbers joined by each straight line is the same. Which number should he write in the top circle? <image1>", "hint": "", "options": {}, "choices": []}]
4
numeric
3
combinatorics
1789
[{"role": "user", "question": "A square piece of paper of area $64 \\mathrm{~cm}^{2}$ is folded twice, as shown in the diagram. What is the sum of the areas of the two shaded rectangles?\n<image1>", "hint": "", "options": {"A": "$10 \\mathrm{~cm}^{2}$", "B": "$14 \\mathrm{~cm}^{2}$", "C": "$15 \\mathrm{~cm}^{2}$", "D":...
D
mcq
1
transformation geometry
179
[{"role": "user", "question": "A square piece of paper has been cut in three pieces. Two of them are in the picture on the right. What is the third one?\n<image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C": "C", "D": "D", "E": "E"}, "choices": []}]
A
mcq
5
combinatorial geometry
1790
[{"role": "user", "question": "Which single digit should be placed in all three of the boxes shown to give a correct calculation? <image1>", "hint": "", "options": {}, "choices": []}]
4
numeric
2
algebra
1791
[{"role": "user", "question": "Nico is learning to drive. He knows how to turn right but has not yet learned how to turn left. What is the smallest number of right turns he could make to travel from $\\mathrm{P}$ to $\\mathrm{Q}$, moving first in the direction shown? <image1>", "hint": "", "options": {}, "choices": []}...
4
numeric
2
graph theory
1792
[{"role": "user", "question": "When she drew two intersecting circles, as shown, Tatiana divided the space inside the circles into three regions. When drawing two intersecting squares, what is the largest number of regions inside one or both of the squares that Tatiana could create? <image1>", "hint": "", "options": {}...
9
numeric
2
combinatorial geometry
1793
[{"role": "user", "question": "What is the largest number of \" $\\mathrm{T}$ \" shaped pieces, as shown, that can be placed on the $4 \\times 5$ grid in the diagram, without any overlap of the pieces? <image1>", "hint": "", "options": {}, "choices": []}]
4
numeric
2
combinatorial geometry
1794
[{"role": "user", "question": "Maria has drawn some shapes on identical square pieces of paper, as shown. Each line she has drawn is parallel to an edge of her paper. How many of her shapes have the same perimeter as the sheet of paper itself? <image1>", "hint": "", "options": {}, "choices": []}]
4
numeric
3
metric geometry - length
1795
[{"role": "user", "question": "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?\n\\begin{tabular}{|l|l|l|l|}\n\\hline...
E
mcq
5
descriptive geometry
1796
[{"role": "user", "question": "The diagram shows a wooden cube of side $3 \\mathrm{~cm}$ with a smaller cube of side $1 \\mathrm{~cm}$ cut out at one corner. A second cube of side $3 \\mathrm{~cm}$ has a cube of side $1 \\mathrm{~cm}$ cut out at each corner. How many faces does the shape formed from the second cube hav...
30
numeric
5
solid geometry
1797
[{"role": "user", "question": "Alisha wrote an integer in each square of a $4 \\times 4$ grid. Integers in squares with a common edge differed by 1 . She wrote a 3 in the top left corner, as shown. She also wrote a 9 somewhere in the grid. How many different integers did she write? <image1>", "hint": "", "options": {},...
7
numeric
2
algebra
1798
[{"role": "user", "question": "The diagram shows a square $P Q R S$ with area $120 \\mathrm{~cm}^{2}$. Point $T$ is the mid-point of $P Q$. The ratio $Q U: U R=2: 1$, the ratio $R V: V S=3: 1$ and the ratio $S W: W P=4: 1$. What is the area, in $\\mathrm{cm}^{2}$, of quadrilateral $T U V W$? <image1>", "hint": "", "opt...
67
numeric
2
metric geometry - area
1799
[{"role": "user", "question": "Emily makes four identical numbered cubes using the net shown. She then glues them together so that only faces with the same number on are glued together to form the $2 \\times 2 \\times 1$ block shown. What is the largest possible total of all the numbers on the faces of the block that E...
68
numeric
3
combinatorics
18
[{"role": "user", "question": "A fifteen-meter log has to be sawn into three-meter pieces. How many cuts are needed for that?\n<image1>", "hint": "", "options": {}, "choices": []}]
4
numeric
2
arithmetic
180
[{"role": "user", "question": "A $3 \\times 3 \\times 3$ cube weighs 810 grams. If we drill three holes through it as shown, each of which is a $1 \\times 1 \\times 3$ rectangular parallelepiped, the weight of the remaining solid is:\n<image1>", "hint": "", "options": {"A": "$540 \\mathrm{~g}$", "B": "$570 \\mathrm{~g}...
C
mcq
3
solid geometry
1800
[{"role": "user", "question": "One slice of a circular cake is $15 \\%$ of the whole cake. What is the size of the angle marked with the question mark? <image1>", "hint": "", "options": {"A": "$30^{\\circ}$", "B": "$45^{\\circ}$", "C": "$54^{\\circ}$", "D": "$15^{\\circ}$", "E": "$20^{\\circ}$"}, "choices": []}]
C
mcq
2
metric geometry - angle
1801
[{"role": "user", "question": "In the picture, the three strips labelled 1,2,3 have the same horizontal width $a$. These three strips connect two parallel lines. Which of these statements is true? <image1>", "hint": "", "options": {"A": "All three strips have the same area.", "B": "Strip 1 has the largest area.", "C": ...
A
mcq
4
metric geometry - area
1802
[{"role": "user", "question": "In figure 1, alongside, the area of the square equals $a$. The area of each circle in both figures equals $b$. Three circles are lined up as shown in figure 2. An elastic band is placed around these three circles without moving them. What is the area inside the elastic band?\n\n<image1>",...
B
mcq
4
metric geometry - area
1803
[{"role": "user", "question": "The cuboid shown has been built using four shapes, each made from four small cubes. Three of the shapes can be completely seen, but the dark one is only partly visible. Which of the following shapes could be the dark one? <image1>\n<image2>", "hint": "", "options": {"A": "A", "B": "B", "C...
C
mcq
3
combinatorial geometry
1804
[{"role": "user", "question": "In the sum on the right, each of the letters $X, Y$ and $Z$ represents a different $X X$ non-zero digit. What does $X$ represent? <image1>", "hint": "", "options": {}, "choices": []}]
8
numeric
3
algebra
1805
[{"role": "user", "question": "What is the ratio of the areas of the triangles $A D E$ and $A B C$ in the picture? <image1>", "hint": "", "options": {"A": "$9: 4$", "B": "$7: 3$", "C": "$4: 5$", "D": "$15: 10$", "E": "$26: 9$"}, "choices": []}]
A
mcq
4
metric geometry - area
1806
[{"role": "user", "question": "A rectangular sheet of paper which measures $6 \\mathrm{~cm} \\times 12 \\mathrm{~cm}$ is folded along its diagonal (Diagram A). The shaded areas in Diagram B are then cut off and the paper is unfolded leaving the rhombus shown in Diagram C. What is the length of the side of the rhombus? ...
C
mcq
4
transformation geometry
1807
[{"role": "user", "question": "In the diagram, $Q R=P S$. What is the size of $\\angle P S R$ ? <image1>", "hint": "", "options": {"A": "$30^{\\circ}$", "B": "$50^{\\circ}$", "C": "$55^{\\circ}$", "D": "$65^{\\circ}$", "E": "$70^{\\circ}$"}, "choices": []}]
D
mcq
2
metric geometry - angle
1808
[{"role": "user", "question": "Roo has a very unusual chessboard of side 7, in which only the squares which lie on the diagonals are shaded. Kanga then asks the question \"What would be the total white area of your chessboard if each side was 2003 squares long?\" What is the correct answer? <image1>", "hint": "", "opti...
A
mcq
4
metric geometry - area