id stringlengths 1 3 | question stringlengths 37 1.19k | answer stringclasses 61
values | solution stringclasses 61
values | subject stringclasses 16
values | level int64 1 5 | options listlengths 0 5 |
|---|---|---|---|---|---|---|
490 | Oli coloured in the following 8 fields in the grid: A2, B1, B2, B3, B4, C3, D3 and D4. Which is his grid?
<image2>
Options:
A) (A)
B) (B)
C) (C)
D) (D)
E) (E) | C | ANSWER: C
SOLUTION:
The correct answer is C. | analytic geometry | 1 | [
"(A)",
"(B)",
"(C)",
"(D)",
"(E)"
] |
455 | Jane shoots two arrows at the target. In the drawing we see that her score is 5. If both arrows hit the target, how many different scores can she obtain? | 6 | ANSWER: 6
SOLUTION:
The correct answer is 6. | combinatorics | 3 | [] |
165 | 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 $5 e+12 f+13 g$? | 60 | ANSWER: 60
SOLUTION:
The correct answer is 60. | metric geometry - length | 5 | [] |
175 | 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 $x$?
Options:
A) $f(x)=-g(x)+2$
B) $f(x)=-g(x)-2$
C) $f(x)=-g(x+2)$
D) $f(x+2)=-g(x)$
E) $f(x+1)=-g(x-1)$ | C | ANSWER: C
SOLUTION:
The correct answer is C. | analytic geometry | 4 | [
"$f(x)=-g(x)+2$",
"$f(x)=-g(x)-2$",
"$f(x)=-g(x+2)$",
"$f(x+2)=-g(x)$",
"$f(x+1)=-g(x-1)$"
] |
495 | A flee stands on the floor and wants to climb the 10 steps. He can either jump 3 steps upwards or jump 4 steps downwards. What is is the smallest number of jumps he must make? | 8 | ANSWER: 8
SOLUTION:
The correct answer is 8. | algebra | 2 | [] |
290 | Bettina chooses five points $A, B, C, D$ and $E$ on a circle and draws the tangent to the circle at point $A$. She realizes that the five angles marked $x$ are all equally big. (Note that the diagram is not drawn to scale!) How big is the angle $\angle A B D$?
Options:
A) $66^{\circ}$
B) $70.5^{\circ}$
C) $72^{\... | C | ANSWER: C
SOLUTION:
The correct answer is C. | metric geometry - angle | 4 | [
"$66^{\\circ}$",
"$70.5^{\\circ}$",
"$72^{\\circ}$",
"$75^{\\circ}$",
"$77.5^{\\circ}$"
] |
145 | 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.
Which path is the kangaroo allowed to take?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | C | ANSWER: C
SOLUTION:
The correct answer is C. | combinatorial geometry | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
34 | Max has cut a rectangle into two pieces. One piece looks like:
What does the other piece look like?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | E | ANSWER: E
SOLUTION:
The correct answer is E. | combinatorial geometry | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
177 | 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:
Options:
A) $\frac{\sqrt{3}}{3}$
B) $\frac{2 \sqrt{3}}{3}$
C) $\sqrt{3}$
D) $\frac{4 \sqrt{3}}{3}$
E) ... | D | ANSWER: D
SOLUTION:
The correct answer is D. | metric geometry - length | 5 | [
"$\\frac{\\sqrt{3}}{3}$",
"$\\frac{2 \\sqrt{3}}{3}$",
"$\\sqrt{3}$",
"$\\frac{4 \\sqrt{3}}{3}$",
"other answer"
] |
146 | Carl writes down a five-digit number.
He then places a shape on each of the five digits (see picture).
He places different shapes on different digits.
He places the same shape on the same digits.
Which number did Carl hide? | 34426 | ANSWER: 34426
SOLUTION:
The correct answer is 34426. | logic | 3 | [] |
169 | 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?
Options:
A) $s^{2}+1-2 s$
B) $s^{2}+4-4 s$
C) $2 s^{2}+1-4 s$
D) $s^{2}-1-2 s$
E) $s^{2}-2 s$ | A | ANSWER: A
SOLUTION:
The correct answer is A. | combinatorial geometry | 5 | [
"$s^{2}+1-2 s$",
"$s^{2}+4-4 s$",
"$2 s^{2}+1-4 s$",
"$s^{2}-1-2 s$",
"$s^{2}-2 s$"
] |
101 | Every night the wizard Tilim makes the weather forecast for the king. When Tilim gets it right he gets 3 gold coins, but when he makes a mistake, he pays a fine of 2 gold coins. After making the prediction for 5 days, Tilim did the math and discovered that he neither won nor lost coins. How many times did he get the we... | 2 | ANSWER: 2
SOLUTION:
The correct answer is 2. | logic | 3 | [] |
254 | An equilateral triangle is being rolled around a unit square as shown. How long is the path that the point shown covers, if the point and the triangle are both back at the start for the first time?
Options:
A) $4 \pi$
B) $\frac{28}{3} \pi$
C) $8 \pi$
D) $\frac{14}{3} \pi$
E) $\frac{21}{2} \pi$ | B | ANSWER: B
SOLUTION:
The correct answer is B. | transformation geometry | 5 | [
"$4 \\pi$",
"$\\frac{28}{3} \\pi$",
"$8 \\pi$",
"$\\frac{14}{3} \\pi$",
"$\\frac{21}{2} \\pi$"
] |
62 | How many blocks are missing in this igloo? | 10 | ANSWER: 10
SOLUTION:
The correct answer is 10. | counting | 1 | [] |
303 | The diagram shows a regular hexagon with side length 1. The grey flower is outlined by circular arcs with radius 1 whose centre's lie in the vertices of the hexagon. How big is the area of the grey flower?
Options:
A) $\frac{\pi}{2}$
B) $\frac{2 \pi}{3}$
C) $2 \sqrt{3}-\pi$
D) $\frac{\pi}{2}+\sqrt{3}$
E) $2 ... | E | ANSWER: E
SOLUTION:
The correct answer is E. | metric geometry - area | 5 | [
"$\\frac{\\pi}{2}$",
"$\\frac{2 \\pi}{3}$",
"$2 \\sqrt{3}-\\pi$",
"$\\frac{\\pi}{2}+\\sqrt{3}$",
"$2 \\pi-3 \\sqrt{3}$"
] |
139 | Anna cuts the picture of a mushroom in two halves.
She then arranges the two pieces together to form a new picture. What could this new picture look like?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | E | ANSWER: E
SOLUTION:
The correct answer is E. | combinatorial geometry | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
132 | Mara built the square by using 4 of the following 5 shapes. Which shape was not used?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | D | ANSWER: D
SOLUTION:
The correct answer is D. | combinatorial geometry | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
274 | The diameters of three semi-circles form the sides of a right-angled triangle. Their areas are $X \mathrm{~cm}^{2}, Y \mathrm{~cm}^{2}$ and $Z \mathrm{~cm}^{2}$ as pictured. Which of the following expressions is definitely correct?
Options:
A) $X+Y<Z$
B) $\sqrt{X}+\sqrt{Y}=\sqrt{Z}$
C) $X+Y=Z$
D) $X^{2}+Y^{2}=... | C | ANSWER: C
SOLUTION:
The correct answer is C. | metric geometry - area | 5 | [
"$X+Y<Z$",
"$\\sqrt{X}+\\sqrt{Y}=\\sqrt{Z}$",
"$X+Y=Z$",
"$X^{2}+Y^{2}=Z^{2}$",
"$X^{2}+Y^{2}=Z$"
] |
469 | Six coins build a triangle (see picture). What is the smallest number of coins that must be moved to create the circle? | 2 | ANSWER: 2
SOLUTION:
The correct answer is 2. | combinatorial geometry | 2 | [] |
456 | A garden of a square shape is divided into a pool (P), a flowerbed (F), a lawn (L) and a sandpit (S) (see the picture). The lawn and the flowerbed are of a square shape. The perimeter of the lawn is $20 \mathrm{~m}$, the perimeter of the flowerbed is $12 \mathrm{~m}$. What is the perimeter of the pool?
Options:
A) $... | D | ANSWER: D
SOLUTION:
The correct answer is D. | metric geometry - length | 3 | [
"$10 \\mathrm{~m}$",
"$12 \\mathrm{~m}$",
"$14 \\mathrm{~m}$",
"$16 \\mathrm{~m}$",
"$18 \\mathrm{~m}$"
] |
151 | Out of how many circles is the beaver made of? | 8 | ANSWER: 8
SOLUTION:
The correct answer is 8. | counting | 1 | [] |
136 | Stan has five toys: a ball, a set of blocks, a game, a puzzle and a car. He puts each toy on a different shelf of the bookcase. The ball is higher than the blocks and lower than the car. The game is directly above the ball. On which shelf can the puzzle not be placed? | 3 | ANSWER: 3
SOLUTION:
The correct answer is 3. | logic | 3 | [] |
306 | In the diagram you can see the calendar page of a certain month. Unfortunately ink has run across parts of the page. Which day of the week does the 27th of that month fall on?
Options:
A) Monday
B) Wednesday
C) Thursday
D) Saturday
E) Sunday | A | ANSWER: A
SOLUTION:
The correct answer is A. | arithmetic | 1 | [
"Monday",
"Wednesday",
"Thursday",
"Saturday",
"Sunday"
] |
406 | Which numbers are written in the area that belongs to the rectangle and to the circle but doesn't belong to the triangle?
Options:
A) 5 and 11
B) 1 and 10
C) 13
D) 3 and 9
E) 6, 7, and 4 | B | ANSWER: B
SOLUTION:
The correct answer is B. | combinatorial geometry | 2 | [
"5 and 11",
"1 and 10",
"13",
"3 and 9",
"6, 7, and 4"
] |
308 | The diagram shows an object made up of 12 dice glued-together. The object is dipped into some colour so that the entire outside is coloured in this new colour. How many of the small dice will have exactly four faces coloured in? | 10 | ANSWER: 10
SOLUTION:
The correct answer is 10. | solid geometry | 3 | [] |
141 | A monkey has torn off a piece of Captain Jack's map.
What does the piece the monkey has torn off look like?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | B | ANSWER: B
SOLUTION:
The correct answer is B. | combinatorial geometry | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
446 | A square piece of paper is folded twice so that the result is a square again. In this square one of the corners is cut off. Then the paper is folded out. Which sample below cannot be obtained in this way?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | E | ANSWER: E
SOLUTION:
The correct answer is E. | transformation geometry | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
84 | The road from Anna's to Mary's house is $16 \mathrm{~km}$ long. The road from Mary's to John's house is $20 \mathrm{~km}$ long. The road from the crossing to Mary's house is $9 \mathrm{~km}$ long. How long is the road from Anna's to John's house?
Options:
A) $7 \mathrm{~km}$
B) $9 \mathrm{~km}$
C) $11 \mathrm{~k... | E | ANSWER: E
SOLUTION:
The correct answer is E. | arithmetic | 2 | [
"$7 \\mathrm{~km}$",
"$9 \\mathrm{~km}$",
"$11 \\mathrm{~km}$",
"$16 \\mathrm{~km}$",
"$18 \\mathrm{~km}$"
] |
416 | At noon the minute hand of a clock is in the position shown on the left and after the quarter of an hour -- in the position shown on the right. Which position the minute hand will take after seventeen quarters from the noon?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | A | ANSWER: A
SOLUTION:
The correct answer is A. | arithmetic | 3 | [
"A",
"B",
"C",
"D",
"E"
] |
181 | We are given three semi-circles as shown. $A B E F$ is a rectangle and the radius of each of the semi-circles is $2 \mathrm{~cm}$. $E$ and $F$ are the centers of the bottom semi-circles. The area of the shaded region (in $\mathrm{cm}^{2}$) is: | 8 | ANSWER: 8
SOLUTION:
The correct answer is 8. | metric geometry - area | 5 | [] |
266 | The vertices of a die are numbered 1 to 8, so that the sum of the four numbers on the vertices of each face are the same. The numbers 1, 4 and 6 are already indicated in the picture. Which number is in position $x$? | 2 | ANSWER: 2
SOLUTION:
The correct answer is 2. | algebra | 5 | [] |
426 | Betty keeps drawing three different figures in the same order. Which figure should be the next?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | D | ANSWER: D
SOLUTION:
The correct answer is D. | transformation geometry | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
253 | Let $a>b$. If the ellipse shown rotates about the $x$-axis an ellipsoid $E_{x}$ with volume $\operatorname{Vol}\left(E_{x}\right)$ is obtained. If it rotates about the $y$-axis an ellipsoid $E_{y}$ with volume $\operatorname{Vol}\left(E_{y}\right)$ is obtained. Which of the following statements is true?
Options:
A) ... | C | ANSWER: C
SOLUTION:
The correct answer is C. | solid geometry | 3 | [
"$\\mathrm{E}_{\\mathrm{x}}=\\mathrm{E}_{\\mathrm{y}}$ and $\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{x}}\\right)=\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{y}}\\right)$",
"$\\mathrm{E}_{\\mathrm{x}}=\\mathrm{E}_{\\mathrm{y}}$ but $\\operatorname{Vol}\\left(\\mathrm{E}_{\\mathrm{x}}\\right) \\neq \\ope... |
322 | The flag of Kangoraland is a rectangle which is split into three equal rectangles as shown. How big is the ratio of the side lengths of the white rectangle?
Options:
A) $1: 2$
B) $2: 3$
C) $2: 5$
D) $3: 7$
E) $4: 9$ | A | ANSWER: A
SOLUTION:
The correct answer is A. | metric geometry - length | 5 | [
"$1: 2$",
"$2: 3$",
"$2: 5$",
"$3: 7$",
"$4: 9$"
] |
477 | Maria describes one of these five shapes in the following way: "It is not a square. It is grey. It is either round or three sided." Which shape did she describe?
Options:
A) A
B) B
C) C
D) D
E) E | B | ANSWER: B
SOLUTION:
The correct answer is B. | logic | 2 | [
"A",
"B",
"C",
"D",
"E"
] |
125 | In the Kangaroo constellation, all stars have a number greater than 3 and their sum is 20 . Which is the Kangaroo constellation?
Options:
A) A
B) B
C) C
D) D
E) E | B | ANSWER: B
SOLUTION:
The correct answer is B. | arithmetic | 2 | [
"A",
"B",
"C",
"D",
"E"
] |
331 | The points of intersection of the network of bars shown are labelled with the numbers 1 to 10. The sums $S$ of the four numbers on the vertices of each square are
all the same. What is the minimum value of $S$? | 20 | ANSWER: 20
SOLUTION:
The correct answer is 20. | algebra | 5 | [] |
223 | The sum of the number in each line, column and diagonal in the Ămagic squareñon the right is always constant. Only two numbers are visible. Which number is missing in field $a$?
Options:
A) 16
B) 51
C) 54
D) 55
E) 110 | D | ANSWER: D
SOLUTION:
The correct answer is D. | logic | 1 | [
"16",
"51",
"54",
"55",
"110"
] |
92 | The picture shows a mouse and a piece of cheese. The mouse is only allowed to move to the neighbouring fields in the direction of the arrows. How many paths are there from the mouse to the cheese? | 6 | ANSWER: 6
SOLUTION:
The correct answer is 6. | combinatorics | 1 | [] |
152 | The picture shows 5 cubes from the front. What do they look like from above?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | B | ANSWER: B
SOLUTION:
The correct answer is B. | descriptive geometry | 2 | [
"A",
"B",
"C",
"D",
"E"
] |
374 | A circle with midpoint $(0 \mid 0)$ has a radius of 5. How many points are there on the circumference where both co-ordinates are integers? | 12 | ANSWER: 12
SOLUTION:
The correct answer is 12. | analytic geometry | 4 | [] |
352 | A large square is divided into smaller squares, as shown. A shaded circle is inscribed inside each of the smaller squares. What proportion of the area of the large square is shaded?
Options:
A) $\frac{8 \pi}{9}$
B) $\frac{13 \pi}{16}$
C) $\frac{3}{\pi}$
D) $\frac{3}{4}$
E) $\frac{\pi}{4}$ | E | ANSWER: E
SOLUTION:
The correct answer is E. | metric geometry - area | 5 | [
"$\\frac{8 \\pi}{9}$",
"$\\frac{13 \\pi}{16}$",
"$\\frac{3}{\\pi}$",
"$\\frac{3}{4}$",
"$\\frac{\\pi}{4}$"
] |
45 | Which of the kangaroo cards shown below can be turned around so that it then looks the same as the card shown on the right?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | E | ANSWER: E
SOLUTION:
The correct answer is E. | transformation geometry | 2 | [
"A",
"B",
"C",
"D",
"E"
] |
85 | Which of these clouds contain only numbers that are smaller than 7 ?
Options:
A) A
B) B
C) C
D) D
E) E | D | ANSWER: D
SOLUTION:
The correct answer is D. | arithmetic | 2 | [
"A",
"B",
"C",
"D",
"E"
] |
109 | Numbers were written on the petals of two flowers, with a number on each petal. One of the petals is hidden. The sum of the numbers written on the back flower is twice the sum of the numbers written on the front flower. What is the number written on the hidden petal? | 30 | ANSWER: 30
SOLUTION:
The correct answer is 30. | arithmetic | 2 | [] |
185 | There are four cards on the table as in the picture. Every card has a letter on one side and a number on the other side. Peter said: "For every card on the table it is true that if there is a vowel on one side, there is an even number on the other side." What is the smallest number of cards Alice must turn in order to ... | 2 | ANSWER: 2
SOLUTION:
The correct answer is 2. | logic | 1 | [] |
78 | In order to get to his bone, the dog has to follow the black line. In total he turns 3-times to the right and 2-times to the left.
Which path does he take?
Options:
A) A
B) B
C) C
D) D
E) E | E | ANSWER: E
SOLUTION:
The correct answer is E. | counting | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
80 | Charles cuts a rope into 3 equally long pieces. Then he makes one knot in one of the pieces, 2 in the next and in the third piece 3 knots. Then he lays the three pieces down in a random order. Which picture does he see?
Options:
A) A
B) B
C) C
D) D
E) E | B | ANSWER: B
SOLUTION:
The correct answer is B. | metric geometry - length | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
194 | In how many ways can all the numbers $1,2,3,4,5,6$ be written in the squares of the figure (one in each square) so that there are no adjacent squares in which the difference of the numbers written is equal to 3? (Squares that share only a corner are not considered adjacent.)
Options:
A) $3 \cdot 2^{5}$
B) $3^{6}$
... | A | ANSWER: A
SOLUTION:
The correct answer is A. | combinatorics | 5 | [
"$3 \\cdot 2^{5}$",
"$3^{6}$",
"$6^{3}$",
"$2 \\cdot 3^{5}$",
"$3 \\cdot 5^{2}$"
] |
214 | We used metal rods to build this nice ensemble. We know there are 61 octagons. How many rods are there? | 446 | ANSWER: 446
SOLUTION:
The correct answer is 446. | algebra | 5 | [] |
472 | A large cube is made from 64 small cubes. The 5 visible faces of the large cube are green, the bottom face is red. How many of the small cubes have 3 green faces? | 4 | ANSWER: 4
SOLUTION:
The correct answer is 4. | counting | 2 | [] |
244 | A clock has three hands in different lengths (for seconds, minutes and hours). We don't know the length of each hand but we know that the clock shows the correct time. At 12:55:30 the hands are in the positions shown on the right. What does the clockface look like at 8:10:00?
<image2>
Options:
A) A
B) B
C) C
... | A | ANSWER: A
SOLUTION:
The correct answer is A. | algebra | 5 | [
"A",
"B",
"C",
"D",
"E"
] |
27 | Theresa moves a pencil along the line. She starts at the arrow shown. In which order will she go past the shapes?
Options:
A) $\Delta, \square, \bullet$
B) $\Delta, \bullet, \square$
C) $\bullet, \Delta, \square$
D) $\square, \Delta, \bullet$
E) $\square, \bullet, \Delta$ | A | ANSWER: A
SOLUTION:
The correct answer is A. | topology | 5 | [
"$\\Delta, \\square, \\bullet$",
"$\\Delta, \\bullet, \\square$",
"$\\bullet, \\Delta, \\square$",
"$\\square, \\Delta, \\bullet$",
"$\\square, \\bullet, \\Delta$"
] |
362 | The solid shown in the diagram has 12 regular pentagonal faces, the other faces being either equilateral triangles or squares. Each pentagonal face is surrounded by 5 square faces and each triangular face is surrounded by 3 square faces. John writes 1 on each triangular face, 5 on each pentagonal face and -1 on each sq... | 50 | ANSWER: 50
SOLUTION:
The correct answer is 50. | solid geometry | 3 | [] |
3 | Which kite has the longest string?
Options:
A) A
B) B
C) C
D) D
E) E | C | ANSWER: C
SOLUTION:
The correct answer is C. | metric geometry - length | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
344 | Two rectangular blocks and a cube are joined to form a larger rectangular block, which volume is $280 \mathrm{~cm}^{3}$. The cube, in dark gray in the picture, has volume equal to $125 \mathrm{~cm}^{3}$ and the smaller rectangular block has volume equal to $75 \mathrm{~cm}^{3}$. What is the area of the face marked with... | A | ANSWER: A
SOLUTION:
The correct answer is A. | solid geometry | 3 | [
"$16 \\mathrm{~cm}^{2}$",
"$18 \\mathrm{~cm}^{2}$",
"$20 \\mathrm{~cm}^{2}$",
"$24 \\mathrm{~cm}^{2}$",
"$56 \\mathrm{~cm}^{2}$"
] |
489 | Father hangs towels on the washing as shown in the picture. For three towels he uses 4 clothes pegs. How many clothes pegs would he use for 5 towels? | 6 | ANSWER: 6
SOLUTION:
The correct answer is 6. | arithmetic | 3 | [] |
305 | Nine whole numbers were written into the cells of a $3 \times 3$-table. The sum of these nine numbers is 500. We know that the numbers in two adjacent cells (with a common sideline) differ by exactly 1. Which number is in the middle cell? | 56 | ANSWER: 56
SOLUTION:
The correct answer is 56. | logic | 1 | [] |
153 | Each bowl has 4 balls. Add up the numbers on the balls. In which bowl is the result biggest?
Options:
A) A
B) B
C) C
D) D
E) E | A | ANSWER: A
SOLUTION:
The correct answer is A. | arithmetic | 2 | [
"A",
"B",
"C",
"D",
"E"
] |
59 | In the picture above we see a cube in two different positions.
The six sides of the cube look like this:
<image2>
Which side is opposite to <image3>?
<image4> | C | ANSWER: C
SOLUTION:
The correct answer is C. | solid geometry | 1 | [] |
73 | The same amount of kangaroos should be in both parks. How many kangaroos have to be moved from the left park to the right park for that to happen? | 5 | ANSWER: 5
SOLUTION:
The correct answer is 5. | arithmetic | 2 | [] |
193 | Points $M$ and $N$ are given on the sides $A B$ and $B C$ of a rectangle $A B C D$. Then the rectangle is divided into several parts as shown in the picture. The areas of 3 parts are also given in the picture. Find the area of the quadrilateral marked with "?". | 25 | ANSWER: 25
SOLUTION:
The correct answer is 25. | metric geometry - area | 5 | [] |
372 | The diagram shows a map with 16 towns which are connected via roads. The government is planning to build power plants in some towns. Each power plant can generate enough electricity for the town in which it stands as well as for its immediate neighbouring towns (i.e. towns that can be reached via a direct connecting ro... | 4 | ANSWER: 4
SOLUTION:
The correct answer is 4. | graph theory | 5 | [] |
319 | On an idealised rectangular billiard table with side lengths $3 \mathrm{~m}$ and $2 \mathrm{m}$ a ball (point-shaped) is pushed away from point $M$ on the long side $A B$. It is reflected exactly once on each of the other sides as shown. at which distance from the vertex $A$ will the ball hit this side again if $B M=1.... | E | ANSWER: E
SOLUTION:
The correct answer is E. | metric geometry - length | 5 | [
"$2 \\mathrm{~m}$",
"$1.5 \\mathrm{~m}$",
"$1.2 \\mathrm{~m}$",
"$2.8 \\mathrm{~m}$",
"$1.8 \\mathrm{~m}$"
] |
425 | Which of the following cubes has been folded out of the plan on the right?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | E | ANSWER: E
SOLUTION:
The correct answer is E. | descriptive geometry | 5 | [
"A",
"B",
"C",
"D",
"E"
] |
480 | In each square of the maze there is a piece of cheese. Ronnie the mouse wants to enter and leave the maze as shown in the picture. He doesn't want to visit a square more than once, but would like to eat as much cheese as possible. What is the maximum number of pieces of cheese that he can eat? | 37 | ANSWER: 37
SOLUTION:
The correct answer is 37. | graph theory | 2 | [] |
400 | The construction in the picture is built of cubes of the same size and weighs 189 grams. How many grams does one cube weigh? | 21 | ANSWER: 21
SOLUTION:
The correct answer is 21. | solid geometry | 5 | [] |
121 | Which of the paths shown in the pictures is the longest?
Options:
A) A
B) B
C) C
D) D
E) E | A | ANSWER: A
SOLUTION:
The correct answer is A. | counting | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
354 | The parabola in the figure has an equation of the form $y=a x^{2}+b x+c$ for some distinct real numbers $a, b$ and $c$. Which of the following equations could be an equation of the line in the figure?
Options:
A) $y=b x+c$
B) $y=c x+b$
C) $y=a x+b$
D) $y=a x+c$
E) $y=c x+a$ | D | ANSWER: D
SOLUTION:
The correct answer is D. | analytic geometry | 4 | [
"$y=b x+c$",
"$y=c x+b$",
"$y=a x+b$",
"$y=a x+c$",
"$y=c x+a$"
] |
286 | The diagram shows a circle with centre $O$ as well as a tangent that touches the circle in point $P$. The arc $A P$ has length 20, the arc $B P$ has length 16. What is the size of the angle $\angle A X P$?
Options:
A) $30^{\circ}$
B) $24^{\circ}$
C) $18^{\circ}$
D) $15^{\circ}$
E) $10^{\circ}$ | E | ANSWER: E
SOLUTION:
The correct answer is E. | metric geometry - angle | 4 | [
"$30^{\\circ}$",
"$24^{\\circ}$",
"$18^{\\circ}$",
"$15^{\\circ}$",
"$10^{\\circ}$"
] |
363 | On a circle 15 points are equally spaced. We can form triangles by joining any 3 of these. Congruent triangles, by rotation or reflection, are counted as only one triangle. How many different triangles can be drawn? | 19 | ANSWER: 19
SOLUTION:
The correct answer is 19. | combinatorics | 5 | [] |
179 | 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?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | A | ANSWER: A
SOLUTION:
The correct answer is A. | combinatorial geometry | 5 | [
"A",
"B",
"C",
"D",
"E"
] |
248 | How big is the angle $\alpha$ in the regular five-sided star shown?
Options:
A) $24^{\circ}$
B) $30^{\circ}$
C) $36^{\circ}$
D) $45^{\circ}$
E) $72^{\circ}$ | C | ANSWER: C
SOLUTION:
The correct answer is C. | metric geometry - angle | 4 | [
"$24^{\\circ}$",
"$30^{\\circ}$",
"$36^{\\circ}$",
"$45^{\\circ}$",
"$72^{\\circ}$"
] |
491 | Mike and Jake play darts. Each of them throws three darts. Who won, and by how many points?
Mike:
Jake: <image2>
Options:
A) Mike won. He had 3 points more.
B) Jake won. He had 4 points more.
C) Mike won. He had 2 points more.
D) Jake won. He had 2 points more.
E) Mike won. He had 4 points more. | E | ANSWER: E
SOLUTION:
The correct answer is E. | arithmetic | 3 | [
"Mike won. He had 3 points more.",
"Jake won. He had 4 points more.",
"Mike won. He had 2 points more.",
"Jake won. He had 2 points more.",
"Mike won. He had 4 points more."
] |
51 | How many ropes can you see in this picture? | 3 | ANSWER: 3
SOLUTION:
The correct answer is 3. | topology | 5 | [] |
449 | Rebecca has drawn a point on a sheet of paper. She now draws four straight lines that pass through this point. Into how many sections do these lines divide the paper? | 8 | ANSWER: 8
SOLUTION:
The correct answer is 8. | algebra | 2 | [] |
270 | In the diagram a closed polygon can be seen whose vertices are the midpoints of the edges of the die. The interior angles are as usual defined as the angle that two sides of the polygon describe in a common vertex. How big is the sum of all interior angles of the polygon?
Options:
A) $720^{\circ}$
B) $1080^{\circ}... | B | ANSWER: B
SOLUTION:
The correct answer is B. | solid geometry | 3 | [
"$720^{\\circ}$",
"$1080^{\\circ}$",
"$1200^{\\circ}$",
"$1440^{\\circ}$",
"$1800^{\\circ}$"
] |
370 | We check the water meter and see that all digits on the display are different. What is the minimum amount of water that has to be used before this happens again?
Options:
A) $0.006 \mathrm{~m}^{3}$
B) $0.034 \mathrm{~m}^{3}$
C) $0.086 \mathrm{~m}^{3}$
D) $0.137 \mathrm{~m}^{3}$
E) $1.048 \mathrm{~m}^{3}$ | D | ANSWER: D
SOLUTION:
The correct answer is D. | arithmetic | 1 | [
"$0.006 \\mathrm{~m}^{3}$",
"$0.034 \\mathrm{~m}^{3}$",
"$0.086 \\mathrm{~m}^{3}$",
"$0.137 \\mathrm{~m}^{3}$",
"$1.048 \\mathrm{~m}^{3}$"
] |
412 | There are five houses on Color Street: a blue, a red, a yellow, a pink, and a green one. The houses are numbered from 1 to 5 (see picture). The red house is the neighbor of the blue house only. The blue house stands between the green and red houses.
Which color is the house with number 3?
Options:
A) Blue
B) Red
... | E | ANSWER: E
SOLUTION:
The correct answer is E. | logic | 2 | [
"Blue",
"Red",
"Yellow",
"Pink",
"Green"
] |
485 | The picture shows a Fortress made from cubes. How many cubes were used to make it? | 56 | ANSWER: 56
SOLUTION:
The correct answer is 56. | solid geometry | 5 | [] |
282 | Maria wants to build a bridge across a river. This river has the special feature that from each point along one shore the shortest possible bridge to the other shore has always got the same length. Which of the following diagrams is definitely not a sketch of this river?
Options:
A) A
B) B
C) C
D) D
E) E | B | ANSWER: B
SOLUTION:
The correct answer is B. | metric geometry - length | 5 | [
"A",
"B",
"C",
"D",
"E"
] |
294 | On the number wall shown the number on each tile is equal to the sum of the numbers on the two tiles directly below it. Which number is on the tile marked with "?"? | 16 | ANSWER: 16
SOLUTION:
The correct answer is 16. | algebra | 5 | [] |
265 | The ratio of the radii of two concentric circles is $1: 3$. The line $A C$ a diameter of the biggest circle. A chord $B C$ of the big circle touches the small circle (see diagram). The line $A B$ has length 12. How big is the radius of the big circle? | 18 | ANSWER: 18
SOLUTION:
The correct answer is 18. | metric geometry - length | 5 | [] |
295 | In the diagram we see 10 islands that are connected by 15 bridges. What is the minimum number of bridges that need to be closed off so that there is no connection from $A$ to $B$ anymore? | 3 | ANSWER: 3
SOLUTION:
The correct answer is 3. | graph theory | 5 | [] |
378 | The numbers 1 to 10 were written into the ten circles in the pattern shown in the picture. The sum of the four numbers in the left and the right column is 24 each and the sum of the three numbers in the bottom row is 25. Which number is in the circle with the question mark?
Options:
A) 2
B) 4
C) 5
D) 6
E) an... | E | ANSWER: E
SOLUTION:
The correct answer is E. | algebra | 5 | [
"2",
"4",
"5",
"6",
"another number"
] |
342 | A large square touches another two squares, as shown in the picture. The numbers inside the smaller squares indicate their areas. What is the area of the largest square? | 13 | ANSWER: 13
SOLUTION:
The correct answer is 13. | metric geometry - area | 5 | [] |
351 | Paula's weather app shows a diagram of the predicted weather and maximum temperatures for the next seven days, as shown. Which of the following represents the corresponding graph of maximum temperatures?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | E | ANSWER: E
SOLUTION:
The correct answer is E. | statistics | 3 | [
"A",
"B",
"C",
"D",
"E"
] |
285 | The rectangles $S_{1}$ and $S_{2}$ shown in the picture have the same area. Determine the ratio $x: y$.
Options:
A) $1: 1$
B) $3: 2$
C) $4: 3$
D) $7: 4$
E) $8: 5$ | E | ANSWER: E
SOLUTION:
The correct answer is E. | analytic geometry | 4 | [
"$1: 1$",
"$3: 2$",
"$4: 3$",
"$7: 4$",
"$8: 5$"
] |
300 | Three circles with centres $A, B, C$ touch each other in pairs from the outside (see diagram). Their radii are 3,2 and 1. How big is the area of the triangle $A B C$? | 6 | ANSWER: 6
SOLUTION:
The correct answer is 6. | metric geometry - area | 5 | [] |
102 | A magician takes animals out of his hat always in the same order, as shown below.
The pattern of the figure is repeated every five animals. What will be the fourteenth animal he will pull out of his hat?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | A | ANSWER: A
SOLUTION:
The correct answer is A. | combinatorics | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
247 | A rectangular piece of paper $A B C D$ with the measurements $4 \mathrm{~cm} \times 16 \mathrm{~cm}$ is folded along the line $\mathrm{MN}$ so that point $C$ coincides with point $A$ as shown. How big is the area of the quadrilateral ANMD'?
Options:
A) $28 \mathrm{~cm}^{2}$
B) $30 \mathrm{~cm}^{2}$
C) $32 \mathr... | C | ANSWER: C
SOLUTION:
The correct answer is C. | transformation geometry | 5 | [
"$28 \\mathrm{~cm}^{2}$",
"$30 \\mathrm{~cm}^{2}$",
"$32 \\mathrm{~cm}^{2}$",
"$48 \\mathrm{~cm}^{2}$",
"$56 \\mathrm{~cm}^{2}$"
] |
184 | We consider the perimeter and the area of the region corresponding to the grey squares. How many more squares can we colour grey for the grey area to increase without increasing its perimeter? | 16 | ANSWER: 16
SOLUTION:
The correct answer is 16. | combinatorial geometry | 5 | [] |
479 | A page is folded along the thick line as shown. Which letter will not be covered by a grey square?
Options:
A) A
B) B
C) C
D) D
E) E | E | ANSWER: E
SOLUTION:
The correct answer is E. | transformation geometry | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
212 | A circle is inscribed in the triangle $A B C$ (see the figure), $A C=5, A B=6, B C=3$. The segment $E D$ is tangent to the circle. The perimeter of the triangle $A D E$ is | 8 | ANSWER: 8
SOLUTION:
The correct answer is 8. | metric geometry - length | 5 | [] |
494 | You need 3 pieces to build this shape. Each piece is made out of 4 , equally sized cubes of the same colour. What is the shape of the white piece?
<image2>
Options:
A) (A)
B) (B)
C) (C)
D) (D)
E) (E) | D | ANSWER: D
SOLUTION:
The correct answer is D. | descriptive geometry | 5 | [
"(A)",
"(B)",
"(C)",
"(D)",
"(E)"
] |
65 | Jim and Ben are sitting in a ferris wheel (see picture on the right). The ferris wheel is turning. Now Ben is in the position where Jim was beforehand. Where is Jim now?
<image2>
Options:
A) A
B) B
C) C
D) D
E) E | C | ANSWER: C
SOLUTION:
The correct answer is C. | transformation geometry | 2 | [
"A",
"B",
"C",
"D",
"E"
] |
439 | Zita walks from left to right and puts the numbers into her basket. Which of the following numbers can be in her basket?
Options:
A) 1, 2 and 4
B) 2, 3 and 4
C) 2, 3 and 5
D) 1, 5 and 6
E) 1, 2 and 5 | C | ANSWER: C
SOLUTION:
The correct answer is C. | graph theory | 2 | [
"1, 2 and 4",
"2, 3 and 4",
"2, 3 and 5",
"1, 5 and 6",
"1, 2 and 5"
] |
155 | Sara says: "My boat has more than one circle. It also has 2 triangles more than squares." Which boat belongs to Sara?
Options:
A) A
B) B
C) C
D) D
E) E | E | ANSWER: E
SOLUTION:
The correct answer is E. | counting | 1 | [
"A",
"B",
"C",
"D",
"E"
] |
345 | The figure shows the lines $r$ and $s$, which equations are, respectively, $y=a x
+b$ e $y=c x+d$. Which of the following statements is true?
Options:
A) $a b+c d<0$
B) $a+b+c+d<0$
C) $a c+b d \geq 0$
D) $a+b+c+d>0$
E) $a b c d>0$ | A | ANSWER: A
SOLUTION:
The correct answer is A. | analytic geometry | 4 | [
"$a b+c d<0$",
"$a+b+c+d<0$",
"$a c+b d \\geq 0$",
"$a+b+c+d>0$",
"$a b c d>0$"
] |
231 | A strip of paper is folded three times as shown. Determine $\beta$ if $\alpha=70^{\circ}$.
Options:
A) $140^{\circ}$
B) $130^{\circ}$
C) $120^{\circ}$
D) $110^{\circ}$
E) $100^{\circ}$ | C | ANSWER: C
SOLUTION:
The correct answer is C. | transformation geometry | 5 | [
"$140^{\\circ}$",
"$130^{\\circ}$",
"$120^{\\circ}$",
"$110^{\\circ}$",
"$100^{\\circ}$"
] |
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