Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>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>
Choices:
A. $1 \mathrm{~cm}^{2}$
B. $4 \mathrm{~cm}^{2}$
C. $9 \mathrm{~cm}^{2}$
D. $16 \mathrm{~cm}^{2}$
E. $25 \mathrm{~cm}^{2}$
Answer: A
Problem: <image>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>
Choices:
A. $3,5,4,2,1$
B. $3,4,5,1,2$
C. $3,2,1,4,5$
D. $3,1,2,4,5$
E. $3,4,2,1,5$
Answer: E
Problem: <image>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>
Choices:
A. $112.5^{\circ}$
B. $120^{\circ}$
C. $125^{\circ}$
D. $135^{\circ}$
E. $150^{\circ}$
Answer: A
Problem: <image>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, as shown. How many points does Adam get from judge III? <image1>
Answer: 1
Problem: <image>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 spheres, a blob of glue is placed. How many blobs of glue will Cleo place?
<image1>
Answer: 96
Problem: <image>Question: The statements on the right give clues to the identity of a four-digit number.
<image1>
What is the last digit of the four-digit number?
Answer: 3
Problem: <image>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>
Answer: -100
Problem: <image>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?
<image1>
Answer: 13837
Problem: <image>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>
Choices:
A. $3 \mathrm{~cm}^{2}$
B. $\frac{7}{2} \mathrm{~cm}^{2}$
C. $4 \mathrm{~cm}^{2}$
D. $\frac{11}{2} \mathrm{~cm}^{2}$
E. $6 \mathrm{~cm}^{2}$
Answer: C
Problem: <image>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. What is the length in centimetres of the overlap between any pair of adjacent planks? <image1>
Answer: 2.5
Problem: <image>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>
Answer: 6
Problem: <image>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 Downend is $7 \mathrm{~km}$ longer than the direct path. What is the length of the shortest of the three direct paths between the villages?
<image1>
Choices:
A. $1 \mathrm{~km}$
B. $2 \mathrm{~km}$
C. $3 \mathrm{~km}$
D. $4 \mathrm{~km}$
E. $5 \mathrm{~km}$
Answer: C
Problem: <image>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.
<image1>
The diagrams show the labels on the cannonballs on three of the faces of the pyramid. What is the label on the hidden cannonball in the middle of the fourth face?
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>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>
Answer: 20
Problem: <image>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 journey? <image1>
Answer: 10
Problem: <image>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 against team U?
<image1>
Answer: 1
Problem: <image>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 .
<image1>
Which of these numbers will Kanga land on?
Choices:
A. 82
B. 83
C. 84
D. 85
E. 86
Answer: C
Problem: <image>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>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: B
Problem: <image>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>
Answer: 58
Problem: <image>Question: Tony the gardener planted tulips $\mathbb{P}$ and daisies in a square flowerbed of side-length $12 \mathrm{~m}$, arranged as shown
What is the total area, in $\mathrm{m}^{2}$, of the regions in which he planted daisies? <image1>
Answer: 48
Problem: <image>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.
What will be the sum of the numbers in the three circles at the bottom of the diagram?
<image1>
Answer: 17
Problem: <image>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>
Choices:
A. $20 \%$
B. $25 \%$
C. $30 \%$
D. $33 \frac{1}{3} \%$
E. $35 \%$
Answer: B
Problem: <image>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.
Which number should she write in the fourth corner cell?
<image1>
Answer: 1
Problem: <image>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>
Choices:
A. $3: 2$
B. $4: 3$
C. $8: 5$
D. $12: 7$
E. $7: 3$
Answer: D
Problem: <image>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 .
What is the surface area of the original brick?
<image1>
Answer: 54
Problem: <image>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>
Answer: 6
Problem: <image>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 $Q T=R T$.
What is the size, in degrees, of angle $Q P R$ ? <image1>
Answer: 36
Problem: <image>Question: Which of the shapes below cannot be divided into two trapeziums by a single straight line?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: A
Problem: <image>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>
Answer: 12
Problem: <image>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>
Choices:
A. $2: 6: 9$
B. $2: 6: 6$
C. $5: 6: 9$
D. $2: 8: 6$
E. $5: 8: 9$
Answer: C
Problem: <image>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 in the shaded box? <image1>
Answer: 7
Problem: <image>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>
Answer: 6
Problem: <image>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>
Choices:
A. $55^{\circ}$
B. $60^{\circ}$
C. $65^{\circ}$
D. $70^{\circ}$
E. $75^{\circ}$
Answer: D
Problem: <image>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>
Answer: 40
Problem: <image>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 lie on the other two sides of the larger rectangle. What is the area, in $\mathrm{cm}^{2}$, of the larger rectangle? <image1>
Answer: 150
Problem: <image>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>
Answer: 16
Problem: <image>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 the diagram? <image1>
Answer: 11
Problem: <image>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 will the number 77 occur in the sum? <image1>
Answer: 6
Problem: <image>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>
Choices:
A. $54 \mathrm{~cm}$
B. $72 \mathrm{~cm}$
C. $80 \mathrm{~cm}$
D. $88 \mathrm{~cm}$
E. $90 \mathrm{~cm}$
Answer: E
Problem: <image>Question: In the diagram, five rectangles of the same size are shown with each side labelled with a number.
<image1>
These rectangles are placed in the positions I to $\mathrm{V}$ as shown so that the numbers on the sides that touch each other are equal.
<image2>
Which of the rectangles should be placed in position I?
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>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>
Answer: 82
Problem: <image>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 $S \times T$ ?
<image1>
Answer: 70
Problem: <image>Question: In the diagram, the small equilateral triangles have area $4 \mathrm{~cm}^{2}$. What is the area of the shaded region? <image1>
Choices:
A. $80 \mathrm{~cm}^{2}$
B. $90 \mathrm{~cm}^{2}$
C. $100 \mathrm{~cm}^{2}$
D. $110 \mathrm{~cm}^{2}$
E. $120 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: In the sum shown, different shapes represent different digits.
<image1>
What digit does the square represent?
Answer: 6
Problem: <image>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.
<image1>
What is the ratio of the area of the shaded parts of the circles to the area of the unshaded parts of the circles?
Choices:
A. $1: 3$
B. $1: 4$
C. $2: 5$
D. $2: 3$
E. $5: 4$
Answer: D
Problem: <image>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>
Choices:
A. $1 \mathrm{~m}$
B. $2 \mathrm{~m}$
C. $3 \mathrm{~m}$
D. $4 \mathrm{~m}$
E. $5 \mathrm{~m}$
Answer: C
Problem: <image>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.
<image1>
How many black tiles would be required to create the 15th shape in the sequence?
Answer: 421
Problem: <image>Question: <image1>
The 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 $\mathrm{V}$ ?
Answer: 540
Problem: <image>Question: It takes 9 litres of paint to cover the surface of the cube on the left.
<image1>
How much paint would it take to cover the surface of the shape on the right?
Choices:
A. 9 litres
B. 8 litres
C. 6 litres
D. 4 litres
E. 2 litres
Answer: A
Problem: <image>Question: Which of the following nets can be used to build the partial cube shown in the diagram?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>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>
Choices:
A. Six-pointed star
B. Dodecagon
C. Hexagon
D. Square
E. Equilateral Triangle
Answer: E
Problem: <image>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.
<image1>
What is the perimeter of the star?
Choices:
A. $40 \mathrm{~cm}$
B. $80 \mathrm{~cm}$
C. $120 \mathrm{~cm}$
D. $160 \mathrm{~cm}$
E. $200 \mathrm{~cm}$
Answer: D
Problem: <image>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 $A G$.
<image1>
What is the area of the shaded rectangle?
Choices:
A. $\frac{1}{16} \mathrm{~m}^{2}$
B. $\frac{1}{8} \mathrm{~m}^{2}$
C. $\frac{1}{4} \mathrm{~m}^{2}$
D. $\frac{1}{2} \mathrm{~m}^{2}$
E. $1 \mathrm{~m}^{2}$
Answer: C
Problem: <image>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.
<image1>
What is the perimeter of the shape drawn with a dark line?
Choices:
A. $10 \mathrm{~cm}$
B. $16 \mathrm{~cm}$
C. $20 \mathrm{~cm}$
D. $24 \mathrm{~cm}$
E. $30 \mathrm{~cm}$
Answer: C
Problem: <image>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 finishes at point $B$. What is the
<image1>
maximum number of days that he can walk without repeating the order in which he crosses the bridges?
Answer: 6
Problem: <image>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>
Choices:
A. $400 \mathrm{~cm}^{2}$
B. $200 \mathrm{~cm}^{2}$
C. $160 \mathrm{~cm}^{2}$
D. $120 \mathrm{~cm}^{2}$
E. $80 \mathrm{~cm}^{2}$
Answer: A
Problem: <image>Question: The diagram shows five congruent right-angled isosceles triangles. What is the total area of the triangles? <image1>
Choices:
A. $25 \mathrm{~cm}^{2}$
B. $30 \mathrm{~cm}^{2}$
C. $35 \mathrm{~cm}^{2}$
D. $45 \mathrm{~cm}^{2}$
E. $60 \mathrm{~cm}^{2}$
Answer: D
Problem: <image>Question: In the addition sum below, $a, b$ and $c$ stand for different digits.
<image1>
What is the value of $a+b+c$ ?
Answer: 16
Problem: <image>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>
Answer: 4
Problem: <image>Question: Beattie wants to walk from $P$ to $Q$ along the paths shown, always moving in the direction from $P$ to $Q$.
<image1>
She will add the numbers on the paths she walks along. How many different totals could she obtain?
Answer: 4
Problem: <image>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?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>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.
<image1>
What is the sum of the lengths of the lines that she draws?
Choices:
A. $18 \mathrm{~cm}$
B. $17 \mathrm{~cm}$
C. $20 \mathrm{~cm}$
D. $19 \mathrm{~cm}$
E. It depends upon the sizes of the rectangles
Answer: A
Problem: <image>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>
Answer: 5
Problem: <image>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>
Choices:
A. More information needed
B. $60 \mathrm{~cm}^{2}$
C. $100 \mathrm{~cm}^{2}$
D. $110 \mathrm{~cm}^{2}$
E. $120 \mathrm{~cm}^{2}$
Answer: E
Problem: <image>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?
<image1>
Choices:
A. $48 \mathrm{~cm}$
B. $60 \mathrm{~cm}$
C. $66 \mathrm{~cm}$
D. $72 \mathrm{~cm}$
E. $96 \mathrm{~cm}$
Answer: D
Problem: <image>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 the second shape than the perimeter of the first shape? <image1>
Choices:
A. $75 \mathrm{~cm}$
B. $50 \mathrm{~cm}$
C. $25 \mathrm{~cm}$
D. $20 \mathrm{~cm}$
E. $0 \mathrm{~cm}$
Answer: B
Problem: <image>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>
Choices:
A. $8 \mathrm{~cm}$
B. $8.5 \mathrm{~cm}$
C. $9 \mathrm{~cm}$
D. $9.5 \mathrm{~cm}$
E. $10 \mathrm{~cm}$
Answer: E
Problem: <image>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>
Choices:
A. $1 \mathrm{~cm}^{2}$
B. $2 \mathrm{~cm}^{2}$
C. $\frac{1}{2} \mathrm{~cm}^{2}$
D. $1 \frac{1}{2} \mathrm{~cm}^{2}$
E. $\frac{3}{4} \mathrm{~cm}^{2}$
Answer: A
Problem: <image>Question: Rory uses four identical standard dice to build the solid shown in the diagram.
Whenever 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?
(On a standard die, the numbers on opposite faces add to 7.)
<image1>
Answer: 5
Problem: <image>Question: Three congruent isosceles trapeziums are assembled to form an equilateral triangle with a hole in the middle, as shown in the diagram.
<image1>
What is the perimeter of the hole?
Choices:
A. $3 a+6 b$
B. $3 b-6 a$
C. $6 b-3 a$
D. $6 a+3 b$
E. $6 a-3 b$
Answer: E
Problem: <image>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?
<image1>
Answer: 2
Problem: <image>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?
<image1>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: E
Problem: <image>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>
Choices:
A. $35^{\circ}$
B. $30^{\circ}$
C. $25^{\circ}$
D. $20^{\circ}$
E. $15^{\circ}$
Answer: A
Problem: <image>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 number is on the card he places in the top left cell?
<image1>
Answer: 3
Problem: <image>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?
<image1>
Answer: 9
Problem: <image>Question: The diagram below shows five rectangles, each containing some of the letters $\mathrm{P}, \mathrm{R}, \mathrm{I}, \mathrm{S}$ and $\mathrm{M}$.
<image1>
Harry wants to cross out letters so that each rectangle contains only one letter and each rectangle contains a different letter. Which letter does he not cross out in rectangle 2?
Choices:
A. P
B. R
C. I
D. S
E. M
Answer: B