Problem 1. Basil wants to paint the slogan Vivat Kangaroo on a wall. He wants to paint different letters different colors, and the same letters the same color. How many colors will he need? If you want to paint the slogan Vivat Kangaroo, and you want to paint each letter a different color, you have to count how many different kinds of letters there are. There are 2 V's 1 I 3 A's 1 T 1 K 1 N 1 G 1 R and 2 O's That means there are 1 2 3 4 5 6 7 8 9 different letters. So the correct answer is C. Problem 2. A blackboard is 6 meters wide. The width of the middle part is 3 meters. The two other parts have equal width. How wide is the right-hand part? In this problem, we know that the total blackboard is 6 meters wide. We also know that the middle part of the blackboard is 3 meters wide. So if we subtract 3 from the total of 6, we know that the rest of the blackboard is going to be 3 meters. Since we know it's 3 meters, and that part is divided into two equal pieces, we can divide 3 by 2, and then we know that the other two pieces of the blackboard are each 1.5 meters wide. So the correct answer is C. Problem 3. Sally can put 4 coins in a square made using 4 matches. See picture. At least how many matches will she need in order to make a square containing 16 coins that do not overlap? We want to create a square that will hold 16 coins. Now we know that 16 is equal to 4 times 4. That means that the size of the square, the area of the square that we want, is going to be 4 times bigger than this area of the square right here, because we want 16 coins. Now, we also know that the area of a square is equal to its side squared. So the area of this square, which is equal to 1 match length, is going to be 1 squared, which is equal to 1. Now, since we know that we want an area that is 4 times bigger, we know that we're going to want an area that is going to equal to 4. Now, we know that to find the side of that square, we have to take a square root of 4, which is equal to 2. That means that each side of that square is going to have 2 match lengths, like this, 1, 2, 3, 4, 5, 6, 7, 8, so that we know that the square that holds 16 coins is equal to 8 matches. So, the correct answer is A. Problem 4. On a certain plane, the rows are numbered from 1 to 25, but there is no row number 13. Row number 15 has only 4 passenger seats. All the other rows have 6 passenger seats. How many seats for passengers are there on this plane? In this problem, we start off with 25 rows. However, row 13 doesn't exist, so there are really only 24 rows. And then we know that out of those 24, 1 only has 4 seats in it, and all the other rows, 1 times 4 is equal to 4, and all the other rows, which are 23 rows, have 6 seats in them, which equals 138 seats. So, when we add 138 plus 4, we get 142 seats total. That means the correct answer is C. Problem 5. When it is 4 o'clock in the afternoon in London, it is 5 o'clock in the afternoon in Madrid, and it is 8 o'clock in the afternoon on the same day in San Francisco. Anne went to bed in San Francisco at 9 o'clock yesterday evening. What was the time in Madrid at that moment? To solve this problem, we have to understand that 5 p.m. can also be written as 17 in the afternoon, because 12, which is noon, plus 5 hours after noon is equal to 17. So, since we know that Anne went to sleep in San Francisco at 9 o'clock yesterday evening, we know that she went to sleep 3 hours before midnight. So, she went to bed 3 hours plus 8 hours, because it is currently 8 o'clock in the morning in San Francisco. We know that she went to sleep 11 hours ago. And since we know that in Madrid it is currently 17 hours after midnight, we can subtract 11 hours and know that Anne went to sleep at 6 o'clock in the morning. Madrid time, which means that the correct answer is E. Problem 6. The picture to the right shows a pattern of hexagons. We draw a new pattern by connecting all the midpoints of neighboring hexagons. Which of the figures below do we get? To solve this problem, all we have to do is understand what the midpoint of a hexagon is. The midpoint is the middle. So, all we have to do is figure out where the middle of these hexagons is, which is basically here where I am drawing it. As you can see, the pattern that has emerged is the pattern that you see in C. Problem 7. To the number 6, we add 3. Then we multiply the result by 2, and then we add 1. Then the final result will be the same as the result of the computation. To get the correct result, we have to carefully read this problem. First, to the number 6, we add 3. Then we multiply the result by 2. That means we put the 6 plus 3 in parentheses, and multiply it times 2, and then we add 1. So the final result is just like the equation in D. Problem 8. The upper coin is rotated without slipping around the fixed lower coin, to a position shown in the picture. Which is the resulting relative position of kangaroos? To begin with, let's enlarge this illustration. As you can see, what we want to do is rotate the top coin around the bottom coin. These are equally sized coins, which is important. First, let's find the center point of each of these coins. Now as you can see, if I draw a line from the point where they touch, to the point where they are going to touch, you'll see that this is a 90 degree arc, right here. And since these two coins are exactly the same, this 90 degree arc is going to be exactly the same as this bottom one. So that when this point A is rotating along this arc, it'll stop at point B. And then we will see, once that process of rotation is finished, that the coin will end up having rotated all the way 180 degrees upside down. And so the correct answer is A. Problem 9. One balloon can lift a basket containing items weighing at most 80 kilograms. Two such balloons can lift the same basket containing items weighing at most 180 kilograms. What is the weight of the basket? In this problem, we know that one balloon can carry 80 kilograms plus one basket. And we know that two balloons can carry 180 kilograms plus one basket. So if we subtract everything, we know that one balloon can carry 100 kilograms. And so we know that 100 kilograms is equal to 80 kilograms plus one basket. So if we subtract minus 80 is equal to a basket, we know that 20 kilograms is equal to a basket. And so the correct answer is B. Problem 10. Vivian and Mike were given some apples and pears by their grandmother. They had 25 pieces of fruit in their basket altogether. On the way home, Vivian ate one apple and three pears. And Mike ate three apples and two pears. At home, they found out that they brought home the same number of pears as apples. How many pears were they given by their grandmother? We know that Vivian and Mike were given 25 fruits by their grandmother. And we know that on their walk, that Vivian ate one apple and three pears. And that Mike ate three apples and two pears. That's a total of four apples and a total of five pears, which together equal nine fruits. So that means that if we subtract 9 from 25, that means they came home with 16 fruits. And we know that they came home with the same amount of pears and apples, so that means they came home with 8 apples and 8 pears. So if we add 8 pears plus the 5 pears that they ate during the walk, you get a total of 13 pears that they started out with. So the correct answer is B.

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