This is the Math Kangaroo Solutions Video Library, with problems for Levels 1 and 2 from the year 2007, presented by Agata Ghazal. The purpose of the Math Kangaroo Solutions Video Library is to help you learn how to solve math problems, such as those presented in the Math Kangaroo Competition. Let me start with a few tips of how to best utilize these solutions. First, make sure that you read the problem, and in this case, listen to it carefully. This will help you understand what kind of information you need to solve the problem. After reading the problem, I will wait for a few seconds. Please use this opportunity to pause the video and try solving the problem on your own. If you get stuck, don't worry. I will start the presentation of the solution with a hint of how to arrive at the correct answer. You can pause the video again at this point and try to finish the problem. My presentation of the solution will follow. Keep in mind that there might be ways of solving the problem other than what I present. I hope that you will learn something new from each problem you attempt, and most importantly, that you will have fun. Problem number one. Which toy is in front of the fifth toy? First, number the toys from left to right to find out which toy is the fifth toy. Toy A will be toy number one, toy B will be toy number two, toy C will be toy number three, toy D will be toy number four, and toy E will be toy number five. So E is the fifth toy. The one directly in front of it is the fourth toy, which is toy D. So it's this one. The answer is D. Question number two. Which number is covered with a question mark? To solve this problem, it is easiest to just do the operations in order until you get to the last car. Let's start with the first operation. The engine has a number one on it, so we will do one plus one to find the number that should go in the first car. One plus one equals two, so we'll put the number two right here. Then we will solve the next operation. Two plus two, two plus two equals four. We'll put four right here. Then we will do four minus three. Four minus three equals one. Put one here. One plus two, one plus two equals three. With three in the next to last car. Then to find the car, the number for the car at the very end, we will do three minus one, which is two. Number covered with a question mark is two, which is answer B. Problem three. How many bicycles can you see in the picture? Hint, think of something that you would only see one of on each bicycle. We'll figure out how many bicycles there are by finding how many bicycle seats we can see. Here's one, here's two, here's three, here's four, and here's five. Obviously, there's one bicycle seat on each bicycle, so there are five bicycles in the picture. The answer is C, five. Problem four. Find the value of each letter, R, A, C, and place the letters in increasing order according to their values. Which word do you get? We are told seven minus two equals R, one plus three equals A, ten minus eight equals C. Start by finding the values of the letters. The value of R will be seven minus two, which is five. The value of A will be one plus three, which is four. The value of C will be ten minus eight, which is two. Now we need to put these values in order from smallest to largest. Our smallest value is two, which is the letter C. The next value is four, which is the letter A, and our largest value is five, which is the letter R. So our word is car, and the answer is A. Problem five. Which elf does not appear in the big picture? If one of the five elves listed with the answers A, B, C, D, and E doesn't appear in the picture, that means that four of them do. Find the ones that do appear in the picture. Let's see if we can find elf A. Can I see him? Right there. Elf B? Here. Elf C? Here. Elf D? Hmm, I don't see an elf with these orange shorts like he has, but let's see if maybe elf E is easier to find. Yes, he's right here. So elf D is the one that does not appear in the picture. Problem number six. From the number of 101 Dalmatians from the animated film, take away the number of Snow White's seven dwarves. What number do you come up with? This is a simple problem where we are subtracting one number from another, but it might help to get down to 100 before subtracting further. First take the number of 101 Dalmatians, 101, minus the number of the seven dwarves, which is 7. Let's think of 7 as 1 and 6. So we can make our problem a little easier, thinking of it as 101 minus 1 minus 6, which is 100, that's 101 minus 1. And then minus 6, which will be 94. So our answer is D, 94. Problem number seven. There are five kinds of dinosaurs in a bag. Of which kind are there the most? You can try using tally marks to keep track of what dinosaurs you see. Let's start in the upper left hand corner. We see this green guy, that's one here, this green one, one over here, orange, purple, orange spiky dinosaur, purple, green t-rex, another green t-rex, another green t-rex, Purple Dinosaur, Green Velociraptor, Orange Dinosaur, and Orange Spiky Dinosaur. So we see that there are three dinosaurs of each kind, except for Dinosaur C, of which there are four. So the answer is C. Problem 8. The road sign shows the distance between villages. How far is it from Behayesti to Mormayesti? The road sign shows Behayesti is to the left of us and Mormayesti is to the right of us, so we're between the two villages. Let's imagine that we are on a road. Here is our road, and here is the sign. It shows that Behayesti is four kilometers this way, and Mormayesti is five kilometers the opposite direction. So to find the total distance, we will need to add the two numbers. So we add four plus five, which is equal to nine. So our answer is A, nine kilometers. It is nine kilometers from Behayesti to Mormayesti. Problem 9. Which letter is missing from each of the words below? Think about simple words. It looks to me like the first word is probably supposed to be school. The second one might be book. The third would probably be problem. And the last one would be question. In each one of those, what is missing is the letter O. School, book, problem, question. So the answer is C. The letter that is missing from each of those words is O. Problem 10. The picture can help you see how old each child is. Which sentence is true? And here are our choices. A. Maria is six years old. B. Maria is seven years old. C. Christy is nine years old. D. Christy is seven years old. E. Christy is eight years old. We will need to follow the paths to find the age of each of the girls. I have made the picture a little bigger so that we can see it better. Let's start with finding out Maria's age. We'll start right here and follow the path. This way. Those tangles. And Maria is eight years old. Now, let's find Christy's age. Start right here. Goes all the way around here. Oops, south. And Christy is seven years old. Now, among our choices, there is only one that is correct. And that is Christy is seven years old. There is no choice here that says that Maria is eight years old. Our answer is D. Christy is seven years old. Problem eleven. When we left, we had filled the gas tank. Fifty liters. When returning, the indicator pointed as shown in the picture. How many liters did we use? Use the number of liters at the beginning and the number of liters remaining to find how many liters were used. Here is a bigger picture of our indicator. The arrow points to the number 30, which is how many liters we have remaining. We started with 50 liters. So, we need to find the difference between 50 and 30 to find how many liters of gasoline we used up. 50 minus 30 is 20. So, we used 20 liters. The answer is B. Problem twelve. Michael glued three cubes together as shown in the picture. And then he covered all of them with paint. How many squares did he paint? Hint. Look at the cubes and think about not only the sides that you see from the picture that is shown, but also the sides that you would see if you rotated the figure. We can first count the number of squares or sides that we see in the figure as it was shown to us in the picture. There is one, two, three, four, five, six, seven. There are seven sides as we can see here. But let's imagine what would happen if we flipped the figure and looked at it from the back, as well as on the two sides that we can see. Here is the tall side on the left and also the bottom. We get something that looks like this. Here we also see one, two, three, four, five, six, seven. Seven sides. So all together we have seven plus seven sides, which is fourteen. So Michael painted fourteen sides or fourteen squares. The answer is D. Problem thirteen. Which of the children will reach the rabbit? Follow the arrows and help them. A quick way of finding the answer is to work backwards from the rabbit. The rabbit is right here. We can look at the arrows and see the arrow from which cell pointed to the cell that we are at, or in this case, the rabbit. Obviously it was from the cell that it came. The cell below pointed to this one. The one to the left pointed to the one we were at. This one was also pointed from the left. The cell above pointed down here. And then the cell on the left and the cell on the left. So this is the child who finds the rabbit. It's right here. Answer D. Now we can check our work by looking at the other children and seeing where their paths lead. So this girl goes here and here and down here. And then the arrow below it bounces back in here. So she doesn't go anywhere. This one goes like this and then down and over. He goes over here. And again you have two arrows facing each other so it kind of gets stuck there. This girl, she would walk like this. And she joins this other boy. And she's also stuck here. The girl on the bottom, well you see right here that there are arrows going back and forth. So she also would get stuck. So this child is the only one that gets anywhere. And he gets to the rabbit. Problem 14. What digit does the apple represent? Because the sum of the two digits we can see in the ones column is already 10. We will need to carry a 1 to the tens column. Let's start by looking at the ones digit. We already have the numbers 7 and 3 which gives us 10. You can see that the apple will represent a digit from 1 to 9. So our sum will be a number that still has a 1 in the tens digit. And an apple in the ones digit. No matter what the apple represents, we will have to carry a 1 over to the tens column. Now the tens column becomes 1 plus apple equals 5. So we can easily see by subtracting 1 from both sides that apple is 4. So if we put in 4 in our original problem, we get 7 plus 4 that's 11 plus 3 that's 14. So we have 4 here. Carry our 1 and 1 plus 4 is 5. So our answer is C. The apple represents the digit 4. Problem 15. The clowns at the circus are standing one behind another. Bibi says to Bibi who is standing behind him, behind me 4 co-workers are standing. Bibi answered, in front of me only 3 co-workers are standing. How many clowns are standing in a line? Let's start by figuring out where the line starts. The problem tells us that Bibi is standing behind Vivi. So the start of the line would be here on the left side. Now, let's see how many clowns we need to put in behind Vivi. Let's see how many clowns we need to put in behind Vivi. It says behind me 4 co-workers or 4 clowns are standing. So there are 4 clowns behind Vivi. But notice one of these clowns is Bibi. So we will need 3 more clowns. Bibi is the first clown. Second clown. The third clown. And that's the fourth. Now, who's standing in front of Bibi? He says there are 3 clowns in front of him. So one of those is Vivi. So as we can now see, there will be 2 more in front of Vivi. And here they come. All we need to do is count how many clowns there are in all. There are 1, 2, 3, 4, 5, 6, 7 clowns in line. So the answer is A, 7. Problem 16. If 2 dolls and 1 car cost $8 and 1 doll and 2 cars cost $7, how much do 3 dolls and 3 cars cost? Hint. See if you can combine the first 2 statements in a way that will help you find the final cost. First, let's draw pictures for our equations. Let's start with 2 dolls. 1, 2. And then let's add the 1 car. And that, together, costs $8. That's our first statement. Now, let's look at the second statement. 1 doll and 2 cars cost $7. 1 doll, cars. That's 2. And together, that costs $7. Now, notice the way we have it drawn. We see that altogether, in the 2 equations, we have 3 dolls and 3 cars. Which means that if we add the equations together, we'll get the cost of 3 dolls and 3 cars, which is 8 plus 7, $15. So our answer is A, 15. Problem 17. What is the sum 3 plus 7 plus 2 plus 8 plus 1 equal to? First, add numbers that make 10 together. Let's rewrite our equation down here. 3 plus 7 plus 2 plus 8 plus 1 equals. We see right away that 3 and 7 make 10, and also 2 and 8 make 10. So we can quickly add those together. 10 plus 10. Now we have plus 1 equal. We have 2 tens. That's 20. And then 1. So the sum equals 21. That's answer D. Problem 18. Dan left his home at 8 a.m. He left school at 12.30 p.m. The walk home takes 30 minutes. How long was he gone from his house? Notice that the problem gives us the time he leaves his house, but not the time when he arrives at home. We have 3 pieces of data that we need to work with. In order to find the length of time that Dan was gone from his home, we need to take into consideration 8 a.m. when he left home, 12.30 when he left school, and the 30-minute walk. Here's a clock face that can help us. Let's focus only on the hour hand. At 8 a.m., the hour hand will be pointing right here. At 12.30, which is also known as half past 12, it will be halfway between 12 and 1, and 30 minutes later, which again, 30 minutes is half an hour, it will be pointing at 1. So we need to find the amount of time that passed from 8 a.m. and 1 p.m. It will be 1, 2, 3, 4 hours until noon, and then 1 more hour until 1 p.m. So that's 5 hours. The answer is C. Problem 19. In a certain number, the first digit is greater than the second digit by 2, and the second digit is greater than the third digit by 3. What number is this? Obviously, there is more than one number, which has the properties given in the problem, but we are given a list of numbers to choose from. So we should work by eliminating the wrong answers. First of all, since the problem refers to a third digit, we know that answer A will not be the correct one, because there are only two digits here. What the problem has told us is that the second digit will be greater than the third digit, which would be the ones digit, by 3, and the hundreds digit, as the first digit, would be greater than the tens digit by 2. So we try the number 530, which is answer B. This seems to work. 0 plus 3 is 3, and 3 plus 2 is 5. This should be our answer. But let's double check the other ones, just to make sure we're not missing something or getting something wrong. If we plug in the number 233, C, this will not work, because 3 plus 3 should be 6. Not 3. And then, obviously, the digit 2 would also not be right. The next choice is 521. Again, instead of the ones digit, plus 3 should be 4, not 2. So this is already wrong. And the last choice is 431. Again, 1 plus 3 should be 4, and here it's 3. So we already see that one is wrong, too. So our answer is B, 530. Problem 20. Simona is younger than Victor, but older than TB. Alice is younger than TB, but older than Barbu. Who is the oldest of them all? This type of problem is most easily solved by drawing out a picture. Since the problem mentions Simona first, let's first draw a picture of her. Here she is. Next is Victor. He's older than Simona, so I put him to the right. Now we also see that Simona is older than TB, so let's get TB to the left. They're behind Simona. Now Alice is younger than TB. There she is behind TB. And then we see that Alice is older than Barbu. Barbu, right behind Alice. So after lining up all the children, we see that Victor is first. It means he's the oldest, so the answer is E, Victor. Problem 21. Which number should be at the question mark in the pyramid? Try to figure out the pattern on the smaller numbers before looking at the top numbers. From the way the pyramid is built, we can guess that each block will somehow be affected by the two blocks right below it, the ones that it touches. If we look at 4, the numbers under it are 1 and 3. If we look at 6, the two numbers under it are 4 and 2. Can you guess the pattern now? 4 is equal to 1 plus 3. 6 is equal to 4 plus 2. So, if we look at the top number, it should be the sum of the two numbers below it. The question mark will be equal to 11 plus 13, which is 24. Our answer is D. Problem 22. What number is missing in the picture? And we're given the sequence 209, 902, and 290. The clown juggling the three balls gives us a hint. The numbers given us, 209, 902, and 290, are all combinations of the digits that the clown is juggling. So the last number is most likely another number that can be made out of these three digits. We already have two numbers that start with 2, which are the only possible combinations for numbers starting with 2. We only have one that starts with 9. So we can also make 920 out of these three digits. We could possibly put the digit 0 first and make 092 and 029, but in that case, we would not write the digit 0, and this would just become a two-digit number, and not all three digits would be used. So our best answer here is E, 920. Problem 23. Dan was given a bag of fruit-flavored candy. Lemon, which is yellow, orange, which is orange, strawberry, red, mint green, and cocoa brown. The bag contains 20 pieces of candy, the same number of each color. Dan first ate only the yellow, red, and orange ones. How many pieces of candy are left in the bag? A good place to start is to figure out how many kinds of candy there are, and how many candies of each kind. We can try solving this problem by using arithmetic. First, we will do division. There are 20 pieces of candy, and there are 1, 2, 3, 4, 5 kinds of candy. If we divide 20 by 5, we will get 4, which means there are 4 pieces of each kind of candy. Dan ate all the yellow, red, and orange pieces of candy. So he ate 4 times 3, that's 4 pieces of 3 kinds, which is 12 pieces of candy. So if there were 20 pieces of candy, and he ate 12, there will be 8 pieces of candy left. Another way to try solving this problem is by drawing a picture. We can make a row for each of the 5 kinds of candy. We'll start by making a row of yellow candies, then a row of orange candies, then red, then green, and finally brown. So far we have 5 pieces of candy. We now need to add to each row, but equally. So we'll add 1 piece of candy to the yellow, 1 to the orange, 1 to red, 1 to green, and 1 to brown. This gives us 10 pieces of candy. Let's add one more row. Yellow, orange, red, green, and brown. That makes 15. So one more. Yellow, orange, red, green, and brown. Now we have 20 pieces of candy. Dan ate all of the yellow, red, and orange candy. So what's left is all the green and brown candy, of which there are 8. 4 and 4 is 8, so our answer is E. 8. Problem 24. Andrea needs an hour to get to the shopping center. If she leaves at 4 p.m., she gets there half an hour after the store closes. If she leaves at 8 a.m., she gets there half an hour before the store opens. What hours does the shopping center open? Hint! Break down each part of the problem into two steps. First, finding when Andrea gets to the shopping center. Then from that, finding what time the store opens or closes. Let's use a clock face to help us with the times. We will start with the first part of the problem. We are told that if Andrea leaves at 4 p.m., she gets to the shopping center half an hour after it closes. So, at 4 p.m., the hour hand points at 4. An hour later, when Andrea would get to the store, it points to 5 p.m. So, 5 p.m. or 5 o'clock is when she gets there. She got there half an hour after the store closed. So, we need to go back half an hour or 30 minutes. So, it will be 4.30 when the shopping center closes. Now, let's find out when the shopping center opens. If Andrea leaves at 8 a.m., she will get there half an hour before it opens. So, the hour hand at 8 a.m. is here. An hour later, it will be 9 a.m. But, 9 a.m. is half an hour before the store opens. So, we need to go forward another half hour or 30 minutes, which puts us at 9.30 a.m. That would be when the store opens. So, the store is open from 9.30 a.m. to 4.30 p.m. That's answer E.

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