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USA Math Kangaroo 2015

1. 3 point problems

Which figure is not in each of four pictures?

2. Find the missing part of the house.

3. Five ladybugs live on a bush. How many spots, in total, do the ladybugs have?

4. Which of the following pictures can be rotated so that it will coincide with the picture shown on the right?

5. What does the round tower look like from above?

6. The diagram to the left shows six numbers. What is the sum of the numbers outside the square?

7. Half of a movie lasts half an hour. How long does the whole movie last?

8. Eric had ten equal metal strips.

He screwed pairs of them together into five long strips as shown below.

Which strip is the shortest?

9. 4 points

There are 11 flags on a straight race track. The first flag is at the start, and the last flag is at the finish. The distance between each flag is 4 meters. How long is the track?

10. Marko has 9 candies and Tomo has 17 candies. How many candies does Tomo need to give to Marko so that each boy will have the same number of candies?

11. Six towers are built with grey cubes and white cubes. Each tower is made with five cubes. Cubes of the same colors do not touch. How many white cubes are there?

12. The date 5/5/2015 has three 5's. The earliest date that will have three 5's again is:

13. Emil placed the numbers 1, 2, 3, 4, and 5 correctly in the boxes in the diagram on the right. What number did he place in the box with the question mark?

14. Vera invited 13 guests to her birthday party. She had 2 pizzas, and each of them was cut into 8 slices. Each person at the party ate one slice of pizza. How many slices of pizza were left over?

15. Don made two bricks by sticking cubes together as shown below.

Which structure could not be built using the two bricks?

16. Which piece is missing?

17. Kanga can jump from one circle to the next only if they are connected by a line. She cannot jump into any circle more than once. Kanga starts from circle S and makes exactly 4 jumps to get to circle F. In how many different ways can Kanga do this?

18. A ship was attacked by pirates. One by one they were climbing a rope to get to the ship. The pirate captain was in the middle and he was also the eighth one from the beginning. How many pirates were on the rope?

19. During 3 days Joy the cat was catching mice. Each day, Joy caught 2 mice more than the previous day. On the third day, Joy caught twice as many mice as on the first day. In total, how many mice did Joy catch during the three days?

20. The numbers 3, 5, 7, 8 and 9 were written into the squares so that the sum of the numbers in the row is equal to the sum of the numbers in the column. Which number was written in the centre square?

21. My grandmother has a dog named Atos, as well as some ducks, hens and geese. She has 40 animals altogether. She has four times as many geese as ducks. Atos and the hens make up one half of all her animals. My grandmother has:

22. One of the six stickers shown below was placed on each of the six faces of a die.

The next picture shows the die in two positions.

Which picture is on the face opposite the face with the kangaroo sticker?

23. Sylvia, Tara, Una and Wanda went out for dessert. They stood in line one after another. Each one of them ordered one of the following desserts: ice cream, waffle, bun, and cake, and each one ordered a different item. We know that:
  • The first girl did not buy the ice cream or the waffle.
  • Una was not last in line, and she bought the cake.
  • Sylvia, who was standing behind Tara and in front of Una, did not buy the waffle.
Which of the following is true?

24. We left for a summer camp yesterday at 4:32 PM and got to our destination today at 6:11 AM. How long did we travel?