Math Kangaroo Practice Problems (Grades 1-8)

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Math Kangaroo

http://www.mathkangaroo.org/2010page/Clark/clark/pdb/#Past Contests

Grade 01-02

Problem Kangur_2005_02_1 (3 pts) http://www.mathkangaroo.org

In the enchanted garden of the Green King, there are apple trees that produce golden apples. Every day, 5 golden apples become ripe on each tree, and at the end of each day they fall from the trees. Today, the Green Gardener has picked up 20 ripe apples that fell under the trees last night. How many enchanted trees are there in the garden?

A) 4 B) 5 C) 6 D) 7 E) 8

Alma, Maria, Anne and Michael had 2 apples each. Each one ate one apple. How many apples do they now have altogether?

A) 1 B) 2 C) 4 D) 6 E) 8

Problem Kangur_2005_02_3 (3 pts) http://www.mathkangaroo.org Only one digit from 1 to 9 is repeated three times in this drawing.

The rest of the digits are repeated twice. Which digit is repeated three times? A) 9

B) 8 C) 3 D) 4 E) 7

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How many different digits can you see in the picture below? A) 3 B) 4 C) 5 D) 6 E) 9

What number is hidden under the question mark in the picture below (on the last car)?

A) 7 B) 4 C) 0 D) 1 E) 2

Problem Kangur_2005_02_6 (3 pts) http://www.mathkangaroo.org 5 - 4 + 3 - 2 + 1 = ? A) 1 B) 2 C) 3 D) 4 E) 0

When Ann was born, Michael was 4. Now Ann is 3 years old. How old is Michael? A) 1

B) 6 C) 7

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D) 8 E) 10

Problem Kangur_2005_02_8 (3 pts) http://www.mathkangaroo.org How many blocks were used to build the figure shown in the picture?

A) 7 B) 12 C) 13 D) 14 E) 16

Which four beads below need to be added to this string:

How many more square tiles do we need to put on the kitchen floor to cover all of it? (See the picture.) A) 12 B) 10 C) 9 D) 6 E) 4

Helga is climbing stairs in such a way that she goes up 2 steps at a time. She is standing on the third step now. On which step will she be after she moves up 3 times?

A) 9 B) 1 C) 6

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E) 8

Some pages are missing from an open book. On the left page you can see page number 12 and on the right page you can see page number 15. How many pages are missing?

A) 1 B) 2 C) 3 D) 4 E) 5

Problem Kangur_2005_02_13 (4 pts) http://www.mathkangaroo.org One hen lays one egg a day. In how many days will two hens lay 6 eggs? A) 1

B) 3 C) 6 D) 9 E) 10

There are two horses, one duck, one fish, an eagle, and a boy in a private garden. How many legs do they have altogether?

A) 10 B) 12 C) 14 D) 16 E) 18

Anne has some apples. Maria has 2 apples more than Anne. Altogether they have 8 apples. How many apples does Anne have?

A) 3 B) 5 C) 6 D) 7 E) 10

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Which figure is next in this sequence:

Monika is 2 years old and Karl is 4. How old will Monika be when Karl is 11? A) 6

B) 7 C) 8 D) 9 E) 10

During the race, right before the finish line, I passed the runner who won the third place. What place did I win?

A) 1 B) 2 C) 3 D) 4 E) 5

There are three weights on the scales in the left picture: 1kg, 4 kg, 2 kg and just one weight of 1 kg on the scales in the right picture. What is the weight of the fruit in the basket?

A) 7 kg B) 6 kg C) 5 kg D) 3 kg E) 2 kg

Problem Kangur_2005_02_20 (5 pts) http://www.mathkangaroo.org Which set of signs +, - needs to be used to make this expression true?

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B) -, +, - C) +, +, - D) +, +, + E) -, +, +

The sum of two digits, one from inside the square and one from outside the square is greater than 10. How many such pairs can you make?

A) 19 B) 11 C) 6 D) 24 E) 18

Problem Kangur_2005_02_22 (5 pts) http://www.mathkangaroo.org What number is covered by ? in the last picture below?

A) 1 B) 2 C) 3 D) 4 E) 5

Hans fills the square table with numbers in such a way that the sum of the numbers in each column is 15 and the sum of the numbers in each row is 15 and the sum on each diagonal is 15. What number will he put in place of ? ?

A) 1 B) 3 C) 2

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D) 6 E) 9

A train has four cars in four colors: red, green, white and yellow. The green car is not the first nor the last. The yellow car is not next to the white car nor next to the red car. The first car is white. What is the order of the cars in that train?

A) white, green, red, yellow B) white, yellow, green, red C) green, yellow, red, white D) red, white, green, yellow E) white, red, green, yellow

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Grade 03-04

A butterfly sat down on a correctly solved problem. What number did it cover up?

A) 250 B) 400 C) 500 D) 910 E) 1800

Problem Kangur_2005_0304_2 (3 pts) http://www.mathkangaroo.org At noon, the minute hand of a clock is in the following position:

What will the position of the minute hand be after 17 quarters of an hour?

A) B) C) D) E)

Joan bought some cookies, each of which costs 3 dollars. She gave the salesperson 10 dollars, and received 1 dollar as change. How many cookies did Joan buy?

A) 2 B) 3 C) 4 D) 5 E) 6

After the trainer's first whistle, the monkeys at the circus formed 4 rows. There were 4

monkeys in each row. After the second whistle, they rearranged themselves into 8 rows. How many monkeys were there in each row after the second whistle?

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A) 1 B) 2 C) 3 D) 4 E) 5

Eva lives with her parents, her brother, one dog, two cats, two parrots, and four fish. What is the total number of legs that they have altogether?

A) 22 B) 24 C) 28 D) 32 E) 40

John has a chocolate bar consisting of square pieces 1 cm x 1 cm in size. He has already eaten some of the corner pieces (see the picture). How many pieces does John have left?

A) 66 B) 64 C) 62 D) 60 E) 58

Two traffic signs mark the bridge in my village (see the picture below). These signs indicate the maximum vehicle width and the maximum vehicle weight allowed on the bridge. Which one of the following trucks is allowed to cross that bridge?

A) It is 315 cm wide and it weights 4400 kg. B) It is 330 cm wide and it weights 4250 kg. C) It is 325 cm wide and it weights 4400 kg.

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E) It is 325 cm wide and it weights 4250 kg.

Each of seven boys has paid the same amount of money for a trip. The total sum of what they paid is a three digit number, which can be written as 3 0. What is the middle digit of this number? A) 3 B) 4 C) 5 D) 6 E) 7

What is the smallest possible number of children in a family where each child has at least one brother and at least one sister?

A) 2 B) 3 C) 4 D) 5 E) 6

Out of all five numbers below, I chose one. The number is even and all of its digits are different. The hundreds digit is double the ones digit. The tens digit is greater than the thousands digit. Which number did I choose?

A) 1246 B) 3874 C) 4683 D) 4874 E) 8462

A square piece of paper has been cut into three pieces. Two of them are shown in the picture:

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A) B) C) D) E)

An elevator cannot carry more than 150 kg. Four friends weigh 60 kg, 80 kg, 80 kg, and 80 kg, respectively. What is the least number of trips necessary to carry the four friends to the highest floor? A) 1 B) 2 C) 3 D) 4 E) 7

Ala has 24 dollars, Barb has 66 dollars, and Sophia has as many dollars more than Ala as she has less than Barb. How many dollars does Sophia have?

A) 33 B) 35 C) 42 D) 45 E) 48

There are eight kangaroos in the cells of the table (see the picture). What is the least number of the kangaroos that need to be moved to the empty cells so that there would be exactly two kangaroos in any row and in any column of the table?

A) 4 B) 3 C) 2 D) 1 E) 0

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Greg needs to bring four full sacks of sand from the river to a house located at the other end of the village. Unfortunately, on his way through the village, half of the sand spills out of the sack through a hole. How many trips does Greg need to make from the river to the house in order to bring the required amount of sand?

A) 4 B) 5 C) 6 D) 7 E) 8

During a Kangaroo camp, Adam solved five problems every day, and Brad solved two problems daily. After how many days did Brad solve as many problems as Adam solved in 4 days?

A) After 5 days B) After 7 days C) After 8 days D) After 10 days

E) After 20 days Problems 5 points each

There were 9 pieces of paper. Some of them were cut into three pieces. As a result, there are 15 pieces of paper now. How many pieces of paper were cut?

A) 2 B) 3 C) 4 D) 5 E) 6

Using 6 matches, only one rectangle with a perimeter of 6 matches can be made (see the picture). How many different rectangles with a perimeter of 14 matches can be made using 14 matches?

A) 2 B) 3 C) 4

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D) 6 E) 12

A picture frame was constructed using pieces of wood which all have the same width. What is the width of the frame if the inside perimeter of the frame is 8 decimeters less than its outside perimeter?

A) 1 dm B) 2 dm C) 4 dm D) 8 dm

E) It depends on the size of the picture

In a trunk there are 5 chests, in each chest there are 3 boxes, and in each box there are 10 gold coins. The trunk, the chests, and the boxes are locked. At least how many locks need to be opened in order to take out 50 coins?

A) 5 B) 6 C) 7 D) 8 E) 9

The figure shows a rectangular garden with dimensions of 16 m by 20 m. The gardener has planted six identical flowerbeds (they are gray in the diagram). What is the perimeter of each of the flowerbeds?

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B) 22 m C) 24 m D) 26 m E) 28 m

Mike chose a three-digit number and a two-digit number. The difference of these numbers is 989. What is their sum?

A) 1001 B) 1010 C) 2005 D) 1000 E) 1009

Five cards are laying on the table in the order: 5, 1, 4, 3, 2 as shown in the top row of the picture. They need to be placed in the order shown in the bottom row. In each move, any two cards may be switched. What is the least number of moves that need to be made?

A) 2 B) 3 C) 4 D) 5 E) 6

Problem Kangur_2005_0304_24 (5 pts) http://www.mathkangaroo.org Which of the cubes has the plan shown in the picture below?

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A) B) C) D) E)

Problem Kangur_2004_0304_1 (3 pts) http://www.mathkangaroo.org 2001+ 2002 + 2003 + 2004 + 2005 = A) 1,015 B) 5,010 C) 10,150 D) 11,005 E) 10,015

Marek was 4 years old when his sister was born. Today he blew out all 9 candles on his birthday cake. What is the difference between Marek's and his sister's age today? A) 4 years

B) 5 years C) 9 years D) 13 years E) 14 years

The picture below shows a road from town A to town B (indicated by solid line) and a detour (marked by a dash line) caused by renovation of the section CD. How many kilometres longer is the road from town A to town B because of the detour now?

A) 3 km B) 5 km C) 6 km D) 10 km

E) This cannot be calculated.

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A) 771 - 489 B) 681 - 399 C) 669 - 391 D) 1871 - 1589 E) 600 - 318

There were some birds sitting on the telegraph wire. At one moment, 5 of them flied away and after some time, 3 birds came back. At that time there were 12 birds sitting on the wire. How many birds were there at the very beginning?

A) 8 B) 9 C) 10 D) 12 E) 14

Which numbers are inside a rectangle and inside a circle but not inside a triangle at the same time? A) 5 and 11 B) 1 and 10 C) 13 D) 3 and 9 E) 6, 7 and 4

Buildings on Color Street are numbered from 1 to 5 (see the picture). Each building is

colored with one of the following colors: blue, red, yellow, pink, and green. It is known that: - The red building neighbours with the blue one only.

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What is the color of the building numbered with 3? A) Blue B) Red C) Yellow D) Pink E) Green

How many white squares need to be shaded so that the number of shaded squares equals exactly to half of the number of white squares?

A) 2 B) 3 C) 4 D) 6

E) It is impossible to calculate it.

Five identical sheets of a plastic rectangles were divided into white and black squares. Which of the sheets from A) to E) has to be covered with the sheet to the right in order to get totally black rectangle?

A) B) C) D) E)

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scales. What is the weight of the pen in grams? A) 6 g B) 7 g C) 8 g D) 9 g E) 10 g

I notice four clocks on the wall (see the picture). Only one of them shows correct time. One of them is 20 minutes ahead, another is 20 minutes late, and the other is stopped. What is the time at the moment?

A) 4:45 B) 5:05 C) 5:25 D) 5:40 E) 12:00

Ella brought a basket of apples and oranges for a birthday party. Guests ate half of the apples and the third part of the oranges. In the basket remained:

A) Half of all fruits

B) More than half of all fruits C) Less than half of all fruits

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D) A third part of all fruits

E) Less than a third part of all fruits

Ania divided a certain number by 10 instead of multiplying it by 10. As a result she got 600. What would the result have been if she hadn't made that mistake?

A) 6 B) 60 C) 600 D) 6,000 E) 60,000

Kathy found a book, which was lack of certain number of sheets. When she opened the book she saw number 24 on the left side and number 45 on the right side. How many sheets between those sides were missing?

A) 9 B) 10 C) 11 D) 20 E) 21

Eva is 52 days older than her girlfriend Ania. Eva had her birthday on Tuesday in March of this year. On which day of the week will Ania celebrate her birthday this year?

A) Monday B) Tuesday C) Wednesday D) Thursday E) Friday

Into the squares of diagram numbers were placed so that the sum of the numbers in the first row is equal to so that the sum of the numbers in the first row is equal to 3, the sum of the numbers in the second row is equal to 8, and the sum of the numbers in the first column is equal to 4. What is the sum of the numbers in the second column?

A) 4 B) 6 C) 7

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E) 11

The cube (see the picture) is colored with three colors so that every side of this cube is one color and every two opposite sides are the same color. From which of the patterns below this kind of cube can be made?

Four square tiles were arranged in a way shown in the picture. The lengths of the sides of two tiles are indicated in the picture. What is the length of the side of the largest tile?

A) 24 B) 56 C) 64 D) 81 E) 100

Girls and boys from Maria's and Mathew's class have formed a line. There are 16 students on Maria's right, and Mathew is among them. There are 14 students on Mathew's left, and Maria is among them. There are 7 students between Maria and Mathew. How many students are in this class? A) 37 B) 30 C) 23 D) 22 E) 16

The sum of the digits of the 10-digit number is 9.What is the product of the digits of this number?

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A) 0 B) 1 C) 45

D) 9 x 8 x 7 x ... x 2 x 1 E) 10

Out of 125 small, white and black cubes, the big cube was formed (see the picture). Every two adjacent cubes have different colors. The vertices of the big cube are black. How many white cubes does the big cube contain?

A) 62 B) 63 C) 64 D) 65 E) 68

A lottery-ticket was 4 dollars. Three boys: Paul, Peter, and Robert made a contribiution and bought two tickets. Paul gave 1 dollar, Peter gave 3 dollars, and Robert gave 4 dollars. One of the tickets they bought was worth 1000 dollars. Boys shared the award fairly, meaning, proportionally to their contributions. How much did Peter receive?

A) 300 B) 375 C) 250 D) 750 E) 425

In three soccer games the Dziobak's team scored three goals and lost one. For every game won the team gets 3 points, for a tie it gets 1 point, and for the game lost it gets 0 points. For sure, the number of points the team earned in those three games was not equal to which of the following numbers? A) 7 B) 6 C) 5 D) 4 E) 3

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In every white section of a diagram, the products of two numbers from grey sections - one from above and one from the left - was placed (for example: 42 = 7 · 6 ). Some of these products are represented by letters. Which two letters represent the same number?

A) L and M B) T and N C) R and P D) K and P E) M and S

The picture below shows the letter U drawn on grid paper. How many squares does the letter U cover? A) 10 B) 8 C) 11 D) 13 E) 12

Problem Kangur_2003_0304_2 (3 pts) http://www.mathkangaroo.org What is the sum of 0 + 1 + 2 + 3 + 4 - 3 - 2 - 1 - 0?

A) 0 B) 2 C) 4

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D) 10 E) 16

The first train car, right behind the engine, contains 10 boxes. In each of the other cars there are twice as many boxes as in the car in front of it. How many boxes are there in the fifth car?

A) 100 B) 120 C) 140 D) 160 E) 180

Zosia is drawing kangaroos. The first one is blue, the next one green, followed by red, and finally yellow, and then again blue, green, red, yellow, and so on, in the same order. What color will the seventeenth kangaroo be?

A) Blue B) Green C) Red D) Black E) Yellow

In the teachers' lounge there are 6 tables with 4 chairs by each one, 4 tables with 2 chairs by each, and 3 tables with 6 chairs by each. How many chairs are there in the lounge?

A) 40 B) 25 C) 50 D) 36 E) 44

In one of these pictures, there are three times as many hearts as other shapes. Which picture is it?

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A rectangle with dimensions 7 x 4 was outlined on grid paper. How many squares will a diagonal of this rectangle intersect?

A) 8 B) 9 C) 10 D) 11 E) 12

The figure presented in the picture, made with identical cubes, weighs 189 grams. How much does one cube weigh?

A) 29 g B) 25 g C) 21 g D) 19 g E) 17 g

Peter wrote out consecutive natural numbers starting with 3 until he had written 35 digits. What was the greatest number that Peter wrote?

A) 12 B) 22 C) 23 D) 28 E) 35

Anna fell asleep at 9:30 PM and woke up at 6:45 AM the next day. Her little brother Peter slept 1 hour and 50 minutes longer. How long did Peter sleep?

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A) 30 hr 5 min B) 11 hr 35 min C) 11 hr 5 min D) 9 hr 5 min E) 8 hr 35 min

A pattern, the beginning and the end of which is shown in the picture, is made up of alternating black and white bars. There are 17 bars altogether. The bars on both ends are black. How many white bars are there in the pattern?

A) 9 B) 16 C) 7 D) 8 E) 15

Jumping Kangaroo is practicing for the animal Olympics. His longest jump during the training was 55 dm 50 mm long, but in the finals of the Olympics he won with a jump that was 123 cm longer. How long was Jumping Kangaroo's longest jump during the Olympics? A) 6 m 78 cm

B) 5 m 73 cm C) 5 m 55 cm D) 11 m 28 cm E) 7 m 23 cm

Peter chose a certain number, then he subtracted 203 from it, then he added 2003 to that difference. His final result was 20003. What number did Peter choose at the beginning? A) 23

B) 17797 C) 18203 D) 21803 E) 22209

Barbara likes to add the digits showing the current time on her electronic watch (for example, when the watch shows 21:17, she gets the number 11 as the result). What is the greatest sum she can get?

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13:00. When it is 2P.M. they say it is 14:00, and when it is 12A.M., they say it is 24:00. In this problem 21:17 means 9:17P.M. Time expressed with this method is called military time sometimes.) A) 24 B) 36 C) 19 D) 25 E) 23

Mark said to his friends, "If I had picked twice as many apples as I picked, I would have 24 more apples than I have now." How many apples did Mark pick?

A) 48 B) 24 C) 42 D) 12 E) 36

Points A, B, C, D all of which lie on a straight line, are marked in the figure below. The distance between points A and C is 10 m, between B and D is 15 m, and between A and D is 22 m. What is the distance between points B and C?

A) 1 m B) 2 m C) 3 m D) 4 m E) 5 m

There are 29 students in the class. 12 of the students have a sister and 18 of the students have a brother. In this class, only Tania, Barbara, and Anna do not have any siblings. How many students from this class have both a brother and a sister?

A) None B) 1 C) 3 D) 4 E) 6

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Peter has 11 pieces of paper. He cut some of them into three parts and now he has 29 pieces of paper. How many pieces of paper did he cut?

A) 3 B) 2 C) 8 D) 11 E) 9

Peter bought 3 kinds of cookies: large, medium, and small. The large cookies cost 4 zlotys each, the medium: 2 zlotys each, and the small: 1 zloty each. (A zloty is the Polish unit of money.) Altogether, Peter bought 10 cookies and paid 16 zlotys. How many large cookies did he buy? A) 5 B) 4 C) 3 D) 2 E) 1

Christopher built a rectangular prism using red and blue cubes of identical size. The outer walls of this prism are red but all the inner cubes are blue. How many blue cubes did Christopher use in this construction?

A) 12 B) 24 C) 36 D) 40 E) 48

Jurek is planning to buy some basketballs. If he were to buy 5 balls, he would have 10 zlotys left over, and if he were to buy 7 balls, he would have to borrow 22 zlotys. (A zloty is the Polish unit of money.) How much does one basketball cost?

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B) 16 C) 22 D) 26 E) 32

Mark built a rectangular prism using 3 blocks, each of which is made up of 4 small cubes connected in various ways. Two of the blocks are shown in the picture. Which is the third, white block, of which only two sides are visible?

A) B) C) D) E)

From a square puzzle, two pieces, which made up the shaded region, were cut out (see the figure). Which two of the pieces below are these?

A) 1 and 3 B) 2 and 4 C) 2 and 3 D) 1 and 4 E) 3 and 4

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At the toy store, among other things, you can buy dogs, bears, and kangaroos. Three dogs and two bears together cost as much as four kangaroos. For the same amount of money you can buy one dog and three bears. Then:

A) A dog is twice as expensive as a bear. B) A bear is twice as expensive as a dog.

C) The prices of a dog and of a bear are identical. D) A bear is three times as expensive as a dog. E) A dog is three times as expensive as a bear.

Which of the squares below should be put into the picture to the right, to get the symbol of our competition? A) B) C) D) E)

Problem Kangur_2002_0304_2 (3 pts) http://www.mathkangaroo.org After we simplify 2 + 2 - 2 + 2 - 2 + 2 - 2 + 2 - 2 + 2 what will be the result?

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B) 2 C) 4 D) 12 E) 20

Andrzej received three cars, four balls, three teddy bears, ten pens, two chocolate bars, and a book for his birthday. How many items did he get in all?

A) 15 B) 17 C) 20 D) 23 E) 27

A square was divided into pieces (see the picture). Which of the following pieces does not occur in this divided square?

A)

B)

C)

D)

E)

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Julia, Kasia, Zuzanna, and Helena have their birthdays on March 1st, May 17th, July 20th, and March 20th. Kasia and Zuzanna were born in the same month. Julia and Zuzanna were born on the same day of a month. Which of the girls was born on May 17th?

A) Julia B) Kasia C) Zuzanna E) Helena

E) It cannot be determined from the given informfation.

A human heart beats an average of 70 times per minute. On average how many times does it beat during one hour?

A) 42,000 B) 7,000 C) 4,200 D) 700 E) 420

Quadrilateral ABCD is a square and its side is 10 cm long. Quadrilateral ATMD is a

rectangle and its shorter side is 3 cm. What is the difference between the sum of the lengths of all the sides of the square and the sum of the lengths of all the sides of the rectangle?

A) 14 cm B) 10 cm C) 7 cm D) 6 cm E) 4 cm

Which of the figures below (see the picture) couldn't be made with folding a rectangular sheet just once?

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B)

C)

D)

E)

Houses on the street where John lives are numbered from 1 to 24. How many times does the digit 2 appear in the numbering of those houses?

A) 2 B) 4 C) 8 D) 16 E) 32

There are six identical oranges on one scale of the balance and two identical melons on the other scale. After we put one melon on the scale with the oranges, the scales will be balanced. How many oranges weigh as much as one melon?

A) 2 B) 3 C) 4 D) 5 E) 6

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This picture below is a sketch of a castle. Which of the lines below does not belong to the sketch? A) B) C) D) E)

We add 17 to the smallest two-digit number and then we divide the sum by the largest one-digit number. What is the result?

A) 3 B) 6 C) 9 D) 11 E) 27

In a certain ancient country the numbers: one, ten, and sixty were expressed with the following symbols:

one, ten, sixty.

Using those symbols people were writing down other numbers, for example the number 22 was written as

Which of the following notations represents the number 124 ? A)

B) C)

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E)

A face of a clock was divided into four parts. The sums of the numbers in each of those parts are consecutive E numbers. Which of the following pictures satisfies this rule?

A)

B)

C)

D)

E)

Klara and Zosia had 60 matches altogether. Klara took as many matches as she needed to build a triangle, each side 6 matches long. Zosia used the remaining matches to build a rectangle, which had one side equal to 6 matches. How many matches long is each of the longer sides of this rectangle?

A) 9 B) 12 C) 15 D) 18 E) 30

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Three kangaroos: Miki, Niki, and Oki participated in a competition. Jumping at the same speed, they jumped along the lines you can see in the picture. Only one of the following sentences A, B, C, D and E is true. Which one?

A) Miki and Oki finished at the same time. B) Niki finished first.

C) Oki finished last.

D) All kangaroos finished at the same time. E) Miki and Niki finished at the same time.

Each boy: Mietek, Mirek, Pawel, and Zbyszek has exactly one of the following animals: a cat, a dog, a gold fish, and a canary-bird. Mirek has a pet with fur. Zbyszek has a pet with four legs. Pawel has a bird, and Mietek and Mirek don't like cats. Which of the following sentences is not true?

A) Zbyszek has a dog. B) Pawel has a canary. C) Mietek has a golden fish. D) Zbyszek has a cat. E) Mirek has a dog.

Marysia leaves her house at 6:55 and arrives at school at 7:32. Zosia needs 12 minutes less than Marysia to get to school. Yesterday Zosia showed up at school at 7:45. What time did she leave her house?

A) At 7:07 B) At 7:20 C) At 7:25 D) At 7:30 E) At 7:33

Robert had a certain number of identical cubes. He glued a tunnel using half of his blocks (see Picture 1). With some of the remaining cubes he formed a pyramid (see Picture 2). How

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A) 34 B) 28 C) 22 D) 18 E) 15

Daughter is 3 years old, and her mother is 28 years older than the daughter. How many years later will the mother be three times older than her daughter?

A) 9 B) 12 C) 10 D) 1 E) 11

A conductor wanted to make a trio consisting of a fiddler, a pianist, and a drummer. He had to choose one of two fiddlers, one of two pianists, and one of two drummers. He decided to try each of the possible trios. How many attempts did he have to make?

A) 3 B) 4 C) 8 D) 24 E) 25

One medal can be cut out from a golden square plate. If four medals are made from four plates, the remaining parts of those four plates can be used to make one more plate. What is the largest number of medals that could be formed when 16 plates are used?

A) 17 B) 19 C) 20 D) 21 E) 32

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Twenty eight students from the fourth grade competed in the math competition. Each student earned a different number of points. The number of students who received more points than Tomek is two times smaller than the number of students who had less points than Tomek. In which position did Tomek finish that competition?

A) 6th B) 7th C) 8th D) 9th E) 10th

An odometer in a car shows the number 187569 of passed kilometers. This number consists of all different digits. After passing how many kilometers will the odometer show a number consisting of all different digits again?

A) After 777 km B) After 12,431 km C) After 431 km D) After 21 km E) After 11 km

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Grade 05-06

A butterfly sat down on a correctly solved problem. What number did it cover up?

2005 + 205 = 3500 - A) 1295 B) 1190 C) 1390 D) 1195 E) 1290

Together, Anna and Olla have ten pieces of candy. Olla has two more pieces of candy than Anna. How many pieces of candy does Olla have?

A) 8 B) 7 C) 6 D) 5 E) 4

There are eight kangaroos in the diagram (see the picture). What is the least number of kangaroos that have to be moved to the empty boxes in order to have two kangaroos in each row and each column?

A) 0 B) 1 C) 2 D) 3 E) 4

(39)

Eva lives with her parents, a brother, a dog, two cats, two parrots, and four gold fish. How many legs do they have altogether?

A) 40 B) 32 C) 28 D) 24 E) 22

Problem Kangur_2005_0506_5 (3 pts) http://www.mathkangaroo.org 2005 x 100 + 2005 = A) 2005002005 B) 20052005 C) 20072005 D) 202505 E) 22055

An ant is walking from point A to point B on a cube along the indicated path. The edge of the cube is 12 cm long. How far does the ant need to travel?

On a shelf, there are 24 balls in three colors: white, red and brown. of them are white, and of the rest of the balls are red. How many of them are brown?

A) 4 B) 5 C) 6

(40)

E) 8

There are five cards on the table, labeled with numbers 1 to 5 as shown in the top row. One move consists of switching two cards. How many moves do you need to make so that the cards are arranged in the way shown in the bottom row?

A) 2 B) 4 C) 1 D) 3 E) 5

Tom picked a natural number and multiplied it by 3. Which number CANNOT be the result of this multiplication? A) 987 B) 444 C) 204 D) 105 E) 103

Problem Kangur_2005_0506_10 (3 pts) http://www.mathkangaroo.org How many hours is half of a third part of a quarter of 24 hours?

A) B) C) 1 D) 2 E) 3

Eva cut a paper napkin into 10 pieces. She then also cut one of the pieces into 10 pieces. She repeated this process two more times. Into how many pieces did she cut the napkin?

(41)

A) 27 B) 30 C) 37 D) 40 E) 47

Mowgli usually walks from home to the beach, and returns on an elephant. It takes him 40 minutes altogether. One day he traveled on the elephant from home to the beach and back, which took him 32 minutes. How much time would he need to travel the same distance on foot? A) 24 min B) 42 min C) 46 min D) 48 min E) 50 min

A rectangular garden with an area of 30 m² was divided into three rectangular sections of flowers, vegetables, and strawberries (some of the dimensions are shown in the diagram). What is the area of the vegetable section, if the flower part has an area of 10 m²?

A) 4 m² B) 6 m² C) 8 m² D) 10 m² E) 12 m²

Grandpa suggested dividing all peanuts between the family members in the following way: one person would get 5 kilos, two people would get 4 kilos each, four people would get 2 kilos each, two people would get 1.5 kilo each, and one person would not get any nuts. Grandma suggested dividing the peanuts equally among all of the family members. For how many people would the division suggested by Grandma be better than the one suggested by Grandpa?

(42)

B) 4 C) 5 D) 6 E) 7

How many two digit numbers are there, which can be expressed only by using different odd digits? A) 15 B) 20 C) 25 D) 30 E) 50

Problem Kangur_2005_0506_16 (4 pts) http://www.mathkangaroo.org Which of the cubes below represents the plan of the cube shown to the right?

Sum of five consecutive natural numbers is equal to 2005. What is the greatest number among them? A) 401 B) 403 C) 404 D) 405 E) 2001

Problem Kangur_2005_0506_18 (4 pts) http://www.mathkangaroo.org What is the number of all divisors of number 100?

(43)

A) 3 B) 6 C) 7 D) 8 E) 9

The frame of a rectangular painting was made out of wooden pieces of the same width. What is the width of those pieces if the outer perimeter of the frame is 8 decimeters longer than the inner perimeter?

A) 4dm B) 2dm C) 1dm D) 8dm

E) The width depends on the dimensions of the painting.

Problem Kangur_2005_0506_20 (4 pts) http://www.mathkangaroo.org How many more triangles than squares are shown in the picture?

A) 4 more B) 2 more C) 1 more D) 5 more E) 3 more

There are five containers in a treasure chest, in each container there are three boxes and in each box there are 10 golden coins. The treasure chest, the containers, and the boxes are all locked. How many locks do you need to open to get 50 coins?

(44)

B) 7 C) 9 D) 6 E) 8

What number should replace x, if we know that the number in the circle in the upper row is the sum of the numbers from the two circles right below it.

A) 32 B) 50 C) 55 D) 82 E) 100

In a two-digit number, a is the tens digit and b is the ones digit. Which of the conditions below ensures that the number will be divisible by 6?

A) a + b = 6 B) b = 6 a C) b = 5 a D) b = 2 a E) a = 2 b

A wooden cube with the length of its side equal to 3 dm was painted with 0.25 kg of paint. The cube was then cut up into unit cubes (side length of 1 dm). How much paint is needed to paint the unpainted sides of the little cubes?

A) 1.25 kg B) 1 kg C) 0.75 kg D) 0.5 kg E) 0.25 kg

(45)

Five circles have radii of the same length (see the picture). Four of them are touching the fifth circle, and their centers are the vertices of a square. The ratio of the area of the shaded region of the circles to the area of unshaded regions of the circles is:

A) 1 : 3 B) 1 : 4 C) 2 : 5 D) 2 : 3 E) 5 : 4

From noon until midnight, Wise Cat sleeps under a chestnut tree. From midnight until noon he is awake telling stories. There is a note on that tree which says: "Two hours ago, Wise Cat was doing the same thing that he will be doing in an hour". How many hours, out of 24 hours, is the note true?

A) 6 B) 12 C) 18 D) 3 E) 21

Mark has 42 cubes with side length of 1 cm. He used them to construct a prism, the base of which has a perimeter of 18 cm. What is the height of that prism?

On the board Peter wrote all the three-digit numbers that have the following properties: the digits in each of the numbers are different, the first digit is the square of the quotient of the second digit and the third digit. How many numbers did Peter write?

A) 1 B) 2

(46)

D) 4 E) 8

Equilateral triangle ABC (all sides congruent) has an area equal to 1. A bigger triangle was constructed out of 49 of these triangles (see the picture). The area of the shaded region is equal to: A) 20 B) 22.5 C) 23.5 D) 25 E) 32

Mary, Dorothy, Sylvia, Ella, and Kathy are sitting on a bench in the park. Mary is not sitting on the farthest right side; Dorothy is not sitting the farthest to the left. Sylvia is not sitting the farthest to the left nor the farthest to the right. Kathy is not sitting next to Sylvia, and Sylvia is not sitting next to Dorothy. Ella is sitting to the right of Dorothy, but not necessarily next to her. Which girl is sitting the farthest to the right?

A) It cannot be determined. B) Dorothy

C) Sylvia D) Ella E) Kathy

Problem Kangur_2004_0506_1 (3 pts) http://www.mathkangaroo.org How much is 1000 - 100 + 10 - 1?

(47)

A) 111 B) 900 C) 909 D) 990 E) 999

In each of the little squares Karolina places one of the digits: 1, 2, 3, 4. She makes sure that in each row and each column each of these numbers is placed. In the figure below, you can see the way of filling these squares. What number should she put in the square marked with an x? 1 x 2 4 1 3 2 A) 1 B) 2 C) 3 D) 4 E) Cannot be determined.

Problem Kangur_2004_0506_3 (3 pts) http://www.mathkangaroo.org (10 · 100) · (20 · 80) = A) 20,000 · 80,000 B) 2000 · 8000 C) 2000 · 80,000 D) 20,000 · 8000 E) 2000 · 800

Problem Kangur_2004_0506_4 (3 pts) http://www.mathkangaroo.org How many hours is 360,000 seconds?

A) 3 hours B) 6 hours C) 8.5 hours D) 10 hours

E) More than 90 hours.

Problem Kangur_2004_0506_5 (3 pts) http://www.mathkangaroo.org What is the remainder when you divide 20042003 by 2004?

(48)

B) 1 C) 2 D) 3 E) 2003

Five identical sheets of a plastic rectangles were divided into white and black squares. Which of the sheets from A to E has to be covered with the sheet to the right in order to get totally black rectangle?

A) B) C) D) E)

Problem Kangur_2004_0506_7 (3 pts) http://www.mathkangaroo.org Which of the following numbers is not a factor of 2004?

A) 3 B) 4 C) 6 D) 8 E) 12

The three members of a rabbit family ate 73 carrots altogether during a week. The father ate five carrots more than the mother. Their son ate 12 carrots. How many carrots did mother eat in that week? A) 27 B) 28 C) 31 D) 33 E) 56

(49)

Nine bus stops are equally spaced along a bus route. The distance between the first stop and the third one is 600 m. How long is the bus route?

A) 1800 m B) 2100 m C) 2400 m D) 2700 m E) 3000 m

Problem Kangur_2004_0506_10 (3 pts) http://www.mathkangaroo.org What is the value of the expression 1 - (2 - (3 - (4 - 5) ) ) equal to? A) 0

B) -3 C) -9 D) 3 E) 9

You are given two identical puzzle pieces and you are not allowed to turn them over. Which figure cannot be made out of these two pieces?

Karol folds a sheet of paper in a half and then repeats this four more times. Then he makes a hole in the folded paper. How many holes does the sheet of paper have after unfolding?

A) 6 B) 10 C) 16 D) 20 E) 32

(50)

A) 9 B) 8 C) 7 D) 6 E) 5

The weight of 3 apples and 2 oranges is 255 g. The weight of 2 apples and 3 oranges is 285 g. Each apple weighs the same and each orange weighs the same. What is the combined weight of 1 apple and 1 orange?

A) 110 g B) 108 g C) 105 g D) 104 g E) 102 g

Tomek, Romek, Andrzej, and Michal said the following about a certain number: Tomek: "This number is equal to 9"; Romek: "This number is prime."; Andrzej: "This number is even."; Michal: "This number is equal to 15." Only one statement given either by Romek or Tomek is true, as well as only one statement given by either Andrzej or Michal is true. What number is it? A) 1 B) 2 C) 3 D) 9 E) 15

What is the smallest number of the little squares that have to be shaded in order to get at least one axis of symmetry of the figure below?

(51)

A) 1 B) 2 C) 3 D) 4 E) 5

One corner of a cube was cut off. Which of the figure below represents the pattern of the cube after unfolding it?

Four snails: Fin, Pin, Rin, and Tin are moving along identical rectangular tiles. The shape and length of each snail's trip is shown below. How many decimeters has snail Tin gone?

Snail Fin has gone 25 dm. Snail Pin has gone 37 dm. Snail Rin has gone 38 dm. Snail Tin has gone ? dm

A) 27 dm B) 30 dm C) 35 dm D) 36 dm E) 40 dm

The Island of Turtles has an unusual weather system: Mondays and Wednesdays are rainy, Saturdays are foggy and the other days are sunny. A group of tourists would like to go on a 44-day long vacation to the island. Which day of the week should be the first day of their vacation in order to enjoy the most of the sunny days?

(52)

B) Wednesday C) Thursday D) Friday E) Tuesday

The sum of two natural numbers is equal to 77. If the first number is multiplied by 8 and the second by 6, then those products are equal. What is the larger of these numbers?

A) 23 B) 33 C) 43 D) 44 E) 54

Problem Kangur_2004_0506_21 (5 pts) http://www.mathkangaroo.org What is the number of all divisors of 2 · 3 · 5 · 7 ?

A) 4 B) 14 C) 16 D) 17 E) 210

Ella and Ola had 70 mushrooms altogether. of Ella's mushrooms are brown and of Ola's mushrooms are white. How many mushrooms did Ella have?

A) 27 B) 36 C) 45 D) 54 E) 10

There are 11 fields in the picture. Number 7 is written in the first field and number 6 in the ninth field. What number has to be placed in the second field so that the sum of the numbers from every three consecutive fields is equal to 21?

A) 7 B) 8 C) 6

(53)

D) 10 E) 21

The square below was divided into small squares. What part of the area of the shaded figure is the area of the figure that is not shaded?

A) B) C) D) E)

In a CD store two CDs have the same price. The price of the first CD was reduced by 5% and the price of the other one was increased by 15%. After this change the prices of the two CDs differed by $6.00. How much is the cheaper CD now?

A) $1.50 B) $6.00 C) $28.50 D) $30.00 E) $34.50

In the little squares of a big square the consecutive natural numbers are placed in a way shown in the figure. Which of the numbers below cannot be placed in the square with letter x?

(54)

B) 256 C) 81 D) 121 E) 400

Ania divided number by 3. What is the number of zeros in the quotient? A) 670

B) 669 C) 668 D) 667 E) 665

Imagine that you have 108 red balls and 180 green balls. The balls have to be packed in boxes in such a way that every box contains the same number of balls and there are balls of only one color in every box. What is the smallest number of boxes that you need?

A) 288 B) 36 C) 18 D) 8 E) 1

During a competition in the Kangaroo Summer Camp in Zakopane students were given 10 problems to solve. For each correct answer a student was given 5 points and for each incorrect one the student was loosing 3 points. Everybody solved all the problems. Mathew got 34 points, Philip got 10 points and John got 2 points. How many problems did they answer correctly all together?

A) 17 B) 18 C) 15 D) 13 E) 21

A right triangle with legs of length 6 cm and 8 cm was cut out of a paper and then folded along a straight line. Which of the numbers below can express the area of the resulting polygon?

(55)

A) 9 cm² B) 12 cm² C) 18 cm² D) 24 cm² E) 30 cm²

Problem Kangur_2003_0506_1 (3 pts) http://www.mathkangaroo.org Which of the following numbers is greatest?

A) 2 + 0 + 0 + 3 B) 2 x 0 x 0 x 3 C) ( 2 + 0 ) x ( 0 + 3 ) D) 20 x 0 x 3

E) ( 2 x 0 ) + ( 0 x 3 )

Zosia is drawing flowers of different colors. The first flower is blue, then white, red, yellow, and again blue, white, red, yellow, and so on in the same order. What is the color of the twenty ninth flower drawn by Zosia?

A) Blue B) White C) Red D) Pink E) Yellow

How many integers are there on the number line between the numbers 2.09 and 15.3? A) 13

B) 14 C) 11 D) 12

E) Infinitely many

Problem Kangur_2003_0506_4 (3 pts) http://www.mathkangaroo.org The least positive integer which, is divisible by 2, 3, and 4, is:

A) 1 B) 6 C) 12

(56)

E) 36

Two of the numbers located on the two circles (see the picture) are represented by letters A and B. The sum of the numbers on each circle is equal to 55. What number is represented by letter A? A) 9 B) 10 C) 13 D) 16 E) 17

Tomek has 9 bills worth 100 zlotys each, 9 bills worth 10 zlotys each, and 10 coins worth 1 zloty each. How much money does Tomek have? (a zloty [zl] is a monetary unit in Poland) A) 1,000 zl

B) 991 zl C) 9, 910 zl D) 9,901 zl E) 99, 010 zl

A square with the length of side equal to x consists of a square with an area of 81 cm², two rectangles with areas of 18 cm² each, and a small square. What is the value of x?

A) 2 cm B) 7 cm C) 9 cm

(57)

D) 10 cm E) 11 cm

The value of the expression is equal to:

A) 2003 B) C) 3 D) E) 6009

Basia likes to add the digits that indicate the actual time on her electronic watch (for example, when the watch shows 21:17, she gets the sum equal to 11). What is the greatest sum she can get? (Hint: in some countries and sometimes in USA, instead of telling it is 1P.M., people say it is 13:00. When it is 2P.M. they say it is 14:00, and when it is 12A.M., they say it is 24:00. In this problem 21:17 means 9:17P.M. Time expressed with this method is called military time sometimes.) A) 24 B) 36 C) 19 D) 25 E) 28

The picture shows Clown Jan dancing on two balls and a cube. The radius of the lower ball is 6 dm, and the radius of the upper ball is three times shorter. The edge of the cube is 4 dm longer than the radius of the upper ball. At what height is Jan dancing?

A) 14 dm B) 20 dm C) 22 dm

(58)

E) 28 dm

Let AC = 10 m, BD = 15 m, AD = 22 m (see the figure below). What is length of segment BC is equal to? A) 1 m B) 2 m C) 3 m D) 4 m E) 5 m

How many shortest distances along the edges of the cube are there that connect vertex A with the opposite vertex B?

A) 4 B) 6 C) 3 D) 12 E) 16

From a square puzzle two pieces are cut out. These two pieces made the shaded region, (see the figure). Among the four figures below, which are these two pieces?

(59)

A) 1 and 4 B) 2 and 4 C) 2 and 3 D) 1 and 3 E) 3 and 4

We add two different numbers chosen from the numbers: 1, 2, 3, 4, 5. How many different sums can we get?

A) 5 B) 6 C) 7 D) 8 E) 9

The figure in the picture consists of 7 squares. Square A has the greatest area, and square B - the smallest area. The lengths of two of the squares are given. How many B squares will it take to fill up square A completely?

A) 16 B) 25 C) 36 D) 49

E) It is impossible.

A certain bar code consists of 17 black bars. A white bar divides each two black bars. The first bar and the last bar in the code are black. There are two kinds of black bars: wide and narrow. The number of white bars is 3 more than the number of wide black bars. How many narrow black bars are there in this bar code?

A) 1 B) 2 C) 3

(60)

E) 5

Ewa has 20 balls of four colors: yellow, green, blue, and black. 17 of them are not green, 5 are black, and 12 are not yellow. How many blue balls does Ewa have?

A) 3 B) 4 C) 6 D) 7 E) 8

There are 17 trees on one side of the street on Tomek's way from his house to school. One day Tomek marked these trees with white chalk in the following way: on the way from his house to the school he marked every other tree, starting with the first one. On his way back home he marked every third tree, starting with the first one. How many trees were not marked? A) 4 B) 5 C) 6 D) 7 E) 8

Today the date is 3.20.2003 and the time is 20:03 (8:03 P.M.) What will be the date after 2003 minutes? A) 3.21.2003 B) 3.22.2003 C) 3.23.2003 D) 4.21.2003 E) 4.22.2003

Problem Kangur_2003_0506_20 (4 pts) http://www.mathkangaroo.org What is the digit of ones in the number 20032003?

A) 7 B) 1 C) 9 D) 5 E) 3

(61)

With how many zeros does the product of the consecutive natural numbers from 1 to 50 end? A) 5 B) 10 C) 12 D) 20 E) 50

The square ABCD consists of a white square and four shaded rectangles. Each of the rectangles has a perimeter of 40 cm. What is the area of square ABCD?

We have six segments with lengths: 1, 2, 3, 2001, 2002, 2003. In how many ways can we select three of these segments to build a triangle?

A) 1 B) 3 C) 5 D) 6 E) 10

Piotrek is writing the numbers from 0 to 109 into a five-column table using a rule which is easy to understand (see the picture below). Which of the pieces below can not be filled in

(62)

In the figure, the beginning part of the path from point A to point B is shown. How long is the whole path? A) 10,200 cm B) 2,500 cm C) 909 cm D) 10,100 cm E) 9,900 cm

At 3:00 o'clock the minute hand and the hour hand make a right angle. What will the measure of the angle between these hands be after 10 minutes?

A) 90° B) 30° C) 80° D) 60° E) 35°

(63)

In the addition, every square stands for a certain digit, every triangle stands for another specific digit, and every circle denotes yet another digit. What is the sum of the numbers represented by the square and the circle?

A) 6 B) 7 C) 8 D) 9 E) 13

The shaded figure at the picture consists of five identical isosceles right triangles (see the figure below). What is the area of the shaded figure?

Red and green dragons lived in a cave. Every red dragon had 6 heads, 8 legs, and 2 tails. Every green dragon had 8 heads, 6 legs, and 4 tails. There were 44 tails altogether, and there were 6 less green legs than red heads. How many red dragons lived in the cave?

A) 6 B) 7 C) 8 D) 9 E) 10

Ania has 9 crayons in a box. At least one of them is blue. From every 4 crayons at least two are of the same color, and from every 5 crayons at most three are of the same color. How many blue crayons are in this box?

(64)

B) 3 C) 4 D) 1 E) 5

The number 2002 read from left to right and from right to left is the same. Which number from the numbers below does not have this property?

A) 1991 B) 2323 C) 2112 D) 2222 E) 4334

The picture below is a sketch of a castle. Which of the lines below does not belong to the sketch? A) B) C) D) E)

Mr. and Mrs. Kowalski have three daughters. Each of them has two brothers. How many children does the Kowalski family have?

(65)

A) 9 B) 7 C) 6 D) 5 D) 11

In which number below is the square of the tens digit equal to the triple of the sum of the digits of hundreds and ones?

A) 192 B) 741 C) 385 D) 138 E) 231

Problem Kangur_2002_0506_5 (3 pts) http://www.mathkangaroo.org What is the product 22 · 22000 · 2 equal to? (· denotes multiplication) A) 24000

B) 22002 C) 22003 D) 24002 E) 24001

On which string is the number of black hearts equal to two thirds of the number of all the hearts on that string?

A) B)

C) D) E)

(66)

B) 0.01 : 100 C) 100 : 0.01

D) 10,000 · 100 : 10 E) 0.1 · 0.01 · 10,000

Problem Kangur_2002_0506_8 (3 pts) http://www.mathkangaroo.org What is the area of the figure in the picture below?

A) 43 B) 88 C) 58 D) 30 E) 15

The area of a certain rectangle is equal to 1 m². What is the area of a triangle that was cut off from that rectangle along the line connecting the midpoints of the two adjacent sides? A) 33 dm²

B) 25 dm² C) 40 dm² D) 3,750 cm² E) 1,250 cm²

We subtracted the smallest digit number with all different digits from the greatest three-digit number with all different three-digits. What is the result?

A) 864 B) 885 C) 800 D) 899

E) Other number

(67)

Figures I, II, III and IV are squares. The perimeter of square I is equal to 16 m, and the perimeter of square II is equal to 24 m. What is the perimeter of square IV ?

A) 56 m B) 60 m C) 64 m D) 72 m E) 80 m

One medal can be cut out from a golden square plate. If four medals are made from four plates, the remaining parts of those four plates can be used to make one more plate. What is the largest number of medals that could be formed when 64 plates are used?

A) 85 B) 64 C) 80 D) 84 E) 100

Rectangle ABCD (see the picture) is built out of 24 little squares with the length of each side equal to 1. What is the area of triangle ALM?

A) 5 B) 6 C) 7 D) 8 E) Other

(68)

coordinates of points C and D if AB = 2 BC, BC = 2 CD ? A) 24 and 32 B) 24 and 28 C) 24 and 26 D) 22 and 24 E) 22 and 23

Mirek has 9 sticks with the lengths of 1 dm, 2 dm, 3 dm, 4 dm, 5 dm, 6 dm, 7 dm, 8 dm, 9 dm. With the sticks he builds triangles of which each side is built with one stick. How many triangles with a side of 1 dm can be built with those sticks?

A) 6 B) 3 C) 2 D) 1 E) 0

How many convex angles with different measures are made by the rays with P as the starting point (see the picture)?

A) 4 B) 6 C) 8 D) 10 E) 11

How many different three-digit numbers divisible by 25 can be made with the digits 0, 3, 5, 7 if the digits can be repeated?

A) 16 B) 9 C) 81

(69)

D) 64 E) 3

Each boy: Mietek, Mirek, Pawel, and Zbyszek has exactly one of the following animals: a cat, a dog, a gold fish, and a canary-bird. Mirek has a pet with fur. Zbyszek has a pet with four legs. Pawel has a bird, and Mietek and Mirek don't like cats. Which of the following sentences is not true?

A) Zbyszek has a dog. B) Pawel has a canary. C) Mietek has a golden fish. D) Zbyszek has a cat. E) Mirek has a dog.

The next day after his birthday Jas said: "The day after tomorrow will be Thursday." On what day of the week did Jas have his birthday?

A) On Monday B) On Tuesday C) On Wednesday D) On Thursday E) On Friday

In the picture below, the area of triangle ABD is equal to 15, the area of triangle ABC is equal to 12 and the area of triangle ABE is equal to 4. What is the area of pentagon ABCED?

A) 19 B) 31 C) 23 D) 27 E) 35

The weight of each possible pair of boys from a group of 5 was recorded. The following results were obtained: 90 kg, 92 kg, 93 kg, 94 kg, 95 kg, 96 kg, 97 kg, 98 kg, 100 kg and 101 kg. What is the total weight of all five boys?