Problem Kangur_2002_0304_1 (3 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_3 (3 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_4 (3 pts) http://www.mathkangaroo.org

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)

Problem Kangur_2002_0304_5 (3 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_6 (3 pts) http://www.mathkangaroo.org

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

Problem Kangur_2002_0304_7 (3 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_8 (3 pts) http://www.mathkangaroo.org

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

A)
B)
C)
D)
E)

Problem Kangur_2002_0304_9 (4 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_10 (4 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_11 (4 pts) http://www.mathkangaroo.org

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)

Problem Kangur_2002_0304_12 (4 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_13 (4 pts) http://www.mathkangaroo.org

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)
D)
E)

Problem Kangur_2002_0304_14 (4 pts) http://www.mathkangaroo.org

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)

Problem Kangur_2002_0304_15 (4 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_16 (4 pts) http://www.mathkangaroo.org

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.

Problem Kangur_2002_0304_17 (5 pts) http://www.mathkangaroo.org

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.

Problem Kangur_2002_0304_18 (5 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_19 (5 pts) http://www.mathkangaroo.org

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 many blocks were not used to build those structures?

Problem Kangur_2002_0304_20 (5 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_21 (5 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_22 (5 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_23 (5 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0304_24 (5 pts) http://www.mathkangaroo.org

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?