Problem Kangur_2002_0506_1 (3 pts) http://www.mathkangaroo.org

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

Problem Kangur_2002_0506_2 (3 pts) http://www.mathkangaroo.org

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)

Problem Kangur_2002_0506_3 (3 pts) http://www.mathkangaroo.org

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

Problem Kangur_2002_0506_4 (3 pts) http://www.mathkangaroo.org

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)

Problem Kangur_2002_0506_6 (3 pts) http://www.mathkangaroo.org

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)

Problem Kangur_2002_0506_7 (3 pts) http://www.mathkangaroo.org

Which of the numbers below is the greatest? (· denotes multiplication, : denotes division)

A) 10 · 0.001 · 100
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?

Problem Kangur_2002_0506_9 (3 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0506_10 (3 pts) http://www.mathkangaroo.org

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

Problem Kangur_2002_0506_11 (4 pts) http://www.mathkangaroo.org

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 ?

Problem Kangur_2002_0506_12 (4 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 64 plates are used?

Problem Kangur_2002_0506_13 (4 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0506_14 (4 pts) http://www.mathkangaroo.org

In the picture below the coordinates of points A and B were indicated. What are the coordinates of points C and D if AB = 2 BC, BC = 2 CD ?

Problem Kangur_2002_0506_15 (4 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0506_16 (4 pts) http://www.mathkangaroo.org

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

Problem Kangur_2002_0506_17 (4 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0506_18 (4 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_0506_19 (4 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0506_20 (4 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0506_21 (5 pts) http://www.mathkangaroo.org

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?

Problem Kangur_2002_0506_22 (5 pts) http://www.mathkangaroo.org

There are four congruent squares. In each of them the midpoints of the sides are indicated and some regions with areas S1, S2, S3 and S4 are shaded. Which expression below is true?

A) S3 < S4 < S1 = S2
B) S3 < S1= S2 = S4
C) S3 < S1 = S4 < S2
D) S3 < S4 < S1 < S2
E) S4 < S3 < S1 < S2

Problem Kangur_2002_0506_23 (5 pts) http://www.mathkangaroo.org

You count from 1 to 100 and you clap when you say the multiples of number 3 and the numbers that are not multiples of 3 but have 3 as the last digit. How many times will you clap your hands?

Problem Kangur_2002_0506_24 (5 pts) http://www.mathkangaroo.org

The cyclist went up the hill with the speed of 12 km/h and went down the hill with the speed of 20 km/h. The ride up the hill took him 16 minutes longer than the ride down the hill. How many minutes did the cyclist take to go down the hill?

Problem Kangur_2002_0506_25 (5 pts) http://www.mathkangaroo.org

Symbols P, Q, R, S indicate the total weight of the figures drawn above them.

It is known that any two figures of the same shape have the same weight. If P < Q < R, then:

A) P < S < Q
B) Q < S < R
C) S < P
D) R < S
E) R = S

Problem Kangur_2002_0506_26 (5 pts) http://www.mathkangaroo.org

Ada has 14 gray balls, 8 white balls and 6 black balls in a bag. What is the least number of the balls she has to take out of her bag having her eyes closed to make sure that she took at least one ball of each color?

Problem Kangur_2002_0506_27 (5 pts) http://www.mathkangaroo.org

A computer virus destroys computer memory. On the first day it destroyed of this memory. On the second day it destroyed of the memory remaining after the first day; on the third day it destroyed of the memory remaining after two days and on the fourth day it destroyed of the memory remaining after three days. What part of all the computer memory was left after those four days?

Problem Kangur_2002_0506_28 (5 pts) http://www.mathkangaroo.org

What is the greatest value of the sum of the digits of the number made from the sum of the digits of a three-digit number?

Problem Kangur_2002_0506_29 (5 pts) http://www.mathkangaroo.org

In the chess competition 32 players were competing. The competition was taking place by steps. In each step all the players were divided into groups of four. In each of these groups every player played once with every other player. The two best players from the group went to the next level and the two worst players were out of the competition. After the step in which four last players played, the two best players were playing an additional final game. How many games were played during the whole competition?

Problem Kangur_2002_0506_30 (5 pts) http://www.mathkangaroo.org

A net with 32 hexagonal spaces in three rows was made out of matches (see the picture.) How many matches were used to make this net?