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 )

Problem Kangur_2003_0506_2 (3 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_3 (3 pts) http://www.mathkangaroo.org

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
D) 24
E) 36

Problem Kangur_2003_0506_5 (3 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_6 (3 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_7 (3 pts) http://www.mathkangaroo.org

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
D) 10 cm
E) 11 cm

Problem Kangur_2003_0506_8 (3 pts) http://www.mathkangaroo.org

The value of the expression is equal to:

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

Problem Kangur_2003_0506_9 (3 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_10 (3 pts) http://www.mathkangaroo.org

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
D) 24 dm
E) 28 dm

Problem Kangur_2003_0506_11 (4 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_12 (4 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_13 (4 pts) http://www.mathkangaroo.org

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?

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

Problem Kangur_2003_0506_14 (4 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_15 (4 pts) http://www.mathkangaroo.org

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.

Problem Kangur_2003_0506_16 (4 pts) http://www.mathkangaroo.org

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
D) 4
E) 5

Problem Kangur_2003_0506_17 (4 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_18 (4 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_19 (4 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_21 (5 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_22 (5 pts) http://www.mathkangaroo.org

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?

A) 100 cm²
B) 200 cm²
C) 160 cm²
D) 400 cm²
E) 80 cm²

Problem Kangur_2003_0506_23 (5 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_24 (5 pts) http://www.mathkangaroo.org

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 with numbers to fit Piotrek's table?

Problem Kangur_2003_0506_25 (5 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_26 (5 pts) http://www.mathkangaroo.org

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°

Problem Kangur_2003_0506_27 (5 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_28 (5 pts) http://www.mathkangaroo.org

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?

A) 20 cm²
B) 25 cm²
C) 35 cm²
D) 45 cm²
E) 60 cm²

Problem Kangur_2003_0506_29 (5 pts) http://www.mathkangaroo.org

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

Problem Kangur_2003_0506_30 (5 pts) http://www.mathkangaroo.org

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?

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