Problem Kangur_2004_0708_1 (3 pts) http://www.mathkangaroo.orgWhat is the value of the expression: 2004 - 200 · 4?A) 400,800
B) 0
C) 1204
D) 1200
E) 2804Problem Kangur_2004_0708_2 (3 pts) http://www.mathkangaroo.orgTom has $147 and Stan has $57. How much money does Tom need to give to Stan, so that he would have twice as much money left as Stan would have then?A) $11
B) $19
C) $30
D) $45
E) $49Problem Kangur_2004_0708_3 (3 pts) http://www.mathkangaroo.orgWhat is the remainder when dividing the sum: 2001 + 2002 + 2003 + 2004 + 2005 by 2004?A) 1
B) 2001
C) 2002
D) 2003
E) 1999Problem Kangur_2004_0708_4 (3 pts) http://www.mathkangaroo.orgIn 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 she started. In how many ways can she fill the square marked with an x?
B) 0
C) 1204
D) 1200
E) 2804
B) $19
C) $30
D) $45
E) $49
B) 2001
C) 2002
D) 2003
E) 1999
| 1 | x | ||
| 4 | 1 | ||
| 3 | |||
| 2 |
A) None
B) 1
C) 2
D) 3
E) 4
B) 1
C) 2
D) 3
E) 4
Problem Kangur_2004_0708_5 (3 pts) http://www.mathkangaroo.org
What is the value of the expression: (1 - 2) - (3 - 4) - (5 - 6) - (7 - 8) - (9 - 10) - (11 - 12)?
A) -6
B) 0
C) 4
D) 6
E) 13
B) 0
C) 4
D) 6
E) 13
Problem Kangur_2004_0708_6 (3 pts) http://www.mathkangaroo.org
A section was made on a cube. On the net of the cube this section was indicated with a perforated line (see the figure). What figure was made by the section?
A) Equilateral triangle
B) A rectangle but not a square
C) Right triangle
D) Square
E) Hexagon
B) A rectangle but not a square
C) Right triangle
D) Square
E) Hexagon
Problem Kangur_2004_0708_7 (3 pts) http://www.mathkangaroo.org
By how much does the area of a rectagle increase if its length and the width are increased by 10% each?
A) 10%
B) 20%
C) 21%
D) 100%
E) 121%
B) 20%
C) 21%
D) 100%
E) 121%
Problem Kangur_2004_0708_8 (3 pts) http://www.mathkangaroo.org
What is the length of the diameter of the circle shown in the figure?
A) 18
B) 16
C) 10
D) 12
E) 14
B) 16
C) 10
D) 12
E) 14
Problem Kangur_2004_0708_9 (3 pts) http://www.mathkangaroo.org
An ice cream stand was selling ice cream in five different flavors. A group of children came to the stand and each child bought two scoops of ice cream with two different flavors. If none of the children chose the same combination of flavors and every such combination of flavors was chosen, how many children were there?
A) 5
B) 10
C) 20
D) 25
E) 30
B) 10
C) 20
D) 25
E) 30
Problem Kangur_2004_0708_10 (3 pts) http://www.mathkangaroo.org
The number x was multiplied by 0.5 and the product was divided by 3. The result was squared and 1 was added to it. The final result was 50. What was the value of number x?
A) 18
B) 24
C) 30
D) 40
E) 42
B) 24
C) 30
D) 40
E) 42
Problem Kangur_2004_0708_11 (4 pts) http://www.mathkangaroo.org
Alfonso the ostrich was training for the Head in the Sand Competition in the Animal Olympiad. He put his head in the sand at 8:15 on Monday morning and reached his new personal record by keeping it underground for 98 hours and 56 minutes. When did Alfonso pull his head out of the sand?
A) On Thursday at 5:19 A.M.
B) On Thursday at 5:41 A.M.
C) On Thursday at 11:11 A.M.
D) On Friday at 5:19 A.M.
E) On Friday at 11:11 A.M.
B) On Thursday at 5:41 A.M.
C) On Thursday at 11:11 A.M.
D) On Friday at 5:19 A.M.
E) On Friday at 11:11 A.M.
Problem Kangur_2004_0708_12 (4 pts) http://www.mathkangaroo.org
Two semicircles with diameters AB and AD were inscribed in square ABCD (see the figure). If |AB| = 2, then what is the area of the shaded region?
A) 1
B) 2
C)
D) 2
E)
B) 2
C)
D) 2
E)
Problem Kangur_2004_0708_13 (4 pts) http://www.mathkangaroo.org
If a and b are positive integers, neither of which is divisible by 10, and if a · b = 10,000 then what is the sum a + b?
A) 1024
B) 641
C) 1258
D) 2401
E) 1000
B) 641
C) 1258
D) 2401
E) 1000
Problem Kangur_2004_0708_14 (4 pts) http://www.mathkangaroo.org
There were more Thursdays than Tuesdays in the first of two consecutive years. Which day of the week appeared the most in the second year, if neither of these years was a leap year?
A) Tuesday
B) Wednesday
C) Friday
D) Saturday
E) Sunday
B) Wednesday
C) Friday
D) Saturday
E) Sunday
Problem Kangur_2004_0708_15 (4 pts) http://www.mathkangaroo.org
Isosceles triangle ABC satisfies: |AB| = |AC| = 5, and angle BAC > 60°. The length of the perimeter of this triangle is expressed with a whole number. How many triangles of that kind are there?
A) 1
B) 2
C) 3
D) 4
E) 5
B) 2
C) 3
D) 4
E) 5
Problem Kangur_2004_0708_16 (4 pts) http://www.mathkangaroo.org
How many divisors does number 2 x 3 x 5 x 7 x 11 have?
A) 2310
B) 10
C) 5
D) 2004
E) 32
B) 10
C) 5
D) 2004
E) 32
Problem Kangur_2004_0708_17 (4 pts) http://www.mathkangaroo.org
Tad has a large number of building blocks which are rectangular prisms with dimensions 1 x 2 x 3. What is the smallest number of blocks needed to build a solid cube?
A) 12
B) 18
C) 24
D) 36
E) 60
B) 18
C) 24
D) 36
E) 60
Problem Kangur_2004_0708_18 (4 pts) http://www.mathkangaroo.org
Each of 5 children wrote one of the numbers: 1, 2, 4 on the board. Then the written numbers were multiplied. Which number can be the product of those numbers?
A) 100
B) 120
C) 256
D) 768
E) 2048
B) 120
C) 256
D) 768
E) 2048
Problem Kangur_2004_0708_19 (4 pts) http://www.mathkangaroo.org
The average age of a grandmother, a grandfather and 7 grandchildren is 28. The average age of 7 grandchildren is 15 years. How old is the grandfather, if he is 3 years older than the grandmother?
A) 71
B) 72
C) 73
D) 74
E) 75
B) 72
C) 73
D) 74
E) 75
Problem Kangur_2004_0708_20 (4 pts) http://www.mathkangaroo.org
The equilateral triangle ACD is rotated counterclockwise around point A. What is the angle of rotation when triangle ACD covers triangle ABC the first time?
A) 60°
B) 120°
C) 180°
D) 240°
E) 300°
B) 120°
C) 180°
D) 240°
E) 300°
Problem Kangur_2004_0708_21 (5 pts) http://www.mathkangaroo.org
There are at least two kangaroos in the enclosure. One of them said: "There are 6 of us here" and he jumped out of the enclosure. Afterwards, every minute one kangaroo was jumping out of the enclosure saying: "Everybody who jumped out before me was lying." This continued until there were no kangaroos left in the enclosure. How many kangaroos were telling the truth?
A) 0
B) 1
C) 2
D) 3
E) 4
B) 1
C) 2
D) 3
E) 4
Problem Kangur_2004_0708_22 (5 pts) http://www.mathkangaroo.org
Points A and B are placed on a line which connects the midpoints of two opposite sides of a square with side of 6 cm (see the figure). When you draw lines from A and B to two opposite vertices, you divide the square in three parts of equal area. What is the length of segment AB?
A) 3.6 cm
B) 3.8 cm
C) 4.0 cm
D) 4.2 cm
E) 4.4 cm
B) 3.8 cm
C) 4.0 cm
D) 4.2 cm
E) 4.4 cm
Problem Kangur_2004_0708_23 (5 pts) http://www.mathkangaroo.org
Jack rides his bike from home to school uphill with average speed of 10 km/h. On the way back home his speed is 30km/h. What is the average speed of his round trip?
A) 12 km/h
B) 15 km/h
C) 20 km/h
D) 22 km/h
E) 25km/h
B) 15 km/h
C) 20 km/h
D) 22 km/h
E) 25km/h
Problem Kangur_2004_0708_24 (5 pts) http://www.mathkangaroo.org
John put magazines on a bookshelf. They have either 48 or 52 pages. Which one of the following numbers cannot be the total number of pages of all the magazines on the bookshelf?
A) 500
B) 524
C) 568
D) 588
E) 620
B) 524
C) 568
D) 588
E) 620
Problem Kangur_2004_0708_25 (5 pts) http://www.mathkangaroo.org
Inside the little squares of a big square the consecutive natural numbers were placed in a way shown in the picture. Which of the following numbers cannot be placed in square x?
A) 128
B) 256
C) 81
D) 121
E) 400
B) 256
C) 81
D) 121
E) 400
Problem Kangur_2004_0708_26 (5 pts) http://www.mathkangaroo.org
In the figure there are 11 boxes. Number 7 was written in the first box and number 6 was written in the ninth box. What was the number placed in the second field with the following condition: the sums of each three consecutive numbers in the boxes are equal to 21?
A) 7
B) 10
C) 8
D) 6
E) 21
B) 10
C) 8
D) 6
E) 21
Problem Kangur_2004_0708_27 (5 pts) http://www.mathkangaroo.org
For each triple of numbers (a, b, c) another triple of numbers (b + c, c + a, a + b) was created. This was called operation. 2004 such operations were made starting with numbers (1, 3, 5), and resulting with numbers (x, y, z). What is the difference x - y equal to?
A) -2
B) 2
C) 4008
D) 2004
E) (-2)2004
B) 2
C) 4008
D) 2004
E) (-2)2004
Problem Kangur_2004_0708_28 (5 pts) http://www.mathkangaroo.org
Number 2004 is divisible by 12 and the sum of its digits is equal to 6. Altogether, how many four-digit numbers have these two properties?
A) 10
B) 12
C) 13
D) 15
E) 18
B) 12
C) 13
D) 15
E) 18
Problem Kangur_2004_0708_29 (5 pts) http://www.mathkangaroo.org
Rings with dimensions shown in the figure were linked together, forming 1.7m long chain. How many rings were used to create the chain?
A) 30
B) 21
C) 42
D) 85
E) 17
B) 21
C) 42
D) 85
E) 17
Problem Kangur_2004_0708_30 (5 pts) http://www.mathkangaroo.org
On each face of a cube a certain natural number was written, and at each vertex a number equal to the product of the numbers on the three faces adjacent to that vertex was placed. If the sum of the numbers on the vertices is 70 then what is the sum of the numbers on all the faces of the cube?
A) 12
B) 35
C) 14
D) 10
E) Cannot be determined.
B) 35
C) 14
D) 10
E) Cannot be determined.
Problem Kangur_2005_0708_1 (3 pts) http://www.mathkangaroo.org
2005 · 5002 =
A) 1291
B) 102910
C) 10029010
D) 1000290010
E) 100002900010 ( · denotes multiplication)
B) 102910
C) 10029010
D) 1000290010
E) 100002900010 ( · denotes multiplication)
Problem Kangur_2005_0708_2 (3 pts) http://www.mathkangaroo.org
How many hours are there in half of a third part of a quarter of a day?
A) 
B)
C) 1
D) 2
E) 3
B)
C) 1
D) 2
E) 3
Problem Kangur_2005_0708_3 (3 pts) http://www.mathkangaroo.org
The edge of the cube is 12 cm long. The ant moves on the cube surface from point A to point B along the path shown in the figure. Find the length of the ant's path.
A) 60cm
B) 50cm
C) 48cm
D) 40cm
E) It cannot be determined.
B) 50cm
C) 48cm
D) 40cm
E) It cannot be determined.
Problem Kangur_2005_0708_4 (3 pts) http://www.mathkangaroo.org
The sum of the volume of three pitchers and two bottles equals 16 liters. The volume of each pitcher is two times greater than the volume of each bottle. What is the sum of the volume of two pitchers and three bottles?
A) 12 liters
B) 13 liters
C) 14 liters
D) 16 liters
E) 17 liters
B) 13 liters
C) 14 liters
D) 16 liters
E) 17 liters
Problem Kangur_2005_0708_5 (3 pts) http://www.mathkangaroo.org
At our school, 50% of the students have bikes. Of the students who have bikes, 30% have skateboards. What percent of the students at our school have both a bike and a skateboard?
A) 15
B) 20
C) 25
D) 40
E) 80
B) 20
C) 25
D) 40
E) 80
Problem Kangur_2005_0708_6 (3 pts) http://www.mathkangaroo.org
In triangle ABC, the measure of the angle at vertex A is three times the measure of the angle at vertex B and half the measure of the angle at vertex C. What is the measure of the angle at vertex A?
A) 30º
B) 36º
C) 54º
D) 60º
E) 72º
B) 36º
C) 54º
D) 60º
E) 72º
Problem Kangur_2005_0708_7 (3 pts) http://www.mathkangaroo.org
How many three-digit numbers are there in which all the digits are even?
A) 25
B) 64
C) 75
D) 100
E) 125
B) 64
C) 75
D) 100
E) 125
Problem Kangur_2005_0708_8 (3 pts) http://www.mathkangaroo.org
The diagram shows the floor plan of a room. Adjacent walls are perpendicular to each other. Letters a and b represent the lengths of some the walls. What is the area of the room?
A) 2ab + a(b-a)
B) 3a(a+b) - a²
C) 3a²b
D) 3a(b-a) + a²
E) 3ab
B) 3a(a+b) - a²
C) 3a²b
D) 3a(b-a) + a²
E) 3ab
Problem Kangur_2005_0708_9 (3 pts) http://www.mathkangaroo.org
In the diagram, the five circles have the same radii, and they touch as shown. The small square joins the centres of the four outer circles. What is the ratio of the shaded area of all the circles to the non-shaded area of all the circles?
A) 2 : 3
B) 1 : 3
C) 2 : 5
D) 5 : 4
E) 1 : 4
B) 1 : 3
C) 2 : 5
D) 5 : 4
E) 1 : 4
Problem Kangur_2005_0708_10 (3 pts) http://www.mathkangaroo.org
There was a certain number of crows sitting on trees in the garden. If there had been just one crow sitting on each tree, then one crow would not have had a tree to sit on. However, if two crows had been sitting on each tree, then there would not be any crows on one tree. How many trees were there in the garden?
A) 2
B) 3
C) 4
D) 5
E) 6
B) 3
C) 4
D) 5
E) 6
Problem Kangur_2005_0708_11 (4 pts) http://www.mathkangaroo.org
Anna, Barbara, Teddy, and Wally went to a dance. They danced in pairs. Anna danced with Teddy and with Wally. Barbara danced with Teddy, but she didn't dance with Wally. Decide which statement is false.
A) Each of the girls danced with one of the two boys.
B) One of the two girls didn't dance with one of the two boys.
C) One of the boys danced with both girls.
D) Each of the boys danced with one of the two girls.
E) One of the boys didn't dance with any of the two girls.
B) One of the two girls didn't dance with one of the two boys.
C) One of the boys danced with both girls.
D) Each of the boys danced with one of the two girls.
E) One of the boys didn't dance with any of the two girls.
Problem Kangur_2005_0708_12 (4 pts) http://www.mathkangaroo.org
A group of classmates was planning a trip. If each of them paid $14, then they would be $4 short to pay for the trip. On the other hand, if each of them paid $16, they would have $6 more than they needed. How much should each of the classmates contribute so they collect the exact amount needed for the trip?
A) $14.40
B) $14.60
C) $14.80
D) $15.00
E) $15.20
B) $14.60
C) $14.80
D) $15.00
E) $15.20
Problem Kangur_2005_0708_13 (4 pts) http://www.mathkangaroo.org
Carla cut a sheet of paper into 10 pieces. Then she took one piece and cut it again into 10 pieces. She then repeated this three more times. How many pieces of paper did she have after the last cutting?
A) 36
B) 40
C) 46
D) 50
E) 56
B) 40
C) 46
D) 50
E) 56
Problem Kangur_2005_0708_14 (4 pts) http://www.mathkangaroo.org
A doorman works according the following schedule: he works for 4 consecutive days and has the fifth day off. Last Sunday he had the day off, and on Monday he started work according to his schedule. After how many days, including that Monday, will he have a day off on Sunday again?
A) 30
B) 36
C) 12
D) 34
E) 7
B) 36
C) 12
D) 34
E) 7
Problem Kangur_2005_0708_15 (4 pts) http://www.mathkangaroo.org
Two rectangles ABCD and DBEF are shown in the picture. What is the area of rectangle DBEF?
A) 10 cm²
B) 12 cm²
C) 13 cm²
D) 14 cm²
E) 16 cm²
B) 12 cm²
C) 13 cm²
D) 14 cm²
E) 16 cm²
Problem Kangur_2005_0708_16 (4 pts) http://www.mathkangaroo.org
What is the measure of angle indicated in the picture?
A) 110º
B) 115º
C) 120º
D) 126º
E) 130º
B) 115º
C) 120º
D) 126º
E) 130º
Problem Kangur_2005_0708_17 (4 pts) http://www.mathkangaroo.org
From noon until midnight, Clever Cat sleeps under the oak tree, and from midnight until noon he tells stories. There is a sign on the oak tree saying: "Two hours ago Clever Cat was doing the same thing that he will be doing in an hour." How many hours a day is the information given on the sign true?
A) 6
B) 12
C) 18
D) 3
E) 21
B) 12
C) 18
D) 3
E) 21
Problem Kangur_2005_0708_18 (4 pts) http://www.mathkangaroo.org
The diagram shows an equilateral triangle and a regular pentagon. What is the measure of angle x?
A) 124º
B) 128º
C) 132º
D) 136º
E) 140º
B) 128º
C) 132º
D) 136º
E) 140º
Problem Kangur_2005_0708_19 (4 pts) http://www.mathkangaroo.org
Which of the numbers below is the sum of four consecutive whole numbers?
A) 15
B) 2000
C) 2002
D) 2004
E) 2005
B) 2000
C) 2002
D) 2004
E) 2005
Problem Kangur_2005_0708_20 (4 pts) http://www.mathkangaroo.org
Each pair vertices of a cube are connected with a segment. How many different points are there that are the midpoints of these segments?
A) 8
B) 12
C) 16
D) 19
E) 28
B) 12
C) 16
D) 19
E) 28
Problem Kangur_2005_0708_21 (5 pts) http://www.mathkangaroo.org
Let's call the number of prime factors of a natural number n, the product of which is equal to the given natural number n, "the length". For example, the length of 90 = 2x3x3x5 equals 4. How many odd numbers less than 100 have the length of 3?
A) 2
B) 3
C) 5
D) 7
E) Other number.
B) 3
C) 5
D) 7
E) Other number.
Problem Kangur_2005_0708_22 (5 pts) http://www.mathkangaroo.org
In each of the four small squares shown in the picture, a different natural odd number less than 20 was written. Only one of the statements below is true. Which one is it?
A)The sum of the numbers that are inscribed in the square equals 66.
B)The sum of the numbers that are inscribed in the square equals 12.
C)Product of all the numbers inscribed in the square equals 2005.
D)The product of the numbers on each diagonal equals 21.
E)The sum of the number on each diagonal equals 20.
B)The sum of the numbers that are inscribed in the square equals 12.
C)Product of all the numbers inscribed in the square equals 2005.
D)The product of the numbers on each diagonal equals 21.
E)The sum of the number on each diagonal equals 20.
Problem Kangur_2005_0708_23 (5 pts) http://www.mathkangaroo.org
The sequence of letters AGKNORU in alphabetical order corresponds to a sequence of different digits placed in increasing order. What is the greatest number that corresponds with the word KANGOUROU?
A) 987654321
B) 987654354
C) 436479879
D) 536479879
E) 597354354
B) 987654354
C) 436479879
D) 536479879
E) 597354354
Problem Kangur_2005_0708_24 (5 pts) http://www.mathkangaroo.org
Peter wrote down all three-digit numbers which have the following features: each number consists of three different digits, and the first digit is equal to the second power of the quotient of the second and the third digit. How many numbers did Peter write down?
A) 8
B) 4
C) 3
D) 2
E) 1
B) 4
C) 3
D) 2
E) 1
Problem Kangur_2005_0708_25 (5 pts) http://www.mathkangaroo.org
Five lines: l1, l2, l3, l4, l5 intersect point O and they are intersected by five other lines k1, k2, k3, k4, k5 (see the picture). What is the sum of the measures of 10 shaded angles, shown in the picture?
A) 300
B) 450
C) 360
D) 600
E) 720
B) 450
C) 360
D) 600
E) 720
Problem Kangur_2005_0708_26 (5 pts) http://www.mathkangaroo.org
There were 64 liters of juice in a barrel. Then, 16 liters of juice were dumped out and replaced with 16 liters of water. After being mixed together, again 16 liters of the mixture were dumped and replaced with 16 liters of water. After being mixed together, this was done again, 16 liters of the mixture were dumped and replaced with water. How many liters of juice are there in the mixture now?
A) 27
B) 24
C) 16
D) 30
E) 48
B) 24
C) 16
D) 30
E) 48
Problem Kangur_2005_0708_27 (5 pts) http://www.mathkangaroo.org
How many two-digit numbers with the ones digit greater than zero are there that are greater than three times the number that is created out of these numbers by reversing its digits?
A) 6
B) 10
C) 15
D) 22
E) 33
B) 10
C) 15
D) 22
E) 33
Problem Kangur_2005_0708_28 (5 pts) http://www.mathkangaroo.org
ABC is a right triangle. AH is the height of the triangle and AK is a bisector of right angle A. If the ratio CK : KB equals then what is the ratio of CH : HB?
then what is the ratio of CH : HB?A) 1 : 3
B) 1 : 9
C) 1 :
D) 1 : 6
E) 1 : 4
B) 1 : 9
C) 1 :
D) 1 : 6
E) 1 : 4
Problem Kangur_2005_0708_29 (5 pts) http://www.mathkangaroo.org
If the average of 10 different positive integers is 10, how large can the greatest of these numbers be?
A) 91
B) 55
C) 50
D) 45
E) 10
B) 55
C) 50
D) 45
E) 10
Problem Kangur_2005_0708_30 (5 pts) http://www.mathkangaroo.org
A particle moves through the first quadrant of the figure as follows: during the first minute it moves from the origin to (1,0). Then, it continues to follow the pattern indicated in the figure, going back and forth between the positive x and y axes, moving one unit of distance parallel to an axis in one minute. Which point will the particle reach after exactly 2 hours?
A) (10,0)
B) (1,11)
C) (10,11)
D) (2,10)
E) (11,11)
B) (1,11)
C) (10,11)
D) (2,10)
E) (11,11)
