Đề thi Toán Kangaroo năm 2004 Cấp độ Minor, Benjamin, Cadet, Junior, Student

 Questions of Kangaroo 2004
 MINOR (grades 3 and 4 )
3-POINT QUESTIONS
 M1. How much is 2001 + 2002 + 2003 + 2004 + 2005?
 A 1015 B 5010 C 10,150 D 11,005 E 10,015
 M2. Jerome was 4 years old when his sister was born. Today he blows out 9 birthday candles.
 What is the age difference between him and his sister?
 A 4 years B 5 years C 9 years D 13 years E 14 years
 M3. In the picture below you can see a road from town M to town N (a solid line) and a detour
 (a dashed line) of segment KL, which is under repair. How many more kilometers does one
 have to travel from M to N using the detour?
 MKL N
 3km
 A 3 B 5 C 6 D 10 E Impossible to calculate
 M4. There were some swallows on a telegraph line. All at once 5 of them flew away, and a
 while later 3 swallows came back. Then there were 12 swallows on the line. How many
 swallows were there on the line at the very beginning?
 A 8 B 9 C 10 D 12 E 14
 M5. Which numbers are written in the area that belongs 8
 to the rectangle and to the circle but doesn’t belong
 to the triangle? 6 7 9
 A 5 and 11 B 1 and 10 C 13 1
 D 3and9 E 6, 7, and 4 2 13 10 11
 3
 12
 5 4
 M6. How many white squares must you paint grey so that the number of
 grey squares is exactly half that of the white squares?
 A 2 B 3 C 4 D 6 E It cannot be done
 M7. Mary and Peter’s classmates are standing in line. Mary has 16 students in back of her,
 including Peter. Peter has 14 students in front of him including Mary. Between Mary and
 Peter there are 7 students. How many students are there, altogether, in Mary and Peter’s
 class?
 A 37 B 30 C 23 D 22 E 16 Minor (3and4grades) 111
M15. Which difference is not equal to 671 − 389?
 A 771 − 489 B 681 − 399 C 669 − 391 D 1871 − 1589 E 600 − 318
M16. Inside each of the four squares of a 2 × 2 grid there is a number. If the sum of the numbers
 of the first line is 3, the sum of the numbers of the second line is 8, and the sum of the
 numbers of the first column is 4, what is the sum of the numbers in the second column?
 A 4 B 6 C 7 D 8 E 11
5-POINT QUESTIONS
M17. This figure is made of squares. What is the side of the
 biggest square? 16
 A 24 B 56 C 64 D 81 E 100
 40
M18. Robert has 147 euros, and Lisa has 57 euros. How many euros must Robert give to Lisa so
 that Robert has twice as much as Lisa?
 A 11 B 19 C 30 D 45 E 49
M19. There are five houses on Color Street: a blue, a red, a yellow, a pink, and a green one. The
 houses are numbered from 1 to 5 (see picture). The red house is the neighbor of the blue
 house only. The blue house stands between the green and red houses.
 1 2 3 4 5
 Which color is the house with number 3?
 A Blue B Red C Yellow D Pink E Green
M20. The sum of the digits of a ten-digit number is equal to 9. What is the product of the digits
 of this number?
 A 0 B 1 C 45 D 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 E Depends on the given number
M21. A large cube consists of 125 small black and white cubes, such that
 any two adjacent faces of the small cubes have different colors, the
 corner cubes being black. How many small black cubes are used?
 A 62 B 63 C 64 D 65 E 68
M22. One lottery ticket costs 4 euros. Three boys – Paul, Peter, and Robert – pooled their money
 for two tickets. Paul gave 1 euro, Peter – 3 euros, Robert – 4 euros. One of the tickets
 they bought won 1000 euros. The boys shared the prize fairly, i.e., according to how much
 money each of them had contributed. How many euros did Peter get?
 A 300 B 375 C 250 D 750 E 425 Benjamin (grades 5 and 6 ) 113
 B9. Nine bus stops are equally spaced along a bus route. The distance from the first stop to the
 third stop is 600 m. How many meters is it from the first to the last?
 A 1800 B 2100 C 2400 D 2700 E 3000
 B10. The sum of the digits of a ten-digit number is equal to 9. What is the product of the digits
 of this number?
 A 0 B 1 C 45 D 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 E Depends of the given number
4-POINT QUESTIONS
 B11. You have two identical pieces that you can turn around but not
 upside down. Which picture can you not make with these two
 pieces?
 ABC DE
 B12. Harry folds a sheet of paper five times. Then he makes a hole in the folded paper, after
 which he unfolds it.
 How many holes has the unfolded paper?
 A 6 B 10 C 16 D 20 E 32
 B13. Different figures represent different digits. Find the digit corresponding to the
 square. +
 A 9 B 8 C 7 D 6 E 5
 B14. The weight of 3 apples and 2 oranges is 255 g. The weight of 2 apples and 3 oranges is
 285 g. Each apple has the same weight, and each orange has the same weight. What is the
 weight in grams of 1 apple and 1 orange together?
 A 110 B 108 C 105 D 104 E 102
 B15. The best mathematician in the 7th grade was asked to guess the positive integer about which
 his friends made the following statements:
 Thomas: “This number is 9.”
 Ronald: “This number is prime.”
 Andrew: “This number is even.”
 Michael: “This number is 15.”
 Ronald and Thomas together made one true statement, as well as Andrew and Michael. This
 number is:
 A 1 B 2 C 3 D 9 E 15 Benjamin (grades 5 and 6 ) 115
 B23. In the picture we have 11 fields.
 In the first field there is a 7, and in the ninth field we have a 6. What positive integer has to
 be written in the second field for the following condition to be valid: the sum of any three
 adjoining fields is equal to 21?
 A 7 B 8 C 6 D 10 E 21
 B24. This is a multiplication table. Which two letters represent the
 ´
 same number? 7
 A L and M B P and N C R and S J K L 56
 D K and R E M and T
 M 36 8 N
 P 27 6 R
 6 18 S T 42
 B25. In a CD store two CD’s have the same price. The first CD becomes 5% cheaper, and the
 other one increases 15% in price. Now the two prices differ by 6 euros. What is the price
 in euros of the cheaper CD now?
 A 1.50 B 6 C 28.50 D 30 E 34.50
 B26. You write a number in each square as shown in the square x
 figure. Then, the number x cannot be:
 A 128 B 256 C 81 D 121 E 400 ...
 10
 4 9
 3 5 8
 1 2 6 7
 B27. Bill divided 111
 ...1 by 3. The number of zeros in the quotient he obtained is equal to
 2004
 A 670 B 669 C 668 D 667 E 665
 B28. Imagine that you have 108 red balls and 180 green balls. You want to put all of them in
 bags, and there must be the same number of balls in each bag, and all the balls in each bag
 must be the same color. What is the minimum number of bags you need?
 A 288 B 36 C 18 D 8 E 1
 B29. In the Kangaroo summer camp a math competition was organized with 10 problems. Each
 correct answer was worth 5 points. For each incorrect answer 3 points were deducted.
 Everybody answered all the problems. Matt had 34 points, Zsolt had 10 points, and Ga´bor
 had 2 points. How many correct answers did they have altogether?
 A 17 B 18 C 15 D 13 E 21
 B30. A right triangle with legs of length 6 cm and 8 cm is cut out of a sheet of paper and then
 folded along a straight line. What can the area be, in cm2, of the resulting polygon?
 A 9 B 12 C 18 D 24 E 30 Cadet (grades 7 and 8) 117
 C10. We link rings together as shown in the figure below; the length of the chain is 1.7m.
 2cm ...
 3cm
 1.7 m
 How many rings are there?
 A 17 B 21 C 30 D 42 E 85
4-POINT QUESTIONS
 C11. In the picture a square ABCD and two semicircles with diameters AB
 AB and AD have been drawn. If AB = 2, what is the area of the
 shaded region?
 A 4 B 8 C 8π D 2π E 3
 C12. In the picture we have 11 fields.
 D C
 In the first field there is a 7, and in the ninth field we have a 6. What positive integer has to
 be written in the second field for the following condition to be valid: the sum of any three
 adjoining fields is equal to 21?
 A 7 B 8 C 6 D 10 E 21
 C13. In the first year of two consecutive years there were more Thursdays than Tuesdays. Which
 day of the week was there more of in the second year, considering that neither of these years
 was a leap year?
 A Tuesday B Wednesday C Friday D Saturday E Sunday
 C14. ABC is an isosceles triangle with AB = AC = 5cmand ∠BAC > 60◦. The length of its
 perimeter is a whole number of centimeters. How many such triangles are possible?
 A 1 B 2 C 3 D 4 E 5
 C15. Romeo the ostrich is training for the Head in the Sand Competition. He put his head into
 the sand at 8:15 on Monday morning and having been underground for 98 hours and 56
 minutes reached a new personal record. When did Romeo pull his head out of the sand?
 A On Thursday at 5:19 B On Thursday at 5:41 C On Thursday at 11:11
 D On Friday at 5:19 E On Friday at 11:11
 C16. Somebody has a large amount of building bricks 1 × 2 × 3. What is the smallest number of
 bricks needed to build a cube?
 A 12 B 18 C 24 D 36 E 60
 C17. Each of five children thinks of a number, which can be either 1, 2, or 4. Their numbers are
 multiplied. Which number could be the result?
 A 100 B 120 C 256 D 768 E 2048
 C18. The average age of grandmother, grandfather, and 7 grandchildren is 28 years. The average
 age of 7 grandchildren is 15 years. Find the age of grandfather, if it is known that grandfather
 is 3 years older than grandmother.
 A 71 B 72 C 73 D 74 E 75