Sample+Problems+Levels+7-8

**Problem Kangur_2004_0708_1** (3 pts) [|http://www.mathkangaroo.org] What is the value of the expression: 2004 - 200 · 4? A) 400,800 B) 0 C) 1204 D) 1200 E) 2804 Tom 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) $49 What is the remainder when dividing the sum: 2001 + 2002 + 2003 + 2004 + 2005 by 2004? A) 1 B) 2001 C) 2002 D) 2003 E) 1999 In 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?
 * NEW! ** (February 18, 2010)
 * Problem Kangur_2004_0708_2** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_3** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_4** (3 pts) [|http://www.mathkangaroo.org]


 * 1 ||  || x ||   ||
 * 4 || 1 ||  ||   ||
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A) None B) 1 C) 2 D) 3 E) 4 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 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 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% What is the length of the diameter of the circle shown in the figure? A) 18 B) 16 C) 10 D) 12 E) 14 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 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 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. 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) 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 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 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 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 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 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 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 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° 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 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 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 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 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 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 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 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 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 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. 2005 · 5002 = A) 1291 B) 102910 C) 10029010 D) 1000290010 E) 100002900010 ( · denotes multiplication) 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 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. 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 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
 * Problem Kangur_2004_0708_5** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_6** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_7** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_8** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_9** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_10** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_11** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_12** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_13** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_14** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_15** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_16** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_17** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_18** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_19** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_20** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_21** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_22** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_23** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_24** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_25** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_26** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_27** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_28** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_29** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0708_30** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2005_0708_1** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2005_0708_2** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2005_0708_3** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2005_0708_4** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2005_0708_5** (3 pts) [|http://www.mathkangaroo.org]