Sample+Problems+Levels+3-4

Sample Problems (February 18 2010) **Problem Kangur_2004_0304_1** (3 pts) [|http://www.mathkangaroo.org] 2001+ 2002 + 2003 + 2004 + 2005 = A) 1,015 B) 5,010 C) 10,150 D) 11,005 E) 10,015 Marek was 4 years old when his sister was born. Today he blew out all 9 candles on his birthday cake. What is the difference between Marek's and his sister's age today? A) 4 years B) 5 years C) 9 years D) 13 years E) 14 years The picture below shows a road from town A to town B (indicated by solid line) and a detour (marked by a dash line) caused by renovation of the section CD. How many kilometres longer is the road from town A to town B because of the detour now? A) 3 km B) 5 km C) 6 km D) 10 km E) This cannot be calculated. Which of the results below is not identical to the difference 671 - 389? A) 771 - 489 B) 681 - 399 C) 669 - 391 D) 1871 - 1589 E) 600 - 318 There were some birds sitting on the telegraph wire. At one moment, 5 of them flied away and after some time, 3 birds came back. At that time there were 12 birds sitting on the wire. How many birds were there at the very beginning? A) 8 B) 9 C) 10 D) 12 E) 14 Which numbers are inside a rectangle and inside a circle but not inside a triangle at the same time? A) 5 and 11 B) 1 and 10 C) 13 D) 3 and 9 E) 6, 7 and 4 Buildings on Color Street are numbered from 1 to 5 (see the picture). Each building is colored with one of the following colors: blue, red, yellow, pink, and green. It is known that: - The red building neighbours with the blue one only. - The blue building is between the red one and the green one. What is the color of the building numbered with 3? A) Blue B) Red C) Yellow D) Pink E) Green How many white squares need to be shaded so that the number of shaded squares equals exactly to half of the number of white squares? A) 2 B) 3 C) 4 D) 6 E) It is impossible to calculate it. Five identical sheets of a plastic rectangles were divided into white and black squares. Which of the sheets from A) to E) has to be covered with the sheet to the right in order to get totally black rectangle? A) B)  C)  D)  E) The scales in the pictures had been balanced. There are pencils and a pen on the arms of the scales. What is the weight of the pen in grams? A) 6 g B) 7 g C) 8 g D) 9 g E) 10 g I notice four clocks on the wall (see the picture). Only one of them shows correct time. One of them is 20 minutes ahead, another is 20 minutes late, and the other is stopped. What is the time at the moment? A) 4:45 B) 5:05 C) 5:25 D) 5:40 E) 12:00 Ella brought a basket of apples and oranges for a birthday party. Guests ate half of the apples and the third part of the oranges. In the basket remained: A) Half of all fruits B) More than half of all fruits C) Less than half of all fruits D) A third part of all fruits E) Less than a third part of all fruits Ania divided a certain number by 10 instead of multiplying it by 10. As a result she got 600. What would the result have been if she hadn't made that mistake? A) 6 B) 60 C) 600 D) 6,000 E) 60,000 Kathy found a book, which was lack of certain number of sheets. When she opened the book she saw number 24 on the left side and number 45 on the right side. How many sheets between those sides were missing? A) 9 B) 10 C) 11 D) 20 E) 21 Eva is 52 days older than her girlfriend Ania. Eva had her birthday on Tuesday in March of this year. On which day of the week will Ania celebrate her birthday this year? A) Monday B) Tuesday C) Wednesday D) Thursday E) Friday Into the squares of diagram numbers were placed so that the sum of the numbers in the first row is equal to so that the sum of the numbers in the first row is equal to 3, the sum of the numbers in the second row is equal to 8, and the sum of the numbers in the first column is equal to 4. What is the sum of the numbers in the second column? A) 4 B) 6 C) 7 D) 8 E) 11 The cube (see the picture) is colored with three colors so that every side of this cube is one color and every two opposite sides are the same color. From which of the patterns below this kind of cube can be made? Four square tiles were arranged in a way shown in the picture. The lengths of the sides of two tiles are indicated in the picture. What is the length of the side of the largest tile? A) 24 B) 56 C) 64 D) 81 E) 100 Girls and boys from Maria's and Mathew's class have formed a line. There are 16 students on Maria's right, and Mathew is among them. There are 14 students on Mathew's left, and Maria is among them. There are 7 students between Maria and Mathew. How many students are in this class? A) 37 B) 30 C) 23 D) 22 E) 16 The sum of the digits of the 10-digit number is 9.What is the product of the digits of this number? A) 0 B) 1 C) 45 D) 9 x 8 x 7 x ... x 2 x 1 E) 10 Out of 125 small, white and black cubes, the big cube was formed (see the picture). Every two adjacent cubes have different colors. The vertices of the big cube are black. How many white cubes does the big cube contain? A) 62 B) 63 C) 64 D) 65 E) 68 A lottery-ticket was 4 dollars. Three boys: Paul, Peter, and Robert made a contribiution and bought two tickets. Paul gave 1 dollar, Peter gave 3 dollars, and Robert gave 4 dollars. One of the tickets they bought was worth 1000 dollars. Boys shared the award fairly, meaning, proportionally to their contributions. How much did Peter receive? A) 300 B) 375 C) 250 D) 750 E) 425 In three soccer games the Dziobak's team scored three goals and lost one. For every game won the team gets 3 points, for a tie it gets 1 point, and for the game lost it gets 0 points. For sure, the number of points the team earned in those three games was not equal to which of the following numbers? A) 7 B) 6 C) 5 D) 4 E) 3 In every white section of a diagram, the products of two numbers from grey sections - one from above and one from the left - was placed (for example: 42 = 7 · 6 ). Some of these products are represented by letters. Which two letters represent the same number? A) L and M B) T and N C) R and P D) K and P E) M and S
 * Problem Kangur_2004_0304_2** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_3** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_4** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_5** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_6** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_7** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_8** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_9** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_10** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_11** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_12** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_13** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_14** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_15** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_16** (4 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_17** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_18** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_19** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_20** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_21** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_22** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_23** (5 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2004_0304_24** (5 pts) [|http://www.mathkangaroo.org]

Sample Problems 3-4 (week of January 10th) **Problem Kangur_2005_0304_1** (3 pts) [|http://www.mathkangaroo.org] A butterfly sat down on a correctly solved problem. What number did it cover up? A) 250 B) 400 C) 500 D) 910 E) 1800 At noon, the minute hand of a clock is in the following position: What will the position of the minute hand be after 17 quarters of an hour? A) B)  C)  D)  E) Joan bought some cookies, each of which costs 3 dollars. She gave the salesperson 10 dollars, and received 1 dollar as change. How many cookies did Joan buy? A) 2 B) 3 C) 4 D) 5 E) 6 After the trainer's first whistle, the monkeys at the circus formed 4 rows. There were 4 monkeys in each row. After the second whistle, they rearranged themselves into 8 rows. How many monkeys were there in each row after the second whistle? A) 1 B) 2 C) 3 D) 4 E) 5 Eva lives with her parents, her brother, one dog, two cats, two parrots, and four fish. What is the total number of legs that they have altogether? A) 22 B) 24 C) 28 D) 32 E) 40
 * Problem Kangur_2005_0304_2** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2005_0304_3** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2005_0304_4** (3 pts) [|http://www.mathkangaroo.org]
 * Problem Kangur_2005_0304_5** (3 pts) [|http://www.mathkangaroo.org]