International Kangaroo Mathematics Contest 2012

International Kangaroo Mathematics Contest 2012

Level Ecolier (Class 3 & 4)

Time Allowed: 2 hours

1.     Basil wants to write the word MATHEMATICS on a sheet of paper. He wants

 different letters to be colored differently, and the same letter to be colored                identically. How many colors will he need?

A.    7

B.     8

C.     9

D.    10

E.     13

2.     13 children are playing hide and seek. One of them is the “seeker” and the others hide. After a while 9 children have been found. How are still hiding?

A.    3

B.     4

C.     5

D.    9

E.     22

3.     The year 2012 is a leap year that means there are 29 days in February. Today, on the 15^th March 2012, the ducklings of my grandfather are 20 days old. When did they hatch from their eggs?

A.    On 19^th of February

B.     On 21^th of February

C.     On23^th of February

D.    On 24^th of February

E.     On 26^th of February

4.     Three balloons costs 12 cents more than one balloon. How much does one balloon cost?

A.    4

B.     6

C.     8

D.    10

E.     12

5.     Grandmother made 20 gingerbread biscuits for her grandchildren. She decorated them with raisins and nuts. First she decorated 15 cakes with raisins and then 15 cakes with nuts. At least how many cakes will were decorated both with raisins and nuts?

A.    4

B.     5

C.     6

D.    8

E.     10

6.     Among Nikolay’s classmates there are twice as many girls as boys. Which of the following numbers can be equal to the number of all children in this class?

A.    30

B.     20

C.     24

D.    25

E.     29

7.     In the animal’s school, 3 kittens, 4 ducklings, 2 goslings and several lambs are taking lessons. The teacher owl found out that all of her pupils have 44 legs altogether. How many lambs are among them?

A.    6

B.     5

C.     4

D.    3

E.     2

8.     At a Christmas party there was exactly one candlestick on each of the 15 tables. There were 6 five-branched candlesticks, the rest of them were three-branched ones. How many candles had to be bought for all the candle sticks?

A.    45

B.     50

C.     57

D.    60

E.     75

9.      George forms two numbers with the digits 1, 2, 3, 4, 5 and 6. Both numbers have three digits, each digit is used only once. He adds these two numbers. What is the greatest sum George can get?

A.    975

B.     999

C.     1083

D.    1173

E.     1221

10.  Laura, Iggy, Val and Kate want to be in one photo together. Kate and Laura are best friends and they want to stand next to each other. Iggy want to stand next to Laura because he like her. In how many possible ways can they arrange for the photo?

A.    3

B.     4

C.     5

D.    6

E.     7

11. Michael chose some positive number, multiplied it by itself, added 1, multiplied the result by 10, added 3 and multiplied the result by 4. His final answer was 2012. What number did Michael choose?

A.    11

B.     9

C.     8

D.    7

E.     5

12.  A rectangular paper sheet measures 192 × 84 mm. you cut the sheet along just one straight line to get two parts, one of which is a square. Then you do same with the non-square part of the sheet, and so on. What is the length of the side of the smallest square you can get with this procedure?

A.    1 mm

B.     4mm

C.     6mm

D.    10 mm

E.     12 mm

13.  In a soccer game the winner gains 3 points, while the loser gains 0 points. If the game is a draw, then the two teams gain one point each. A team has played 38 games gaining 80 points. Find the greatest possible number of games that the team lost.

A.    12

B.     11

C.     10

D.    9

E.     8

14.  Basil wants to paint the KANGAROO. He painted one letter each day. He starts on Wednesday. On what day will he paint the last letter?

A.    Monday

B.     Tuesday

C.     Wednesday

D.    Thursday

E.     Friday

15.   Simon got up one hour and a half ago. In three hours and a half ago, he will take the train to grandmothers. How long before the train departure did he get up?

A.    2 hours

B.     3 and a half hours

C.     4 hours

D.    hours

E.     4 and a half hours

16.  Lenka paid 1 euro and 50 cents for three scoop of ice-cream. Miso paid 2 euro and 40 cents for two cakes. How much did Igor pay for one scoop of ice-cream and one cake?

A.    1 euro 70 cents

B.     1 euro 90 cents

C.     2 euro 70 cents

D.    2 euro 20 cents

E.     3 euro 90 cents

17.  A tower clock strikes on the hour (that is, at 8:00, 9:00, 10:00 and so on) as many times as the hour. The clock also strikes once when the time is half past an hour (that is, at 8:00, 9:00, 10:00 and so on). How many times did the clock strike from :55 to 10:45?

A.    6

B.     18

C.     27

D.    30

E.     33

18.   The poulterer has boxes of 6 eggs and boxes of 12 eggs. What is the smallest number of boxes he need on order to store 66 eggs?

A.    5

B.     6

C.     9

D.    11

E.     13

19.  There are 13 coins in john’s pocket. Each coin is either 5 or 10 cents. Which of the following cannot be the total value of john’s coins?

A.    80 cents

B.     60 cents

C.     70 cents

D.    115 cents

E.     125 cents

20.  Ann, Bob, Cleo, Dido, Eef and Fer each roll a die. They all get different numbers.

The number Ann rolled is twice Bob’s number.

The number Ann rolled is three times the Cleo’s.

The number Dido rolled is four times the Eef.

What number did fer roll?

A.    2

B.     3

C.     4

D.    5

E.     6

21.  A quiz show has the following rules. Every participant has 10 points in the beginning and has to answer 10 questions. For a correct answer 1 point is added and for an incorrect answers 1 point is taken away. Mrs Smith had 14 points at the end of the quiz show. How many incorrect answers did she give?

A.    3

B.     4

C.     5

D.    6

E.     7

22.  During the party each of the two identical cakes are divided into four equal parts. Then each of these parts divided into equal three slices. Each person at a party got a slice of cake and three slices will left over. How many people were at the party?

A.    24

B.     21

C.     18

D.    27

E.     13

23.   In London 2012, the USA won the most medals: 46 gold, 29 silver and 29 bronze. China was second with 38 gold, 27 silver and 23 bronze. How many more medals did the USA win than China?

A.    6

B.     14

C.     16

D.    24

E.     26

24.  Daniel had a 36 packets of candies. He divided all the candies equally among all his friends. Which of the following was not definitely the number of the friends?

A.    2

B.     3

C.     4

D.    5

E.     6

25. Vero’s mum prepare sandwiches with two slices of bread each. A package of bread has 24 slices. How many sandwiches can she prepare from two and half packages of bread?

A.    24

B.     30

C.     48

D.    34

E.     26

26.  About the number 325, five boys said:

Andrie: “This is a three digit number”

Boris: “All digits are distinct”

Vitiya: “The sum of the digits is 10”

Grisha: “The unit digit is 5”

Danya: “All digits are odd”

Which of the boys was wrong?

A.    Andrie

B.     Boris

C.     Vitiya

D.    Grisha

E.     Danya

27.  When Pinocchio lies, his nose gets 6 cm long. When he tells the truth his nose gets 2 cm shorter. When his nose was 9 cm long, he told three lies and made two true statements. How long was Pinocchio’s nose afterwards?

A.    14 cm

B.     15 cm

C.     19 cm

D.    23 cm

E.     31 cm

28.  In a shop you can buy oranges in boxes of three different sizes: with 5 oranges, with 9 oranges and with 10 oranges. Pedro wants to buy exactly 48 oranges. What is the smallest number of boxes he can buy?

A.    8

B.     7

C.     6

D.    5

E.     4

29. Schoolmates Andy, Batty, Cathie and Dannie were born in the same year. Their birthday were on February 20^th, April 12^th and May 26^th, not necessarily in this order. Betty and Andy were born in a same month. Andy and Cathie were born in a same day of different months. Who of these schoolmates is the oldest?

A.    Andy

B.     Cathie

C.     Betty

D.    Dannie

E.     Impossible to determine

30.  30 children from Adventure Park took part in events. 15 of them took part in the “moving bridge” contest and 20 of them went down to the zip-wire. How many children from Adventure Park took part in both events?

A.    25

B.     15

C.     30

D.    10

E.     5

31.  The number 35 has the property that it is divisible by the digit in the unit position, because 35 divisible by 5 is 7. The number 38 does not have this property. How many numbers greater than 21 and smaller than 30 have this property?

A.    2

B.     3

C.     4

D.    5

E.     6

32.  After the First January 2013, how many years will pass before the following event happens for the first time: the product of digits in the notation of the year is greater than the sum of these digits?

A.    87

B.     98

C.     101

D.    102

E.     103

33.  In December Tosha-the –cat slept for exactly 3 weeks. How many minutes did he stay awake during this month?

A.    (31 - 7). 3 . 24 . 60

B.     (31 - 7. 3). 24 . 60

C.     (30 - 7. 3). 24 . 60

D.    (31 - 7). 24 . 60

E.     (31 - 7. 3). 24 . 60 .60

34. Cristi has to sell 10 glass bells that vary in price: 1 euro, 2 euro, euro, 3 euro, 4 euro, 5 euro, 6 euro, 7 euro, 8 euro, 9 euro, 10 euro. In how many ways can Cristi divide all the glass bells in three packages so that all packages has same price.

A.    1

B.     2

C.     3

D.    4

E.     Such a division is not possible

35. Baby Roo wrote down several numbers using only the digits 0 and 1. The sum of these numbers is 2013. It turned out that it is impossible to get the same sum with the smaller number of summands of this kind. How many numbers are written by Baby Roo.

A.    2

B.     3

C.     4

D.    5

E.     204