Question 1
The poulterer has boxes of 6 eggs and boxes of 12 eggs. What is the least amount of boxes he needs to store 66 eggs?
(A) 5 (B) 6 (C) 9 (D) 11 (E) 13
Question 2
In a school class all pupils have at least one pet and at most two pets. The pupils have recorded how many pets they have all together. Among the pupils two have both a dog and a fish. Three of the pupils have both a cat and a dog. No other pupils have two pets. How many pupils are there in this class?
(A) 11 (B) 12 (C) 13 (D) 14 (E) 17
Question 3
There are 13 coins in John?s pocket, each of them is either 5 or 10 cents. Which value cannot be the total value of John's coins?
(A) 80 (B) 60 (C) 70 (D) 115 (E) 125
Question 4
The sheet is folded along the thick line. Which letter will not be covered by a gray square?
(A) A (B) B (C) C (D) D (E) E
Question 5
Ann, Bob, Cleo, Dido, Eef, and Fer each roll a die. They all get different numbers.
The number Ann rolled is twice as much as Bob's.
The number Ann rolled is three times as much as Cleo's.
The number Dido rolled is four times as much as Eef's.
What number did Fer roll?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
Question 6
In a quiz show there are the following rules: every participant has 10 points at the beginning and has to answer 10 questions. For a correct answer 1 point is added and for an incorrect answer 1 point is taken away. Mrs. Smith had 14 points at the end of this quiz show. How many incorrect answers did she give?
(A) 7 (B) 4 (C) 5 (D) 3 (E) 6
Question 7
At each square of the magic maze there is a piece of cheese. Mouse Ron wants to enter and go out taking as many pieces of cheese as he can. He cannot step on any square twice. What is the largest number of pieces of cheese he can get?
(A) 17 (B) 33 (C) 37 (D) 41 (E) 49
Question 8
During a party each of two identical cakes was divided into four equal pieces. Then each of these pieces was divided into three equal pieces. After that each of the participants of this party got such a piece of cake and three more pieces were left. How many people were at this party?
(A) 24 (B) 21 (C) 18 (D) 27 (E) 13
Question 9
Four girlfriends Masha, Sasha, Dasha and Pasha sit on a bench.
First Masha exchanged places with Dasha.
Then Dasha exchanged places with Pasha.
At the end the girls sat on the bench in the following order from left to right: Masha, Sasha, Dasha, Pasha. In what order from left to right did they sit in the beginning?
(A) Masha, Sasha, Dasha, Pasha
(B) Masha, Dasha, Pasha, Sasha
(C) Dasha, Sasha, Pasha, Masha
(D) Sasha, Masha, Dasha, Pasha
(E) Pasha, Masha, Sasha, Dasha
Question 10
How many times a day a digital watch with four digits shows the same digit in the four positions ? In the picture there is an example of a digital watch with two different digits.
(A) 1 (B) 24 (C) 3 (D) 5 (E) 12
Question 11
Four identical dice have been arranged in a structure as shown in the figure. The sum of points (dots) on any two opposite sides is equal to 7. How does this structure look like from behind?
Question 12
You have three cards as shown in the figure. You can form different numbers with them, for example 989 or 986. How many different 3 digit numbers can you form with these three cards?
(A) 4 (B) 6 (C) 8 (D) 9 (E) 12
Question 13
Andra formed the ornament in the picture by using pieces of one single shape several times.
The pieces cannot cover each other. Which of the following pieces cannot be used by Andra to create the ornament?
Question 14
In picture 1 there is a castle built of cubes. When you look at the same castle from above it looks like in the picture 2. How many cubes were used to build the castle?
(A) 56 (B) 60 (C) 64 (D) 68 (E) 72
Question 15
John wrote 6, 7 and 8 in the circles as shown in the following picture. He will then write each of the numbers 1, 2, 3, 4 and 5 in the circles so that the sum of the numbers in each of the sides of the square is equal to 13. What will be the sum of the numbers in the shaded circles?
(A) 12 (B) 13 (C) 14 (D) 15 (E) 16
Question 16
Sylvia drew figures with hexagons like in the picture. How many hexagons will the fifth figure contain, if she continues with this pattern?
(A) 37 (B) 49 (C) 57 (D) 61 (E) 64
Question 17
You have L-shaped tiles, each consisting of 4 squares as shown:
How many of the following shapes can you make by glueing together two of these tiles?
Α) 0 Β) 1 C) 2 D) 3 Ε) 4
Question 18
Three balloons cost 12 cents more than one balloon. How much does one balloon cost?
Α) 4 Β) 6 C) 8 D) 10 Ε) 12
Question 19
Grandmother made 20 gingerbread biscuits for her grandchildren. She decorated them with raisins and nuts. First she decorated 15 biscuits with raisins and then 15 biscuits with nuts. At least how many biscuits were decorated both with raisins and nuts?
Α) 4 Β) 5 C) 6 D) 8 Ε) 10
Question 20
In a Sudoku the numbers 1, 2, 3, 4 can occur only once in each column and in each row. In the mathematical Sudoku below Patrick first writes in the results of the calculations. Then he completes the Sudoku.
Which number will Patrick put in the grey cell?
Α) 1 Β) 2 C) 3 D) 4 E) 1 or 2
Question 21
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 the class?
A) 30 B) 20 C) 24 D) 25 E) 29
Question 22
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
Question 23
A cuboid is made of four pieces, as shown. Each piece consists of four cubes and is a single colour. What is the shape of the white piece?
Question 24
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 candlesticks?
A) 45 B) 50 C) 57 D) 60 E) 75
Question 25
A grasshopper wants to climb a staircase with many steps. She makes only two different jumps: 3 steps up or 4 steps down. Beginning at the ground level, at least how many jumps will she have to make in order to take a rest on the 22th step?
A) 7 B) 9 C) 10 D) 12 E) 15
Question 26
Frank made a domino snake of seven tiles. He puts the tiles next to eacg other so that the sides with the same number of dots were touching. Originally the snake has 33 dots on its back. However his brother George took away two tiles from the snake (see the picture). How many dots were in the place with the question mark?
A) 2 B) 3 C) 4 D) 5 E) 6
Question 27
Gregor 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 Gregor can get?
A) 975 B) 999 C) 1083 D) 1173 E) 1221
Question 28
Anna, John, Helena and Kate want to be in one photo together. Kate and Anna are best friends and they want to stand next to each other. John wants to stand next to Anna because he likes her. In how many possible ways can they stand for the photo?
A) 3 B) 4 C) 5 D) 6 E) 7
Question 29
A special clock has 3 hands of different length (for hours, for minutes, and for seconds). We do not know which hand is which, but we know that the clock runs correctly. At 12:55:30pm the hands were in position depicted here.
How will this clock look like at 8:11:00pm?
Question 30
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 chose at the beginning?
A) 11 B) 9 C) 8 D) 7 E) 5
Question 31
A rectangular paper sheet measures 192 x 84 mm. You cut the sheet along just one straight line to get two parts, one of which is a square. Then you do the 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) 1mm B) 4mm C) 6mm D) 10mm E) 12mm
Question 32
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 1 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
Answer Keys
Question 1: B
Question 2: B
Question 3: B
Question 4: E
Question 5: D
Question 6: D
Question 7: C
Question 8: B
Question 9: C
Question 10: C
Question 11: C
Question 12: E
Question 13: D
Question 14: A
Question 15: E
Question 16: D
Question 17: E
Question 18: B
Question 19: E
Question 20: C
Question 21: D
Question 22: B
Question 23: D
Question 24: C
Question 25: D
Question 26: C
Question 27: D
Question 28: B
Question 29: E
Question 30: D
Question 31: E
Question 32: C