Math competition "Kangaroo" - 2009 - Benjamin - Lithuania

---

Among these numbers, which is even?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

Where is the kangaroo?



Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

How many integers are there between 2.008 and 20.09?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

The smallest number of digits to be erased in the number 12323314 in order to get a number that reads identically from left to right and from right to left, is equal to


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

There are three boxes: white, red and green. One of them contains a bar of chocolate, the second contains an apple, and the third is empty. Find the chocolate, if it is known, that the chocolate is either in the white or in the red box, and the apple is neither in the white nor in the green box.


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

KLMN is a square and К LP is an equilateral triangle. What is the measure of LQM?




Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

 A bridge is built across the river. The river is 120 meters wide. One quarter of the bridge is over the left river bank and another quarter of the bridge is over the right river bank. How long is the bridge?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

There are squares of three different sizes in the picture. The side of the smallest one is 20 cm long. How long is the marked broken line?




Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

There are cats and dogs in the room. The number of cat's paws is twice the number of dog's noses. Then the number of cats is


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

We use identical small sticks to form digits, as shown on the right. Given a number, by the weight of it we mean the number of sticks needed to compose it. What is the weight of the heaviest 2-digit number?



Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

How many positive integers n have the property that n + 2 is a divisor of number 78?



Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

 The quadrilateral ABCD has sides AB = 11, ВС = 7, CD = 9 and DA = 3 and right angles in A and C. What is the area of this quadrilateral?



Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

There are 39 boys and 23 girls in the dance group. Every week 6 more boys and 8 more girls join the dance group. After a few weeks there will be the same number of boys and girls in the dance group. How many boys and girls all in all will be then in the dance group?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

Two rectangles of 8 x 10 and 9 x 12 partly cover each other. The dark area is 37. What is the grey area?



Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

Eight cards numbered from 1 to 8 are put in the boxes M and N so that both sums of the card numbers in each box are equal. If there are only 3 cards in the box M, then you can be sure that


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

In the picture a "tower" is formed of three structures -square, rectangle, and equilateral triangle. The perimeter of all the three structures is the same. The side of the square is 9 cm long. How long is marked side of the rectangle?



Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

We want to fill up a 40 x 40 x 60 box with rigid cubes all of the same size. Which is the minimum number of cubes that allows us to do that?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

Today is Sunday. Francis begins reading a book of 290 pages. He reads 4 pages each day, except Sundays, on which he always reads 25 pages. How many days will it take him to read the book?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

Andrija Branimir, Celestin and Davor have won the first four places at the fencing tournament If you add the number of places won by Andrija, Branimir and Davor, you will get number 6. You will get the same number if you add the number of places won by Brammir and Celestin. Who won the first place, if Branimir is ranked higher than Andrija?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

Oliver takes 2009 equally sized square pieces and places them all side by side in the form of a full rectangle. How many different rectangles can he have?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

There are 4 statements about the positive integer M:
M is divisible by 5;
M is divisible by 11;
M is divisible by 55;
M is less than 10.
It is known that two of these statements are true, and the other two are false. Then M can be equal to:


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

 The picture shows a solid formed with 6 triangular faces. At each vertex there is a number. For each face we consider the sum of the 3 numbers at the vertices of that face. If all the sums are the same and two of the numbers are 1 and 5, as shown, what is the sum of all the 5 numbers?



Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

The rooms of a hotel are numbered with three digits. The first indicates the floor and the next two the number of the room. For example, 125 indicates room 25 of the first floor. It the hotel has a total of 5 floors numbered from 1 to 5 with 35 rooms per floor, how many times will the digit 2 be used to number all the rooms?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

ABCD is a square with a side 10cm long. The distance from point N to point M is 6 cm. Four of the non-shaded regions are equal isosceles triangles and other four are equal squares. Find the area of the shaded region.



Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

The total of each row and column is given.

What is the value of a + b — с?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

Jadwiga has multiplied 18 multipliers equal 8 and 50 multipliers equal 5. How many digits has the product?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

A complete set of 28 dominoes contains every possible combination of two numbers of pips between 0 and 6 included, including twice the same number. How many pips are there altogether on the set of dominoes?



Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

In а 4 х 2 table, two numbers are written in the first row. Each next row contains the sum and the difference of the numbers written in the previous row (see the picture for an example). In a table 7x2, filled in the same way, the numbers of the last row are 94 and 64. What is the sum of the numbers in the first row?



Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

In the land Funnyfeet, the left foot of each man is one or two sizes bigger than his right foot. Newertheless, the shoes are always sold in pairs of the same size. To save money, a group of friends bought shoes together. After all of them have put on the shoes that fitted them, there were exactly two shoes left, one of size 36 and the another of size 45. What is the smallest possible number of people in the group?



Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija

---

We want to color the squares in the grid using colors a, b, с and d so that the neighboring squares were not of the same color (squares that share a vertex are considered neighbors). Some of the squares have been colored as shown.

What are the possibilities for the shaded square?


Atsakymų variantai rodomi tik registruotiems sistemos eTest.lt vartotojams. Mokytojo registracija, mokinio registracija