2020 Student Test | Test and Chat

Back to KangarooMath

2020 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. What is the last digit of the multiplication 1 × 3 × 5 × 7 × 9 × 7 × 5 × 3 × 1 result ?

3 points

ABCDE

Question 1

Q2. An ant walked 6 m every day to go from point A to point B in a straight line. One day Johnny put a straight cylinder of one meter high in that way. Now the ant walks on the same straight line or above it, having to go up and down the cylinder, as shown in the pic ture. How much does she have to walk now to go from A to B?

3 points

ABCDE

Question 2

Q3. How many integers are there between 2020 , 9 and 2018 , 9 × 2022 , 9 ?

3 points

ABCDE

Question 3

Q4. What is the value of ?

3 points

ABCDE

Question 4

Q5. The pie chart beside refers to the number of inhabitants of the five zones of a city. The central zone has the same population as the north, west and east zones together and the south zone has half of the inhabitants of the west zone. What is the percentage difference between the inhabitants of the north and east zones?

3 points

ABCDE

Question 5

Q6. Be ing a , b e c integers numbers such that 1 ≤ 푎 = 푏 ≤ 푐 and 푎푏푐 = 202 0 , w hat is the highest possible value of a ?

3 points

ABCDE

Question 6

Q7. Which of the following numbers is divisible by 3, whatever the integer n ? 2 2 2 3

3 points

ABCDE

Question 7

Q8. If a dozen bananas nanica s cost the same as a dozen bananas prata and y banana s nanicas cost x reais, how many reais are z bananas prata ?

3 points

ABCDE

Question 8

Q9. Two equal dice have two red faces, two blue and two green each. If we roll the two dice simultaneously, what is the probability that the result will be two faces with different colors ?

3 points

ABCDE

Question 9

Q10. In the addition on the right , different letters represent different numbers. Assuming the account is correct , what is the highest possible value for the sum C + A + N?

3 points

ABCDE

Question 10

Q11. A gray square with an area of 36 cm 2 and a black square with an area of 25 cm 2 are superimposed, as shown be side. What is the perimeter of the overlapping region, represented by the white quadrilateral, which has a vertex on the side of the gray square?

4 points

ABCDE

Question 11

Q12. Two thousand and twenty coins are on a table, with " head " facing up. With each movement you must turn exactly three of these coins. What is the smallest number of moves you must make so that all the coins on the table have " tales " facing up?

4 points

ABCDE

Question 12

Q13. Zilda will use six equal cubes and two different rectangular blocks to form the structure beside with eight faces. Before gluing the pieces, she will paint each one entirely and calcu- lated that she will need 18 liters of paint (the color does not matter). How m any liters of paint would she use if she painted the whole structure only after gluing the parts?

4 points

ABCDE

Question 13

Q14. Let a , b and c be real numbers not null such that ( 푎 − 푎 ) + ( 푏 − 푏 ) + ( 푐 − 푐 ) = 0 . What number below can NOT be the value of 푎 + 푏 + 푐 ?

4 points

ABCDE

Question 14

Q15. The last two digits of a 2020 number are 9 and 9. At most, how many digits does the square of that number have ?

4 points

ABCDE

Q16. The sequence 푓 푛 is given by 푓 1 = 1 , 푓 2 = 2 e 푓 푛 = 푓 푛 − 1 . 푓 푛 + 1 for 푛 ≥ 2 . How many of the first 2020 ele- ments of this sequence are even numbers?

4 points

ABCDE

Question 16

Q17. Matias wrote 15 numbers on the wheel represented beside . Only one of them is visible, the 10 on top of the wheel. The sum of the numbers in any seven consecutive positions, such as the gray positions in the figure, does not vary. When seven numbers in cons ecutive positions are summed up , which of the following results is possible?

4 points

ABCDE

Q18. A large square touches another two squares, as shown in the picture. The numbers inside the smaller squares indicate their areas. What is the area of the largest square?

4 points

ABCDE

Q19. A circle is tangent to one side of a rectangle and passes through two of its vertices, as shown beside . A square of 20 cm 2 area has one side over the side of the rectangle and two vertices over the circle, as shown in the figure. What is the area of the rectan gle?

4 points

ABCDE

Question 19

Q20. Two rectangular blocks and a cube are joined to form a larger rectangular block, wh ich volume is 280 cm 3 . The cube, in dark gray in the picture, has volume equal to 125 cm 3 and the smaller rectangular block has volume equal to 75 cm 3 . What is the area of the face marked with the question mark?

4 points

ABCDE

Question 20

Q21. The figure shows the lines r and s , wh ich equations are, respectively, 푦 = 푎푥 + 푏 e 푦 = 푐푥 + 푑 . Which of the following statements is true?

5 points

ABCDE

Q22. A little kangaroo draws a line passing through point P of the grid and then paints three triangles in black as shown in the picture. The areas of these triangles are proportional to which numbers?

5 points

ABCDE

Q23. A rectangular garden was 50 m long and 40 m wide. An artificial lake was built next to it, so that the whole set forms a 60 m square. Then a fence was stretched, separating both the garden and the lake in two parts with equal areas, as shown in the picture . How long is this fence?

5 points

ABCDE

Question 23

Q24. A positive integer N is divisible by all integers from 2 to 11 except two of these numbers. Among the pairs of integers (6,7), (7,8), (8,9), (9,10) e (10,11), how many could be this exception?

5 points

ABCDE

Q25. At the Sunday fair, in the morning Ana wanted to buy three types of fruit among 12 options and one type of vegetable, among the six types available. In the afternoon some products were sold out and Bela wanted to buy two kinds of fruits and two kinds of vegetables, among the remaining ones. Since the number of possible choices for Bela was a quarter of the number of possible choices fo r Ana, how many products were sold out in the afternoon?

5 points

ABCDE

Question 25

Q26. Vilma took a sheet of paper measuring 10 cm x 20 cm and made two folds, taking the two smaller sides of the sheet to a diagonal of it. She gets a parallelogram, as shown in the picture. What is the area of this quadrilateral, in cm 2 ?

5 points

ABCDE

Q27. The submerged volume of an iceberg in the form of a cube corresponds to 96 , 4% of the volume of the iceberg. If the outside of the water has the same three edges, what is the percentage of the surface area in contact with the air in relation to the total surface area of the iceberg?

5 points

ABCDE

Q28. Maria writes all the positive divi sors of 2020, one on each card and puts all these cards in a box. Then she closes her eyes and starts taking these cards out of the box, one by one. How many cards must she take out of the box to make sure that among the c ards taken there are two with numbers a and b such that a is not a divi sor of b and b is not a divi sor of a ?

5 points

ABCDE

Question 28

Q29. There are n different prime numbers 푝 1 , 푝 2 , … , 푝 푛 writ- ten from left to right on the last line below the table shown beside . The product of two neighboring numbers in the same line is written in the upper two boxes. The number 훼 1 훼 2 훼 푛 퐾 = 푝 1 . 푝 2 … 푝 푛 is written in the last house above. In a table like th is, in which ∝ 2 = 9 , how many numbers are di- visible by number 푝 4 ?

5 points

ABCDE

Question 29

Q30. Adam and Bruna try to find out which is Carla's favorite figure, among st the fig- ures be side. Adam knows that Carla told Bruna what the shape of the figure was. Bruna knows that Carla told Adam what color the figure was. The following conver- sation takes place. Adam: "I don't know what Carla's favorite figure is and I know that Bruna doesn't k now either ” . Bruna: "At first I didn't know what Carla's favorite figure was, but now I know ” . Adam: "Now I know too". What is Carla's favorite figure?

5 points

ABCDE

Question 30

2020 Student Test | Test and Chat