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

(A) 15 4 points 11. A gray square with an area of 36 cm? and a black square with an area of 25 cm? are superimposed, as shown beside. What is the perimeter of the overlapping region, represented by the white quadrilateral, which has a vertex on the side of the gray square? (A) It is not determined. (B) 11 cm (C)16 cm (D) 18 cm (E)20cm 12. 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? (A) 672 (B) 673 (C) 674 (D) 675 (E) It is not possible to make all the "tales" face up. 13. 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 many liters of paint would she use if she painted the whole structure only after gluing the parts? (A) 8,4 (B) 9,6 ( 11,5 (D) 12,8 (E) 16,0 14, Let g, b and c be real numbers not null such that (a a )2+ (b b~ 1%+ (c cH2=0. What number below can NOT be the value of a + b + ? (A) =3 (8) -1 (o (D)1 (E)3 15. The last two digits of a 2020 number are 9 and 9. At most, how many digits does the square of that number have? (A) 2018 (B) 2020 (c) 4018 (D) 4019 (E) 4040 KSF BRASIL LEVEL S 2020 SECOND APPLICATION ALL RIGHTS RESERVED 16. The sequence f, isgiven by fi =1,f, = 2 e f, = fu_1. fu41 for n = 2. How many of the first 2020 ele- ments of this sequence are even numbers? (A) 673 (B) 674 (C) 1010 (D) 1346 (E) 1347 17. 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 consecutive positions are summed up, which of the following results is possible? (A) 49 (B) 70 (7s (D) 105 (E) 150 18. 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? (A) 10 (8) 11 (C) 12 (D) 13 (E) 14 19. 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? 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 rectangle? (A) 40 cm? (B)45 cm? (C) 50 cm? (D) 55 cm? (E) 60 cm? 20. Two rectangular blocks and a cube are joined to form a larger rectangular block, which 5N volume is 280 cm? ., The cube, in dark gray in the picture, has volume equal to 125 cm and ; the smaller rectangular block has volume equal to 75 cm? . What is the area of the face marked with the question mark? (A) 16 cm? (B) 18 cm? (c) 20 cm? (D) 24 ecm? (E) 56 cm? & matematica.pt