Soal Kompetisi Matematika (3)

1. Sam is walking in a straight line towards a lamp post which is 8 m high. When he is 12 m away from the lamp post, his shadow is 4 m in length. When he is 8 m from the lamp post, what is the length of his shadow?

(A) 1 ½ m (B) 2 m (C) 2  ½ m (D) 2 ²/₃m (E) 3 m

2. The homes of Fred (F), Sandy (S), Robert (R), and Guy (G) are marked on the rectangular grid with straight lines joining them. Fred is considering four routes to visit each of his friends:

(i) F→ R→S→G                        (ii) F→S→G→ R

(iii) F→ R→G→S                      (iv) F→S→ R→G

If FS = 5 km, SG = 9 km and SR = 12 km, the difference between the longest and the shortest trip (in km) is

(A) 8

(B) 13

(C) 15

(D) 2

(E) 0

3. A square floor is tiled, as partially shown, with a large number of regular hexagonal tiles. The tiles are coloured blue or white. Each blue tile is surrounded by 6 white tiles and each white tile is surrounded by 3 white and 3 blue tiles. Ignoring part tiles, the ratio of the number of blue tiles to the number of white tiles is closest to

(A) 1:6

(B) 2:3

(C) 3:10

(D) 1:4

(E) 1:2

4. In equilateral triangle ABC, line segments are drawn from a point P to the vertices A, B and C to form three identical triangles. The points D, E and F are the midpoints of the three sides and they are joined as shown in the diagram. What fraction of Δ ABC is shaded?

(A) 1/5    

(B) 5/24     

(C) ¼      

(D) 2/9      

(E) 2/7

5. The cookies in a jar contain a total of 1000 chocolate chips. All but one of these cookies contains the same number of chips; it contains one more chip than the others. The number of cookies in the jar is between one dozen and three dozen. What is the sum of the number of cookies in the jar and the number of chips in the cookie with the extra chocolate chip?

(A) 65     (B) 64     (C) 63     (D) 66    (E) 67