Soal Kompetisi Matematika : UBN 2011 Grade 9 Part C

21. The ones digit of 3²⁰¹¹ - 1 is

(A) 0 (B) 2 (C) 4 (D) 6 (E) 8

22. If x² + x - 1 = 0, then x³ + 2x² + 2011 is equal to

23. In a village there are 100 houses. There is a dog in 90 houses, a cat in 80 houses, a rabbit in 75 houses and a turtle in 65 houses. Among those 100 houses, how many, at least, have a dog, a cat, a rabbit and a turtle ?

(A) 5 (B) 10 (C) 15 (D) 20 (E) None of these

24. A woman minister is receiving guests. Half of the guests are women the other half are men. Each guest gives a flower to the minister and moreover, each woman guest receives a flower from every other guest. In all, 78 flowers have been given. How many guests does the minister receive ?

(A) 10 (B) 12 (C) 14 (D) 16 (E) None of these

25. Let ABC be a triangle with area equal to one. If BD = 2DA and EC = 2AE, then the area of the rectangle DEGF is equal to

(A) 1/3 (B) 4/9 (C) 1/2 (D) 5/9 (E) 2/3

26. Two cyclists ride along a circular path whose circumference is 10 km. The two cyclists start at the same time, from diametrically opposite positions. The first cyclist goes at a constant speed of 30 km/h in the clockwise direction, while the second goes at a constant speed of 20 km/h in the counter clockwise direction. They both cycle for 1 hour. How many times do they meet ?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6