Yusuf Sila: Math Problems : 2011 UNB

Math Problems : 2011 UNB - Grade 9 (Part B)

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Muhammad Yusuf , Posted in Math Competitions , 0 Comments

University Of New Brunswick

Junior High School Mathematics Competition

2011 – Grade 9

PART B

11. Jane has 5 chocolate bars, Karen has 3, and Amel doesn’t have any. The three friends share them evenly. All the chocolate bars cost the same. Amel pays his friends a total of $4.00 for his share. How much of the $4.00 should go to Jane ?

(A) $2.50 (B) $2.75 (C) $3 (D) $3.25 (E) $3.50

12. A rectangle is 245 cm long and 175 cm wide. The rectangle is to be cut into squares that are all the same size. The entire rectangle is to be used. What is the largest possible area, in cm2, of each of the squares ?

(A) 5² (B) 7² (C) 15² (D) 25² (E) 35²

13. In a fenced yard there are sheep, goats, and cows. If all these animals but four are sheep, all these animals but six are goats and all these animals but eight are cows, how many cows are there in this yard ?

(A) 1 (B) 3 (C) 5 (D) 9 (E) None of these

14. How many triangles are there in the following diagram ?

(A) 20 (B) 25 (C) 30 (D) 35 (E) None of these

15. Sports cars are driven by men and each has two women as passengers. Sedan cars are driven by women and each has three men as passengers. If there are a total of 12 cars carrying a total of 43 persons, including the drivers, how many sports cars are there ?

(A) 3 (B) 5 (C) 7 (D) 9 (E) None of these

16. A cyclist is traveling along a path consisting of three sections of the same length. In the first section, pedaling against the wind, he goes at 10 km/h. In the second section, going up a hill, he goes at 5 km/h. In the third section, he bikes downhill at 30 km/h. What is the average speed of this cyclist on the whole path ?

(A) 5 km/h (B) 9 km/h (C) 10 km/h (D) 15 km/h (E) 20 km/h

17. Daryl leaves Fredericton by car and drives at constant speed. At noon, his distance traveled, in kilometers, is a two digit number. At 1 PM, the distance traveled is the same two digits, reversed. At 2 PM, the distance traveled is the same two digits as at noon, but separated by a zero. At what speed is Daryl driving ?

(A) 45 km/h (B) 50 km/h (C) 55 km/h (D) 61 km/h (E) 106 km/h

18. Mark and Tom are playing with two six sided coloured dice. On each die the faces are painted blue or red. They throw both dice at once and Mark wins if the upper faces of the dice are of the same colour, while Tom wins if they are different colours. Each player has exactly the same chance to win. If the first die has one blue face and five red faces, how many red faces are there on the second die ?

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

19. The government decides to use new coins so that only 3 cent and 7 cent coins are used. Some amounts, like 5 cents, cannot be made exactly using the new coins. Which is the largest amount that cannot be made exactly with the new coins ?

(A) 8 cents (B) 9 cents (C) 10 cents (D) 11 cents (E) 12 cents

20. Albert, Bob and Carl are digging identical holes in a field. When Albert works with Bob, they dig a hole in four hours. When Albert works with Carl, they dig a hole in three hours. When Bob works with Carl, they dig a hole in two hours. How many hours does it take Albert to dig a hole when he works alone ?

(A) 9 hours (B) 12 hours (C) 24 hours (D) 36 hours (E) 40 hours