Pascal 2018真题

1. Which of the following is the smallest number?

(A) 1.4 (B) 1.2 (C) 2.0 (D) 1.5 (E) 2.1

2. The value of is

(A) 1010 (B) 2020 (C) 1008 (D) 2017 (E) 1011

3. July 3, 2030 is a Wednesday. What day of the week is July 14, 2030?

(A) Wednesday (B) Saturday (C) Sunday

(D) Monday (E) Tuesday

4. An electric car is charged 3 times per week for 52 weeks. The cost to charge the car each time is $0.78. What is the total cost to charge the car over these 52 weeks?

(A) $104.00 (B) $81.12 (C) $202.80

(D) $162.24 (E) $121.68

5. If 3 × 3 × 5 × 5 × 7 × 9 = 3 × 3 × 7 × n × n, what is a possible value of n?

(A) 15 (B) 25 (C) 45 (D) 35 (E) 5

6. In the diagram, 18 identical 1 × 2 rectangles are put together to form a 6 × 6 square. Part of the square is shaded, as shown. What percentage of the area of the 6 × 6 square is shaded?

(A) 50% (B) 67% (C) 75% (D) 33% (E) 25%

7. A box contains 5 black ties, 7 gold ties, and 8 pink ties. Stephen randomly chooses a tie from the box. Each tie is equally likely to be chosen. The probability that Stephen chooses a pink tie is equivalent to

(A) (B) (C) (D) (E)

8. In the diagram, the number line between 0 and 5 is divided into 20 equal parts. The numbers S and T are marked on the line. What is the value of S + T?

(A) 5.25 (B) 5.5 (C) 4.5 (D) 4.75 (E) 5

9. The symbols ♥ and ∇ represent different positive integers less than 20. If ♥ × ♥ × ♥ = ∇, what is the value of ∇ × ∇?

(A) 12 (B) 16 (C) 36 (D) 64 (E) 81

10. Which of the following points lies on the line that passes through (-2, 1) and (2, 5)?

(A) (0, 0) (B) (0, 2) (C) (0, 3) (D) (0, 4) (E) (0, 5)

11. In the diagram, the circle graph shows how a baby polar bear spent 24 hours. How many hours did it spend

playing?

(A) 6 (B) 7 (C) 8

(D) 9 (E) 10

12. Glenda, Helga, Ioana, Julia, Karl, and Liu participated in the 2017 Canadian Team Mathematics Contest. On their team uniforms, each had a different number chosen from the list 11, 12, 13, 14, 15, 16. Helga’s and Julia’s numbers were even. Karl’s and Liu’s numbers were prime numbers. Glenda’s number was a perfect square. What was Ioana’s number?

(A) 11 (B) 13 (C) 14 (D) 15 (E) 12

13. A rectangle with height x and width 2x has the same perimeter as an equilateral triangle with side length 10. What is the area of the rectangle?

(A) 18 (B) 50 (C) 25 (D) 200 (E) 100

14. In the list 7, 9, 10, 11, 18, which number is the average (mean) of the other four numbers?

(A) 9 (B) 18 (C) 7 (D) 11 (E) 10

15. A digital clock shows the time 4:56. How many minutes will pass until the clock next shows a time in which all of the digits are consecutive and are in increasing order?

(A) 458 (B) 587 (C) 376 (D) 315 (E) 518

16. Reading from left to right, a sequence consists of 6 X’s, followed by 24 Y’s, followed by 96 X’s. After the first n letters, reading from left to right, one letter has occurred twice as many times as the other letter. The sum of the four possible values of n is

(A) 72 (B) 54 (C) 135 (D) 81 (E) 111

17. Suppose that p and q are two different prime numbers and that n = p2q2.The number of possible values of n with n<1000 is

(A) 5 (B) 6 (C) 4 (D) 8 (E) 7

18. In the diagram, △PQR has ∠PQR = 120° . Also, ∠QPS = ∠RPS and ∠QRS = ∠PRS. (In other words, SP and SR bisect ∠QPR and ∠QRP, respectively.) What is the measure of ∠PSR?

(A) 130° (B) 120° (C) 140° (D) 160° (E) 150°

19. On Monday, Mukesh travelled x km at a constant speed of 90 km/h. On Tuesday, he travelled on the same route at a constant speed of 120 km/h. His trip on Tuesday

took 16 minutes less than his trip on Monday. The value of x is

(A) 90 (B) 112 (C) 100 (D) 96 (E) 92

20. In the diagram, PQRST is a pentagon with PQ = 8, QR = 2, RS = 13, ST = 13, and T P = 8. Also, ∠TP Q = ∠PQR = 90° . What is the area of pentagon PQRST?

(A) 76 (B) 84 (C) 92

(D) 100 (E) 108

21. A coin travels along a path that starts in an unshaded square in the top row of the figure, that uses only diagonal

moves, and that ends in an unshaded square in the bottom row. A diagonal move takes the coin either one square down and one square left, or one square down and one square right. How many different paths from the top row to the bottom row are possible?

(A) 16 (B) 20 (C) 32

(D) 24 (E) 28

22. A Miniou circuit contains nodes and wires and obeys the

following rules:

• Each wire connects two different nodes.

• There is at most one wire between each pair of nodes.

• Exactly three wires are connected to each node.

An example of a Miniou circuit is shown. If a Miniou

circuit has 13 788 wires, how many nodes does it have?

(A) 9190 (B) 9192 (C) 9188

(D) 9186 (E) 9184

23. In the diagram, two larger circles with radius 1 have centres P and Q. Also, the smaller circle has diameter P Q. The region inside the two larger circles and outside the smaller circle is shaded.

The area of the shaded region is closest to

(A) 0.36 (B) 0.38 (C) 0.40 (D) 0.42 (E) 0.44

24. In Mrs. Warner’s class, there are 30 students. Strangely, 15 of the students have a height of 1.60 m and 15 of the students have a height of 1.22 m. Mrs. Warner lines up n students so that the average height of any four consecutive students is greater than 1.50 m and the average height of any seven consecutive students is less than 1.50 m. What is the largest possible value of n?

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

25. P.J. starts with m = 500 and chooses a positive integer n with 1 ≤ n ≤ 499. He applies the following algorithm to m and n:

• P.J. sets r equal to the remainder when m is divided by n.

• If r = 0, P.J. sets s = 0.

If r > 0, P.J. sets s equal to the remainder when n is divided by r.

• If s = 0, P.J. sets t = 0.

If s > 0, P.J. sets t equal to the remainder when r is divided by s.

For example, when n = 8, P.J. obtains r = 4, s = 0, and t = 0. For how many of the positive integers n with 1 ≤ n ≤ 499 does P.J.’s algorithm give 1 ≤ r ≤ 15 and 2 ≤ s ≤ 9 and t = 0?