Pascal 2014真题

1. The value of (8 × 6) - (4 ÷ 2) is

(A) 6 (B) 8 (C) 46 (D) 32 (E) 22

2. In the diagram, what is the value of x?

(A) 65 (B) 75 (C) 85

(D) 95 (E) 105

3. 30% of 200 equals

(A) 0.06 (B) 0.6 (C) 6 (D) 60 (E) 600

4. If x = 3, what is the perimeter of the figure shown?

(A) 23 (B) 20 (C) 21

(D) 22 (E) 19

5. A sports team earns 2 points for each win, 0 points for each loss, and 1 point for each tie. How many points does the team earn for 9 wins, 3 losses and 4 ties?

(A) 26 (B) 16 (C) 19 (D) 21 (E) 22

6. At 2 p.m., Sanjay measures the

temperature to be 3℃. He measures

the temperature every hour after this

until 10 p.m. He plots the temperatures

that he measures on the graph shown.

At what time after 2 p.m. does he again

measure a temperature of 3℃?

(A) 9 p.m. (B) 5 p.m. (C) 8 p.m. (D) 10 p.m. (E) 7 p.m.

7. If 2 × 2 × 3 × 3 × 5 × 6 = 5 × 6 × n × n, then n could equal

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

8. In the diagram, a figure is formed dividing a square into eight identical pieces using its two diagonals and the two lines joining the midpoints of opposite sides, and then drawing a

circle in the square as shown. This figure is reflected

in line L. Which of the following shows the final position

of the figure?

9. The value of 24 - 23 is

(A) 01 (B) 21 (C) 22 (D) 23 (E) 11

10. What number should go in the to make the equation

true?

(A) 1 (B) 3 (C) 5 (D) 13 (E) 16

11. Two cubes are stacked as shown. The faces of each cube are labelled with 1, 2, 3, 4, 5, and 6 dots. A total of five faces are shown. What is the total number of dots on the

other seven faces of these two cubes?

(A) 13 (B) 14 (C) 18

(D) 21 (E) 24

12. Strips are made up of identical copies of . Each

has length . Which strip has length 4?

13. In the subtraction shown, X and Y are digits. What is

the value of X + Y ?

(A) 15 (B) 12 (C) 10

(D) 13 (E) 9

14. If x = 2y and y ≠ 0, then (x + 2y) ) (2x + y) equals

(A) - 2y (B) -y (C) 0 (D) y (E) 2y

15. In △PQR, ∠RP Q = 90◦ and S is on P Q. If SQ = 14, SP = 18, and SR = 30, then the area of △QRS is

(A) 84 (B) 168 (C) 210

(D) 336 (E) 384

16. In the 4 × 4 grid shown, each of the four symbols has a

different value. The sum of the values of the symbols in each row is given to the right of that row. What is the value of ?

(A) 5 (B) 6 (C) 7

(D) 8 (E) 9

17. A cube has an edge length of 30. A rectangular solid has

edge lengths 20, 30 and L. If the cube and the rectangular

solid have equal surface areas, what is the value of L?

(A) 15 (B) 21 (C) 42

(D) 40 (E) 96

18. How many pairs of positive integers (x, y) have the property that the ratio x : 4 equals the ratio 9 : y?

(A) 6 (B) 7 (C) 8 (D) 9 (E) 10

19. On each spin of the spinner shown, the arrow is equally likely to stop on any one of the four numbers. Deanna spins the arrow on the spinner twice. She multiplies together the two numbers on which the arrow stops. Which product is most likely to occur?

(A) 2 (B) 4 (C) 6

(D) 8 (E) 12

20. In the diagram, line segment P S has length 4. Points Q and R are on line segment P S. Four semi-circles are drawn on the same side of P S. The diameters of these semi-circles are PS, PQ, QR, and RS. The region inside the largest semicircle and outside the three smaller semi-circles is shaded. What is the area of a square whose perimeter equals the perimeter of the shaded region?

(A) 4 (B) π (C) π2

(D) 2π2 (E)

21. Twenty-four identical 1 × 1 squares form a 4 × 6 rectangle, as shown. A lattice point is a point where a horizontal grid line intersects a vertical grid line. A diagonal of this rectangle passes through the three lattice points P, Q and R. When a

30×45 rectangle is constructed using identical 1×1 squares, how many lattice points will a diagonal of this rectangle pass through?

(A) 19 (B) 16 (C) 15

(D) 18 (E) 12

22. A rectangular flag is divided into four

triangles, labelled Left, Right, Top, and

Bottom, as shown. Each triangle is to be

coloured one of red, white, blue, green,

and purple so that no two triangles that

share an edge are the same colour. How many different flags can be made?

(A) 180 (B) 200 (C) 220 (D) 240 (E) 260

23. In the diagram, the shape consists of 48 identical cubes

with edge length . Entire faces of the cubes are attached to one another, as shown. What is the smallest positive integer n so that the distance from P to Q is an integer?

(A) 17 (B) 68 (C) 7

(D) 28 (E) 3

24. Nadia walks along a straight path that goes directly from her house (N) to her Grandmother’s house (G). Some of this path is on flat ground, and some is downhill or uphill. Nadia walks on flat ground at 5 km/h, walks uphill at 4 km/h, and walks downhill at 6 km/h. It takes Nadia 1 hour and 36 minutes to walk from N to G and 1 hour and 39 minutes to walk from G to N. If 2.5 km of the path between N and G is on flat ground, the total distance from N to G is closest to

(A) 8.0 km (B) 8.2 km (C) 8.1 km (D) 8.3 km (E) 7.9 km

25. Suppose that , where a, b and n are positive integers with in lowest terms. What is the sum of the digits of the smallest positive integer n for which a is a multiple of 1004?