Pascal 2020真题

1. How many symbols are in the figure?

(A) 24 (B) 20 (C) 15

(D) 17 (E) 25

2. The value of 0.8 + 0.02 is

(A) 0.28 (B) 8.02 (C) 0.82 (D) 0.16 (E) 0.01

3. If 2x + 6 = 16, the value of x + 4 is

(A) 7 (B) 8 (C) 9 (D) 15 (E) 13

4. When two positive integers are multiplied, the result is 24. When these two integers are added, the result is 11. When the smaller integer is subtracted from the larger integer, the result is

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

5. In the diagram, △PQR has side lengths as shown. If x = 10, the perimeter of △PQR is

(A) 29 (B) 31 (C) 25

(D) 27 (E) 23

6. The value of is

(A) 1 (B) 0 (C) (D) (E) 2

7. Ewan writes out a sequence where he counts by 11s starting at 3. The resulting sequence is 3, 14, 25, 36, . . .. A number that will appear in Ewan’s sequence is

(A) 113 (B) 111 (C) 112 (D) 110 (E) 114

8. Matilda counted the birds that visited her bird feeder yesterday. She summarized the data in the bar graph shown. The percentage of birds that were goldfinches is

(A) 15% (B) 20% (C) 30%

(D) 45% (E) 60%

9. In the diagram, three lines intersect at a point. What is

the value of x?

(A) 30 (B) 45 (C) 60

(D) 90 (E) 120

10. Starting at 1:00 p.m., Jorge watched three movies. The first movie was 2 hours and 20 minutes long. He took a 20 minute break and then watched the second movie, which was 1 hour and 45 minutes long. He again took a 20 minute break and then

watched the last movie, which was 2 hours and 10 minutes long. At what time did the final movie end?

(A) 6:45 p.m. (B) 7:15 p.m. (C) 7:35 p.m.

(D) 7:55 p.m. (E) 8:15 p.m.

11. Anna thinks of an integer.

• It is not a multiple of three.

• It is not a perfect square.

• The sum of its digits is a prime number.

The integer that Anna is thinking of could be

(A) 12 (B) 14 (C) 16 (D) 21 (E) 26

12. Natalie and Harpreet are the same height. Jiayin’s height is 161 cm. The average (mean) of the heights of Natalie, Harpreet and Jiayin is 171 cm. What is Natalie’s height?

(A) 161 cm (B) 166 cm (C) 176 cm

(D) 183 cm (E) 191 cm

13. The ratio of apples to bananas in a box is 3 : 2. The total number of apples and bananas in the box cannot be equal to

(A) 40 (B) 175 (C) 55 (D) 160 (E) 72

14. A sequence of figures is formed using tiles. Each tile is an equilateral triangle with side length 7 cm. The first figure consists of 1 tile. Each figure after the first is formed by adding 1 tile to the previous figure. The first four figures are as shown:

How many tiles are used to form the figure in the sequence with perimeter 91 cm?

(A) 6 (B) 11 (C) 13 (D) 15 (E) 23

15. In the diagram, the large square has area 49, the medium

square has area 25, and the small square has area 9. The region inside the small square is shaded. The region between the large and medium squares is shaded. What is the total area of the shaded regions?

(A) 33 (B) 58 (C) 45

(D) 25 (E) 13

16. Which of the following expressions is not equivalent to 3x+6?

(A) 3(x + 2) (B) (C)

(D) (E) 3x - 2(-3)

17. Ben participates in a prize draw. He receives one prize that is equally likely to be worth $5, $10 or $20. Jamie participates in a different prize draw. She receives one prize that is equally likely to be worth $30 or $40. What is the probability that the

total value of their prizes is exactly $50?

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

18. A positive integer n is a multiple of 7. The square root of n is between 17 and 18. How many possible values of n are there?

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

19. Each of the following 15 cards has a letter on one side and a positive integer on the other side.

What is the minimum number of cards that need to be turned over to check if the following statement is true?

“If a card has a lower case letter on one side, then it has an odd integer on the other side.”

(A) 11 (B) 9 (C) 7 (D) 5 (E) 3

20. A large 5 × 5 × 5 cube is formed using 125 small 1 × 1 × 1 cubes. There are three central columns, each passing through the small cube at the very centre of the large cube: one from top to bottom, one from front to back, and one from left to right. All of the small cubes that make up these three columns are removed. What is the surface area of the resulting solid?

(A) 204 (B) 206 (C) 200 (D) 196 (E) 192

21. In the 4 × 5 grid shown, six of the 1 × 1 squares are not

intersected by either diagonal. When the two diagonals of an 8×10 grid are drawn, how many of the 1×1 squares are not intersected by either diagonal?

(A) 44 (B) 24 (C) 52

(D) 48 (E) 56

22. In the diagram, P Q is a diameter of a larger circle, point

R is on P Q, and smaller semi-circles with diameters P R and QR are drawn. If P R = 6 and QR = 4, what is the ratio of the area of the shaded region to the area of the unshaded region?

(A) 4 : 9 (B) 2 : 3 (C) 3 : 5

(D) 2 : 5 (E) 1 : 2

23. Ali, Bea, Che, and Deb compete in a checkers tournament. Each player plays each other player exactly once. At the end of each game, either the two players tie or one player wins and the other player loses. A player earns 5 points for a win, 0 points for a loss, and 2 points for a tie. Exactly how many of the following final point distributions are possible?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

24. Lucas chooses one, two or three different numbers from the list 2, 5, 7, 12, 19, 31, 50, 81 and writes down the sum of these numbers. (If Lucas chooses only one number, this number is the sum.) How many different sums less than or equal to 100 are possible?

(A) 43 (B) 39 (C) 42 (D) 40 (E) 41