Pascal 2016真题

1. The result of the addition shown is

(A) 15021 (B) 12231 (C) 12051

(D) 13231 (E) 12321

2. Which of the following has the largest value?

(A) 42 (B) 4 × 2 (C) 4 - 2 (D) (E) 4 + 2

3. In the diagram, the 5 × 6 grid is made out of thirty 1 × 1

squares. What is the total length of the six solid line

segments shown?

(A) 6 (B) 12 (C) 16

(D) 18 (E) 20

4. In the diagram, each of the five squares is 1 × 1. What

percentage of the total area of the five squares is shaded?

(A) 25% (B) 30% (C) 35%

(D) 40% (E) 45%

5. Numbers m and n are on the number line, as shown. The

value of n - m is

(A) 66 (B) 35 (C) 55

(D) 60 (E) 54

6. If the symbol is defined by p × s - q × r, then the value of is

(A) -3 (B) -2 (C) 2 (D) 3 (E) 14

7. Which of the following is equal to 2 m plus 3 cm plus 5 mm?

(A) 2.035 m (B) 2.35 m (C) 2.0305 m

(D) 2.53 m (E) 2.053 m

8. If x = 3, y = 2x, and z = 3y, then the average of x, y and z is

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

9. A soccer team played three games. Each game ended in a win, loss, or tie. (If a game finishes with both teams having scored the same number of goals, the game ends in a tie.) In total, the team scored more goals than were scored against them. Which of the following combinations of outcomes is not possible for this team?

(A) 2 wins, 0 losses, 1 tie (B) 1 win, 2 losses, 0 ties

(E) 1 win, 0 losses, 2 ties

10. Exactly three faces of a 2×2×2 cube are partially shaded,

as shown. (Each of the three faces not shown in the diagram is not shaded.) What fraction of the total surface area of the cube is shaded?

(A) (B) (C)

(D) (E)

11. An oblong number is the number of dots in a rectangular grid with one more row than column. The first four oblong numbers are 2, 6, 12, and 20, and are represented below:

What is the 7th oblong number?

(A) 42 (B) 49 (C) 56 (D) 64 (E) 72

12. In the diagram, the area of square QRST is 36. Also, the length of PQ is one-half of the length of QR. What is the perimeter of rectangle P RSU?

(A) 24 (B) 30 (C) 90

(D) 45 (E) 48

13. Multiplying x by 10 gives the same result as adding 20 to x. The value of x is

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

14. In the diagram, P Q is perpendicular to QR, QR is

perpendicular to RS, and RS is perpendicular to ST. If P Q = 4, QR = 8, RS = 8, and ST = 3, then the distance from P to T is

(A) 16 (B) 12 (C) 17

(D) 15 (E) 13

15. When two positive integers p and q are multiplied together, their product is 75. The sum of all of the possible values of p is

(A) 96 (B) 48 (C) 109 (D) 115 (E) 124

16. An integer from 10 to 99 inclusive is randomly chosen so that each such integer is equally likely to be chosen. The probability that at least one digit of the chosen integer is a 6 is

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

17. What is the tens digit of the smallest six-digit positive integer that is divisible by each of 10, 11, 12, 13, 14, and 15?

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

18. Each integer from 1 to 12 is to be placed around the

outside of a circle so that the positive difference between

any two integers next to each other is at most 2. The

integers 3, 4, x, and y are placed as shown. What is the

value of x + y?

(A) 17 (B) 18 (C) 19

(D) 20 (E) 21

19. Chris received a mark of 50% on a recent test. Chris answered 13 of the first 20 questions correctly. Chris also answered 25% of the remaining questions on the test

correctly. If each question on the test was worth one mark, how many questions in total were on the test?

(A) 23 (B) 38 (C) 32 (D) 24 (E) 40

20. In the diagram, points Q and R lie on P S and ∠QW R = 38◦ . If ∠TQP = ∠T QW = x◦, ∠V RS = ∠V RW = y◦ , and U is the point of intersection of T Q extended and V R extended,

then the measure of ∠QUR is

(A) 71◦ (B) 45◦ (C) 76◦

(D) 81◦ (E) 60◦

21. Grid lines drawn on three faces of a rectangular prism, as

shown. A squirrel walks from P to Q along the edges and grid lines in such a way that she is always getting closer to Q and farther away from P. How many different paths from P to Q can the squirrel take?

(A) 14 (B) 10 (C) 20

(D) 12 (E) 16

22. There are n students in the math club at Scoins Secondary School. When Mrs. Fryer tries to put the n students in groups of 4, there is one group with fewer than 4 students, but all of the other groups are complete. When she tries to put the n students in groups of 3, there are 3 more complete groups than there were with groups of 4, and there is again exactly one group that is not complete. When she tries to put the n students in groups of 2, there are 5 more complete groups than there were with groups of 3, and there is again exactly one group that is not complete. The sum of the digits of the integer equal to n2 - n is

(A) 11 (B) 12 (C) 20 (D) 13 (E) 10

23. In the diagram, △PQR is isosceles with PQ = PR = 39

and △SQR is equilateral with side length 30. The area

of △PQS is closest to

(A) 68 (B) 75 (C) 50

(D) 180 (E) 135

24. Ten very small rubber balls begin equally spaced inside a 55 m long tube. They instantly begin to roll inside the tube at a constant velocity of 1 m/s. When a ball reaches an end of the tube, it falls out of the tube. When two balls bump into each

other, they both instantly reverse directions but continue to roll at 1 m/s. Five Configurations giving the initial direction of movement of each ball are shown. All gaps indicated in the diagram are the same length and are equal in length to the

distance from the ends of the tube to the nearest ball. For which configuration will it take the least time for more than half of the balls to fall out of the tube?

25. A 0 or 1 is to be placed in each of the nine 1 × 1 squares

in the 3×3 grid shown so that each row contains at least one 0 and at least one 1, and each column contains at least one 0 and at least one 1. The number of ways in which this can be done is