Pascal 2019真题

1. The expression 2 × 3 + 2 × 3 equals

(A) 10 (B) 20 (C) 36 (D) 12 (E) 16

2. The perimeter of a square is 28. What is the side length of this square?

(A) 9 (B) 6 (C) 8 (D) 4 (E) 7

3. In the diagram, some of the hexagons are shaded. What

fraction of all of the hexagons are shaded?

(A) (B) (C)

(D) (E)

4. Yesterday, each student at Pascal C.I. was given a snack.

Each student received either a muffin, yogurt, fruit, or a granola bar. No student received more than one of these snacks. The percentages of the students who received each snack are shown in the circle graph. What percentage of students did not receive a muffin?

(A) 27% (B) 38% (C) 52%

(D) 62% (E) 78%

5. What is the smallest integer that can be placed in the box so that

(A) 7 (B) 3 (C) 4 (D) 5 (E) 6

6. If 4x + 14 = 8x - 48, what is the value of 2x?

(A) 17 (B) 31 (C) 35 (D) 24 (E) 36

7. In the diagram, point P is on the number line at 3 and V is at 33. The number line between 3 and 33 is divided into six equal parts by the points Q, R, S, T, U.

What is the sum of the lengths of P S and T V ?

(A) 25 (B) 23 (C) 24 (D) 21 (E) 27

8. The median of the numbers in the list 1920 , , 2019 , 2019, 20 × 19 is

9. In the diagram, each partially shaded circle has a radius of 1 cm and has a right angle marked at its centre. In cm2, what is the total shaded area?

(A) 4π2 (B) 9π2 (C) 4π

(D) 9π (E) 3π

10. Three 1 × 1 × 1 cubes are joined face to face in a single row and placed on a table, as shown. The cubes have a

total of 11 exposed 1×1 faces. If sixty 1×1×1 cubes are joined face to face in a single row and placed on a table, how many 1 × 1 faces are exposed?

(A) 125 (B) 220 (C) 182

(D) 239 (E) 200

11. In a magic square, the numbers in each row, the numbers

in each column, and the numbers on each diagonal have the same sum. In the magic square shown, the value of x is

(A) 3.8 (B) 3.6 (C) 3.1

(D) 2.9 (E) 2.2

12. In the diagram, P R and QS meet at X. Also, △PQX is right-angled at Q with ∠QP X = 62◦ and △RXS is isosceles with RX = SX and ∠XSR = y◦ . The value of y is

(A) 54 (B) 71 (C) 76

(D) 59 (E) 60

13. The list p, q, r, s consists of four consecutive integers listed in increasing order. If p + s = 109, the value of q + r is

(A) 108 (B) 109 (C) 110 (D) 117 (E) 111

14. Many of the students in M. Gamache’s class brought a skateboard or a bicycle to school yesterday. The ratio of the number of skateboards to the number of bicycles was 7 : 4. There were 12 more skateboards than bicycles. How many skateboards and bicycles were there in total?

(A) 44 (B) 33 (C) 11 (D) 22 (E) 55

15. Sophie has written three tests. Her marks were 73%, 82% and 85%. She still has two tests to write. All tests are equally weighted. Her goal is an average of 80% or higher. With which of the following pairs of marks on the remaining tests will Sophie not reach her goal?

(A) 79% and 82% (B) 70% and 91% (C) 76% and 86%

(D) 73% and 83% (E) 61% and 99%

16. If x is a number less than -2, which of the following expressions has the least value?

(A) x (B) x + 2 (C) (D) x - 2 (E) 2x

17. Hagrid has 100 animals. Among these animals,

• each is either striped or spotted but not both,

• each has either wings or horns but not both,

• there are 28 striped animals with wings,

• there are 62 spotted animals, and

• there are 36 animals with horns.

How many of Hagrid’s spotted animals have horns?

(A) 8 (B) 10 (C) 2 (D) 38 (E) 26

18. In the diagram, each of △QPT, △QTS and △QSR is an isosceles, right-angled triangle, with ∠QP T = ∠QT S =∠QSR = 90◦ . The combined area of the three triangles is 56. If QP = P T = k, what is the value of k?

(A) (B) 1 (C) 4

(D) 2 (E)

19. There are six identical red balls and three identical green balls in a pail. Four of these balls are selected at random and then these four balls are arranged in a line in some order. How many different-looking arrangements are possible?

(A) 15 (B) 16 (C) 10 (D) 11 (E) 12

20. In the diagram, square P QRS has side length 40. Points

J, K, L, and M are on the sides of P QRS, as shown, so that JQ = KR = LS = MP = 10. Line segments JZ, KW, LX, and MY are drawn parallel to the diagonals of the square so that W is on JZ, X is on KW, Y is on LX, and Z is on MY . What is the area of quadrilateral WXY Z?

(A) 280 (B) 200 (C) 320

(D) 240 (E) 160

21. What is the units (ones) digit of the integer equal to 52019 - 32019?

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

22. The integer 2019 can be formed by placing two consecutive two-digit positive integers, 19 and 20, in decreasing order. What is the sum of all four-digit positive integers greater than 2019 that can be formed in this way?

(A) 476 681 (B) 476 861 (C) 478 661

(D) 468 671 (E) 468 761

23. A path of length 14 m consists of 7 unshaded stripes, each of length 1 m, alternating with 7 shaded stripes, each of length 1 m. A circular wheel of radius 2 m is divided into four quarters which are alternately shaded and unshaded. The wheel rolls at a constant speed along the path from the starting position shown.

The wheel makes exactly 1 complete revolution. The percentage of time during which a shaded section of the wheel is touching a shaded part of the path is closest to

(A) 20% (B) 18% (C) 16% (D) 24% (E) 22%

24. If p, q, r, and s are digits, how many of the 14-digit positive integers of the form 88 663 311 pqr s48 are divisible by 792?

(A) 48 (B) 56 (C) 40 (D) 60 (E) 50

25. In the diagram, P R and QS intersect at V . Also, W is on P V , U is on P S and T is on P Q with QU and ST passing through W. For some real number x,