Gauss 2019年真题

1. Erin receives $3 a day. How many days will it take Erin to receive a total of $30?

(A) 8 (B) 12 (C) 14 (D) 27 (E) 10

2. In the diagram, point F has coordinates (5, 5). The point

with coordinates (2, 4) is located at

(A) A (B) B (C) C

(D) D (E) E

3. In the diagram, square PQRS is divided into four identical squares. What percentage of square PQRS is shaded?

(A) 33% (B) 40% (C) 25%

(D) 50% (E) 15%

4. The value of 0.9 + 0.09 is

(A) 1.08 (B) 0.909 (C) 1.8 (D) 0.99 (E) 0.18

5. Based on the graph shown, what is the mode for the amount of rainfall for the week?

(A) 9 mm (B) 12 mm (C) 3 mm

(D) 15 mm (E) 6 mm

6. If x = 3, which of the following is true?

(A) 2x = 5 (B) 3x - 1 = 8 (C) x + 5 = 3

(D) 7 - x = 2 (E) 6 + 2x = 14

7. When two numbers are added, the result is -26. If one of the numbers is 11, what is the other number?

(A) -37 (B) 37 (C) -15 (D) 15 (E) -48

8. Joshua is reading a 396-page book. He has read the first third of the book only. How many pages does he have left to read to finish the rest of the book?

(A) 264 (B) 124 (C) 250 (D) 199 (E) 244

9. In the diagram, the value of k is

(A) 180 (B) 210 (C) 240

(D) 270 (E) 300

10. The mean (average) of the numbers 20, 30, 40 is equal to the mean of the numbers

(A) 28, 30, 31 (B) 24, 30, 38 (C) 22, 30, 39

(D) 23, 30, 37 (E) 25, 30, 34

11. The value of is equal to

(A) 3 (B) 32 (C) 33 (D) 34 (E) 35

12. In the diagram, what is the area of rectangle PQRS?

(A) 36 (B) 32 (C) 40

(D) 20 (E) 44

13. A piano has 52 white keys that occur in a repeating pattern of ABCDEFG. The first white key is A. What letter is associated with the 33rd white key?

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

14. A circular spinner is divided into 8 equal sections, as shown. An arrow is attached to the centre of the spinner. The arrow is spun once. What is the probability that the arrow stops in a section containing a prime number that is odd?

(A) (B) (C)

(D) (E)

15. Canadian currency has coins with values $2.00, $1.00, $0.25, $0.10, and $0.05. Barry has 12 coins including at least one of each of these coins. What is the smallest total amount of money that Barry could have?

(A) $3.75 (B) $3.90 (C) $3.70 (D) $3.40 (E) $3.95

16. A positive integer whose digits are the same when read forwards or backwards is called a palindrome. For example 474 and 222 are palindromes. How many palindromes are there between 100 and 1000?

(A) 10 (B) 90 (C) 100 (D) 900 (E) 1000

17. The two equal-arm scales shown are balanced. Of the following, has the same mass as

18. A rectangle has length x and width y. A triangle has base 16 and height x. If the area of the rectangle is equal to the area of the triangle, then the value of y is

(A) 16 (B) 4 (C) 8 (D) 12 (E) 32

19. Each of a, b, c, and d is a positive integer and is greater than 3. If

then which ordering of these four numbers is correct?

(A) a < b < c < d (B) c < b < a < d (C) b < a < c < d

(D) d < a < c < b (E) b < c < a < d

20. The positive integer n has exactly 8 positive divisors including 1 and n. Two of these divisors are 14 and 21. What is the sum of all 8 positive divisors of n?

(A) 35 (B) 47 (C) 53 (D) 96 (E) 103

21. Kathy owns more cats than Alice and more dogs than Bruce. Alice owns more dogs than Kathy and fewer cats than Bruce. Which of the statements must be true?

(A) Bruce owns the fewest cats.

(B) Bruce owns the most cats.

(D) Alice owns the most dogs.

(E) Kathy owns the fewest dogs.

22. Each of the integers 334 and 419 has digits whose product is 36. How many 3-digit positive integers have digits whose product is 36?

(A) 21 (B) 15 C) 18 D) 24 (E) 12

23. Points T, U, V, W, X, Y lie on square P QRS, as shown. If

P T = T U = UQ = QV = V W = W R = XS = SY , what fraction of the area of square P QRS is shaded?

(A) (B) (C)

(D) (E)

24. A dot starts at (20, 19). It can move one unit vertically or horizontally to one of the points (21, 19), (19, 19), (20, 20), or (20, 18). From there it can move two units in either direction that is perpendicular to the first move. All moves thereafter increase in length by one unit (three units, four units, five units, etc.) and must be perpendicular to the direction of the previous move. The dot stops after ten moves. Which of the following final locations is not possible?