Gauss 2021年真题

1. When the five numbers 10 000，1，10, 100, and 1000 are arranged from largest to smallest, the middle number is

(A) 10 000 (B) 1 (C) 10 (D) 100 (E) 1000

2. What is the perimeter of the square shown?

(A) 20 cm (B) 8 cm (C) 5 cm (D) 50 cm (E) 15 cm

3. What value goes in the box to make the equation 5 + £ = 10 + 20 true?

(A) 30 (B) 15 (C) 35 (D) 20 (E) 25

4. The number of hours spent by five students on homework is shown on the graph. Which two students, adding their individual times together, spent the same amount of time on homework as Dan?

(A) Joe and Grace

(B) Joe and Bob

(D) Dan and Bob

(E) Susie and Grace

5.Which of the following fractions is closest to 0?

(A) (B) (c) (D) (E)

6. A bag contains a number of candies. The probability of Judith choosing a red candy from this bag is . The total number of candies in the bag could be

(A) 3 (B) 10 (C) 17 (D) 6 (E) 7

7. In the graph shown, which of the following statements is true about the coordinates of the point P(x, y)?

(A) The values of both x and y are positive.

(B) The value of x is positive and the value of y is negative.

(D) The values of both x and y are negative.

(E) The value of x is 0 and the value of y is negative.

8. The line graph shows the distance that Andrew walked over time. How long did it take Andrew to walk the first 2 km?

(A) 15 minutes

(B) 1 hour, 15 minutes

(D) 2 hours

(E) 45 minutes

9. A list of five numbers repeats to form the pattern

5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, ...

What is the 221st number in the pattern?

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

10. An ant begins its path at A, travels only right or down, and remains on the the line segments shown. The number of different paths from A to C that pass through B is

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

11. Laila writes a list of numbers.Her first number is 4. Each number after the first is 7 more than the previous number. Which of the following numbers appears in Laila's list?

(A) 45 (B) 46 (C) 47 (D) 48 (E) 49

12. The letter A has a vertical line of symmetry and the letter B does not. How many of the letters H L O R X D P E have a vertical line of symmetry?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

13. In the diagram, AB and CD intersect at E. If ΔBCE is equilateral and ΔADE is a right-angled triangle, what is the value of x?

(A ) 90 (B) 60 (C) 25 (D) 45 (E)30

14. Which of the following is the sum of three consecutive integers?

(A) 17 (B) 11 (C) 25 (D) 21 (E) 8

15. A positive integer whose digits are the same when read forwards or backwards is called a palindrome. An example of a palindrome is 13931. What is the sum of the digits of the next palindrome greater than 13931?

(A) 14 (B) 11 (C) 19 (D)10 (E)8

16. The number 6 has exactly 4 positive factors and the number 9 has exactly 3 positive factors. How many numbers in the list 14, 21, 28, 35, 42 have exactly 4 positive factors?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

17. The original price of a shirt is reduced by 50% to obtain a second price. The store advertises an additional sale, and so this second price is reduced by 40% to obtain a third price. What is the discount of the third price off the original price?

(A) 80% (B) 10% (C) 70% (D) 65% (E) 45%

18. In the diagram, ∆ABC is isosceles. M is on BC so that BM = MC. If the perimeter of ∆ABC is 64 and the perimeter of ∆ABM is 40, what is the length of AM?

(A) 10 (B) 8 (C) 16 (D) 12 (E) 24

19. Two different digits from 1 to 9 are chosen. One digit is placed in each box to complete the two 2-digit numbers shown. The result of subtracting the bottom number from the top number is calculated. How many of the possible results are positive?

(A) 36 (B) 32 (C) 30 (D) 34 (E) 38

20. Two standard dice are rolled. What is the probability that the sum of the numbers on the top faces is a prime number?

(A) (B) (c) (D) (E)

21. A large number is written with a one followed by many zeros (1000 ... 000). When 1 is subtracted from this number, the sum of the digits in the result is 252. How many zeros are in the original number?

(A) 27 (B) 28 (C) 29 (D) 42 (E) 252

22. In the diagram shown, each figure after Figure 1 is formed by joining two rectangles to the bottom of the previous figure. Each individual rectangle has dimensions 10 cm by 5 cm. If Figure n has a perimeter of 710 cm, the value of n is

(A) 29 (B) 43 (C) 66 (D) 172 (E) 65

23. To encode a message，James first replaces each letter within the message with its corresponding number， where A = 1, B = 2, …, Y = 25, and Z = 26. Next, James multiplies each number by 3 and then subtracts 5, and continues this process a total of n times. For example, when n = 2 the letter D is encoded to the number 16. If James encoded a four letter message to the four numbers 367 205 8531339, what is the value of n that he used?

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

24. How many different pairs of positive whole numbers have a greatest common factor of 4 and a lowest common multiple of 4620?

(A) 4 (B) 5 (C) 7 (D) 8 (E) 11

25. Jonas has 1728 copies of a 1 × 1 x 1 cube with the net shown，where c is a positive integer and c < 100. Using these 1728 cubes, Jonas builds a large 12×12×12 cube in such a way that the sum of the numbers on the exterior faces is as large as possible. For some values of c, the sum of the numbers on the exterior faces is between 80 000 and 85 000. The number of such values of c is