Gauss 2015年真题

1. In the diagram, the fraction of the circle that is shaded

is equal to

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

2. The value of 10 × (5 - 2) is

(A) 13 (B) 70 (C) 7 (D) 30 (E) 50

3. The graph shows the total distance that each of five runners ran during a one-hour training session. Which runner ran the least distance?

(A) Phil (B) Tom (C) Pete

(D) Amal (E) Sanjay

4. The equal-arm scale shown is balanced.

One has the same mass as

5. Which of the following is closest to 5 cm?

(A) The length of a full size school bus

(B) The height of a picnic table

(D) The length of your foot

(E) The length of your thumb

6. The number of centimetres in 3.5 metres is

(A) 350 (B) 30.5 (C) 3.05 (D) 3.50 (E) 305

7. The perimeter of the figure shown is

(A) 18 (B) 17 (C) 23

(D) 20 (E) 25

8. Hannah scored 312 points during the basketball season. If her average (mean) was 13 points per game, how many games did she play?

(A) 24 (B) 41 (C) 17 (D) 13 (E) 30

9. The number 6 has exactly four positive divisors: 1, 2, 3, and 6. How many positive divisors does 20 have?

(A) 2 (B) 6 (C) 3 (D) 5 (E) 8

10. How many different 3-digit whole numbers can be formed using the digits 4, 7 and 9, assuming that no digit can be repeated in a number?

(A) 6 (B) 3 (C) 5 (D) 12 (E) 9

11. At Gaussville School, a total of 480 students voted for their favourite subject. The results are summarized in the pie chart shown. How many students voted for math?

(A) 184 (B) 192 (C) 96 (D) 144 (E) 288

12. A piece of paper is folded in half, creating two layers of paper. The paper is then folded in half again. This is continued until the paper has been folded in half a total of five times. The total number of layers of paper in the folded sheet is

(A) 16 (B) 32 (C) 25 (D) 8 (E) 64

13. How many even whole numbers between 1 and 99 are multiples of 5?

(A) 5 (B) 7 (C) 9 (D) 11 (E) 13

14. In the 3 × 3 table shown, the numbers 1, 2 and 3 are

placed so that each number occurs only once in each row

and only once in each column. The value of X + Y is

(A) 3 (B) 2 (C) 5

(D) 6 (E) 4

15. In the rectangle shown, the area of the shaded region is

(A) 60 cm2 (B) 20 cm2 (C) 30 cm2

(D) 40 cm2 (E) 50 cm2

16. You have exactly $4.40 (440 ¢) in quarters (25 ¢ coins), dimes (10 ¢ coins), and nickels (5 ¢ coins). You have the same number of each type of coin. How many dimes do you have?

(A) 20 (B) 11 (C) 10 (D) 12 (E) 4

17. One corner of a cube is cut off, creating a new triangular

face, as shown. How many edges does this new solid have?

(A) 18 (B) 14 (C) 24

(D) 15 (E) 13

18. In the graph shown, which of the following represents the

image of the line segment P Q after a reflection across the

x-axis?

(A) PS (B) TU (C) MN

(D) WV (E) FG

19. When expressed as a repeating decimal, the fraction 1

7 is written as 0.142857142857 . . . (The 6 digits 142857 continue to repeat.) The digit in the third position to the right

of the decimal point is 2. In which one of the following positions to the right of the decimal point will there also be a 2?

(A) 119th (B) 121st (C) 123rd (D) 125th (E) 126th

20. In a triangle, the measure of one of the angles is 45° . The measures of the other two angles in the triangle are in the ratio 4 : 5. What is the measure of the largest angle in the triangle?

(A) 80° (B) 90° (C) 75° (D) 85° (E) 100°

21. The numbers 1 through 25 are arranged into 5 rows and 5 columns in the table below.

1 2 3 4 5

10 9 8 7 6

11 12 13 14 15

20 19 18 17 16

21 22 23 24 25

What is the largest possible sum that can be made using five of these numbers such that no two numbers come from the same row and no two numbers come from the same column?

(A) 75 (B) 73 (C) 71 (D) 70 (E) 68

22. The width of a rectangle is doubled and the length is halved. This produces a square with a perimeter of P. What is the perimeter of the original rectangle?

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

23. A palindrome is a positive integer that is the same when read forwards or backwards. The numbers 101 and 4554 are examples of palindromes. The ratio of the number of

4-digit palindromes to the number of 5-digit palindromes is

(A) 4 : 5 (B) 5 : 2 (C) 2 : 7 (D) 4 : 3 (E) 1 : 10

24. In the diagram, rectangle P QRS is made up of six identical squares. Points U, V, W, X, Y, and Z are midpoints of sides of the squares, as shown. Which of the following triangles has the greatest area?

(A) PV U (B) PXZ (C) PVX

(D) PYS (E) PQW

25. Two different 2-digit positive integers are called a reversal pair if the position of the digits in the first integer is switched in the second integer. For example, 52 and 25 are a reversal pair. The integer 2015 has the property that it is equal to the product

of three different prime numbers, two of which are a reversal pair. Including 2015, how many positive integers less than 10 000 have this same property?

(A) 18 (B) 14 (C) 20 (D) 17 (E) 19