Gauss 2016年真题

1. The value of 333 + 33 + 3 is

(A) 396 (B) 399 (C) 669 (D) 369 (E) 963

2. The graph shows the number of text messages received by Tanner in a given week. On what day did Tanner receive the most text messages?

(A) Friday (B) Tuesday (C) Thursday

(D) Saturday (E) Wednesday

3. Which of the following is a multiple of 7?

(A) 75 (B) 76 (C) 77 (D) 78 (E) 79

4. Which of these fractions is larger than ?

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

5. A cube has exactly one face painted as shown.

The other five faces of the cube are not painted.

If the cube is rolled, which of the following could

be the same cube?

6. The measures of two angles of a triangle are 25° and 70° . The measure of the third angle is

(A) 85° (B) 105° (C) 65° (D) 95° (E) 75°

7. A box of fruit contains 20 apples, 10 oranges, and no other fruit. When a fruit is randomly chosen from the box, what is the probability that the fruit is an orange?

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

8. Alex pays $2.25 to take the bus. Sam pays $3.00 to take the bus. If they each take the bus 20 times, how much less would Alex pay than Sam in total?

(A) $25 (B) $10 (C) $15 (D) $45 (E) $60

9. Carrie is travelling at a constant speed of 85 km/h. If Carrie is halfway through a 510 km trip, how much longer will the trip take?

(A) 5 hours (B) 425 hours (C) 12 hours

(D) 1.5 hours (E) 3 hours

10. Points P, Q and R are on a number line. Q is halfway between P and R. If P is at -6 and Q is at -1, then R is at

(A) 4 (B) -11 (C) 3 (D) -7 (E) 5

11. The diagram shown contains octagons and squares only.

The ratio of the number of octagons to the number of squares is

(A) 1 : 1 (B) 2 : 1 (C) 25 : 12

(D) 5 : 4 (E) 5 : 3

12. In the sum shown, P and Q each represent a digit. The

value of P + Q is

(A) 3 (B) 5 (C) 7

(D) 6 (E) 4

13. A larger cube has volume 64 cm3 . A smaller cube has edges that are half the length of the edges of the larger cube. What is the volume of the smaller cube?

(A) 24 cm3 (B) 48 cm3 (C) 8 cm3 (D) 16 cm3 (E) 27 cm3

14. Ahmed chooses two different items for a snack. His choices are an apple, an orange, a banana, and a granola bar. How many different pairs of snacks could he choose?

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

15. Sophia did push-ups every day for 7 days. Each day after the first day, she did 5 more push-ups than the day before. In total she did 175 push-ups. How many push-ups did Sophia do on the last day?

(A) 55 (B) 35 (C) 50 (D) 45 (E) 40

16. Each of , △ and represents a non-zero number. If and , then equals

17. Triangle T is reflected once. Which of the following

triangles cannot be this reflection of triangle T?

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

(D) D (E) E

18. The mean (average) of a set of six numbers is 10. When the number 25 is removed from the set, the mean of the remaining numbers is

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

19. Suzy’s 5 m long ribbon has shaded and unshaded sections of equal length, as shown. Points A, B, C, D, E are equally spaced along the ribbon.

If Suzy wants a ribbon that is of the size of this ribbon, at which point could she make a single vertical cut?

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

20. In the diagram, four different integers from 1 to 9

inclusive are placed in the four boxes in the top row. The integers in the left two boxes are multiplied and the integers in the right two boxes are added and these results are then divided, as shown. The final result is placed in the bottom box. Which of the following integers cannot appear in the bottom box?

(A) 16 (B) 24 (C) 7

(D) 20 (E) 9

21. A 10 by 10 grid is created using 100 points, as shown. Point P is given. One of the other 99 points is randomly chosen to be Q. What is the probability that the line segment P Q is vertical or horizontal?

(A) (B) (C)

(D) (E)

22. The eight vertices of a cube are randomly labelled with the integers from 1 to 8 inclusive. Judith looks at the labels of the four vertices of one of the faces of the cube. She lists these four labels in increasing order. After doing this for all six faces,

she gets the following six lists: (1, 2, 5, 8),(3, 4, 6, 7), (2, 4, 5, 7),(1, 3, 6, 8),(2, 3, 7, 8), and (1, 4, 5, 6). The label of the vertex of the cube that is farthest away from the vertex labelled 2 is

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

23. Angie has a jar that contains 2 red marbles, 2 blue marbles, and no other marbles.

She randomly draws 2 marbles from the jar. If the marbles are the same colour, she discards one and puts the other back into the jar. If the marbles are different colours, she discards the red marble and puts the blue marble back into the jar. She repeats

this process a total of three times. What is the probability that the remaining marble is red?

(A) (B) (C) (D) (E) 0

24. How many of the five numbers 101, 148, 200, 512, 621 cannot be expressed as the sum of two or more consecutive positive integers?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

25. In the triangle shown, the first diagonal line, 1, 2, 3, 4, . . . ,

begins at 1 and each number after the first is one larger than the previous number. The second diagonal line, 2, 4, 6, 8, . . . begins at 2 and each number after the first is two larger than the previous number. The nth diagonal line begins at n and each number after the first is n larger than the previous number. In which horizontal row does the number 2016 first appear?