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2018 AMC Junior Questions Questions { Junior Division 1. What is 2 + 0 + 1 + 8? (A) 9 (B) 10 (C) 11 (D) 38(E) 2018 2. Callie has $47 and then gets $25 for her birthday. How much does she have now? (A) $52 (B) $62(C) $65 (D) $69 (E) $72 3. The value of 4 10000 + 3 1000 + 2 10 + 4 1 is (A) 4324 (B) 43024 (C) 43204 (D) 430204 (E) 430024 4. Kate made this necklace from alphabet beads. She put it on the wrong way around, showing the back of the beads. What does this look like?K A T E (A) K A T E (B) K A T E (C) K A T E (D) K A T E (E) K A T E 5.What is the time 58 minutes before 5.34 pm? (A) 5.32 pm (B) 5.36 pm (C) 6.32 pm (D) 6.12 pm (E) 4.36 pm 6. What value is indicated on this charisma-meter? (A) 36.65 (B) 37.65 (C) 38.65 (D) 37.15 (E) 37.3 38 36 7. Starting at 1000, Ishrak counted backwards, taking 7 o each time. What was the last positive number he counted? (A) 2 (B) 3(C) 4 (D) 5 (E) 6 c Australian Mathematics Trust www.amt.edu.au 16

2018 AMC Junior Questions 8. What is the value of z? (A) 75 (B) 85 (C) 95 (D) 100 (E) 105 40  55  z  9. Five friends (Amelia, Billie, Charlie, David and Emily) are playing together and decide to line up from oldest to youngest.  Amelia is older than Billie who is older than Emily.  David is also older than Billie.  Amelia is not the oldest.  Emily is not the youngest. Who is the second-youngest of the ve friends? (A) Amelia (B) Billie (C) Charlie (D) David (E) Emily 10. A length of ribbon is cut into two equal pieces. After using one piece, one-third of the other piece is used, leaving 12 cm of ribbon. How long, in centimetres, was the ribbon initially? (A) 24 (B) 32(C) 36 (D) 48 (E) 50 11. 1000% of a number is 100. What is the number? (A) 0.1 (B) 1(C) 10 (D) 100 (E) 1000 12. Nora, Anne, Warren and Andrew bought plastic capital letters to spell each of their names on their birthday cakes. Their birthdays are on di erent dates, so they planned to reuse letters on di erent cakes. What is the smallest number of letters they needed? (A) 8 (B) 9(C) 10 (D) 11 (E) 12A A A N N N N N N E E E 13. The cost of feeding four dogs for three days is $60. Using the same food costs per dog per day, what would be the cost of feeding seven dogs for seven days? (A) $140 (B) $200 (C) $245 (D) $350 (E) $420 c Australian Mathematics Trust www.amt.edu.au 17

2018 AMC Junior Questions 14. What fraction of this regular hexagon is shaded? (A)1 2 (B) 2 3 (C) 3 4 (D) 3 5 (E) 4 5 15. Leila has a number of identical square tiles that she puts together edge to edge in a single row, making a rectangle. The perimeter of this rectangle is three times that of a single tile. How many tiles does she have? (A) 3 (B) 5 (C) 6(D) 8 (E) 9 16. James is choosing his language electives for next year. He has to choose two di erent electives, one from Group A and one from Group B. Group A Group B Mandarin Mandarin Japanese German Spanish Arabic Indonesian Italian How many di erent pairs of elective combinations are possible? (A) 7 (B) 8 (C) 12(D) 15 (E) 16 17. In the diagram, AB C Dis a 5 cm 4 cm rectangle and the grid has 1 cm 1 cm squares. What is the shaded area, in square centimetres? (A) 1 (B) 1 :5 (C) 0:5 (D) 2 (E) 3 A B CD 18. Fill in this diagram so that each of the rows, columns and diago- nals adds to 18. What is the sum of all the corner numbers? (A) 20 (B) 22 (C) 23 (D) 24 (E) 25 4 6 c Australian Mathematics Trust www.amt.edu.au 18

2018 AMC Junior Questions 19. A square of paper is folded along a line that joins the midpoint of one side to a corner. The bottom layer of paper is then cut along the edges of the top layer as shown.

When the folded piece is unfolded, which of the following describes all the pieces of paper? (A) a kite and a pentagon of equal area (B) a rectangle and a pentagon of equal area (C) an isosceles triangle and a pentagon, with the pentagon of larger area (D) a kite and a pentagon, with the kite smaller in area (E) a rectangle and a pentagon, with the rectangle larger in area 20. A 3-dimensional ob ject is formed by gluing six identical cubes together. Four of the diagrams below show this ob ject viewed from di erent angles, but one diagram shows a di erent ob ject. Which diagram shows the di erent ob ject? (A) (B) (C) (D) (E) 21. Approximately how long is a millimonth, de ned to be one-thousandth of a month? (A) 20 seconds (B) 70 seconds (C) 8 minutes (D) 40 minutes (E) 3 hours 22. The numbers from 1 to 8 are entered into the eight circles in this diagram, with the number 3 placed as shown. In each triangle, the sum of the three numbers is the same. The sum of the four numbers which are at the corners of the central square is 20. What is x+ y? (A) 10 (B) 11 (C) 12 (D) 13 (E) 14 3 xy c Australian Mathematics Trust www.amt.edu.au 19

2018 AMC Junior Questions 23. A long narrow hexagon is composed of 22 equilateral triangles of unit side length. In how many ways can this hexagon be tiled by 11 rhombuses of unit side length? Hexagon Rhombus (A) 6 (B) 8 (C) 9(D) 12 (E) 16 24. In this expression 1 3 1 4 1 5 1 6 1 7 we place either a plus sign or a minus sign in each box so that the result is the smallest positive number possible. The result is (A) between 0 and 1 100 (C) between 1 50 and 1 20 (B) between 1 100 and 1 50 (D) between 1 20 and 1 10 (E) between 1 10 and 1 25. In this subtraction, the rst number has 100 digits and the second number has 50 digits. 111: : : : : : 111 | {z } 100 digits 222 : : :222 | {z } 50 digits What is the sum of the digits in the result? (A) 375 (B) 420 (C) 429(D) 450 (E) 475 26. Using only digits 0, 1 and 2, this cube has a di erent number on each face. Numbers on each pair of opposite faces add to the same 3-digit total. What is the largest that this total could be?121 201 220 27.I ha ve a three-digit number, and I add its digits to create its digit sum. When the digit sum of my number is subtracted from my number, the result is the square of the digit sum. What is my three-digit number? c Australian Mathematics Trust www.amt.edu.au 20

2018 AMC Junior Questions 28. A road from Tamworth to Broken Hill is 999 km long. There are road signs each kilometre along the road that show the distances (in kilometres) to both towns as shown in the diagram. 0j999 1j998 2j997 3j996


998j1 999j0 How many road signs are there that use exactly two di erent digits? 29. In the multiplication shown, X,Y and Zare di erent non-zero digits. X Y Z  1 8 Z X Y Y What is the three-digit number X Y Z? 30. LetAbe a 2018-digit number which is divisible by 9. Let Bbe the sum of all digits of A and Cbe the sum of all digits of B. Find the sum of all possible values of C. c Australian Mathematics Trust www.amt.edu.au 21