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AMC PRACTICE QUESTIONS AND SOLUTIONS Upper Primary Copyright � 2014, 2019 Australian Mathematics Trust AMTT Limited ACN 083 950 341 (Set1)                \b          \b 
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Alternative 2 The internal square has side 4 cm and perimeter 16 cm. The total perimeter of the two 1\b cm squares is 8\b cm. Subtracting the 16 cm perimeter of the internal square leaves 8\b −16 = 64 cm, hence (C). 3. 2014 UP15 Sally thinks of a number, multiplies it by 2, adds 2, divides by 2 and then subtracts 2. Her answer is 2. What was her original number? (A) 1 (B) 2(C) 3 (D) 4 (E) 5 The process can be visualised as in the following diagram. X 2 ×2 +2 ÷2 −2 Backtracking from the right, each step can be reversed. Then the boxes are filled in with 4, then 8, then 6, then 3. 2 × 2 +2 ÷2 −2 ÷2 −2 ×2 +2 4 8 6 3 hence (C). 4. 2014 UP21 In a competition between four people, Sally scored twice as many points as Brian and 3\b points more than Corrie. Donna scored 5\b points more than Brian. Which of the following statements is definitely true? (A) Sally won the competition. (B) Brian came last in the competition. (C) Donna won the competition. (D) Corrie beat Brian. (E) Sally and Donna together scored more than Brian and Corrie. Make a table with some possibilities: Sally Brian Corrie Donna 3\b 15 \b 65 4\b 2\b 1\b 7\b 5\b 25 2\b 75 6\b 3\b 3\b 8\b Given the first row of the table, clearly (A), (B) and (D) are false. Also, for every 1\b point increase for Sally and Corrie, there is a 5 point increase in the scores of Brian and Donna. So Sally’s score would overtake Donna’s score when it passed 1\b\b. Sally Brian Corrie Donna 9\b 45 6\b 95 1\b\b 5\b 7\b 1\b\b 11\b 55 8\b 1\b5 AMC Practice Questions and Solutions — Upper Primary

So (C) can be false. We are told that Sally scored 30 po\bnts more than Corr\be and Donna scored 50 po\bnts more than Br\ban, and so together Sally and Donna always scored 80 po\bnts more than Corr\be and Br\ban, hence (E). 5. 2014 UP25 F\bve d\bfferent whole numbers, chosen from the numbers from 1 to 30, add up to 30. What \bs the greatest poss\bble value of the largest of these numbers? (A) 6 (B) 10 (C) 15 (D) 20 (E) 26 To make the largest number as large as poss\bble, we make all the others as small as poss\bble. The smallest four numbers from 1 to 30 are 1 + 2 + 3 + 4 = 10, and so the largest the fifth can be \bs 30 −10 = 20, hence (D). 6. 2014 UP27 A cube \bs made up of 1 cm ×1 cm ×1 cm blocks and measures 12 cm ×12 cm ×12 cm. Sharyn \bs us\bng the same set of blocks to make a set of sta\brs. The p\bcture shows how she started, mak\bng a set of sta\brs 4 blocks h\bgh, 4 blocks from front to back and 5 blocks w\bde. Her fin\bshed set of sta\brs w\bll use all the blocks and be 8 blocks h\bgh and 8 blocks from front to back. How many blocks w\bde w\bll they be? The end of the sta\brcase has 8 + 7 + ∙∙∙+ 2 + 1 = 36 blocks. The number of blocks ava\blable \bs 12 ×12 ×12. 12 ×12 ×12 36 = 12 ×12 ×4× 3 12 ×3 = 12 ×4 1 = 48 So the w\bdth of the sta\brcase \bs 48 blocks, hence (48). AMC Practice Questions and Solutions — Upper Primary