[PDF] Australian Mathematics Competition AMC Practice Questions and Solutions - Middle Primary.pdf | Plain Text

AMC PRACTICE QUESTIONS AND SOLUTIONS Middle Primary Copyright � 2014, 2019 Australian Mathematics Trust AMTT Limited ACN 083 950 341 (Set1)              \b                 
   
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\b 4. 2014 MP20 A party game played with a six-sided dice is fair if the chance of winning is equal to the chance of losing each time the dice is rolled\b Which one of these games is fair? (A) You win if you roll a 6\b (B) You win if you roll a 2 or a 5\b (C) You win if you roll a number greater than 4\b (D) You win if you roll a number less than 3\b (E) You win if you roll an odd number\b AMC Practice Questions and Solutions — Middle Primary

For each game there are 6 possible numbers you can roll and each is just as likely. \bo a game will be fair if there are 3 winning rolls and 3 losing rolls. Game (A) (B) (C) (D) (E) Winning rolls 6 2,5 5,6 1,2 1,3,5 Losing rolls 1,2,3,4,5 1,3,4,6 1,2,3,4 3,4,5,6 2,4,6 hence (E). 5. 2014 MP25 In this magic square, the even numbers 2,4 ,6 ,..., 18 are placed so that the sums of the numbers in each row, column and diagonal are equal. What is the sum of the two numbers in the shaded squares? (A) 12 (B) 14(C) 18 (D) 22 (E) 28 18 14 6 16 The total of nine numbers in the square is 2+4+6+8+10+12+14+16+18 = 90 . Then each row, and each column, must add to 30. Looking at the last column and the middle row, the shaded squares can be filled in to make totals of 30. 18 8 14 10 6 16 The two shaded squares are 10 + 8 = 18, hence (C). 6. 2014 MP27 A numb er is palindromicif it reads the same forwards as backwards. For example, 686 is palindromic. How many numbers from 100 to 300 are palindromic? From 100 to 199 the numbers must start and end with 1. \bo 101, 111, 121, . . . , 191, giving 10 palindromes. \bimilarly there are another 10 from 200 to 299, and 300 is not one. In total there are 20, hence (20). AMC Practice Questions and Solutions — Middle Primary