S.A.T. Math Testing Tactics Tactic 14: Systematically Make Lists

If asked, “how many?” Try making an organized list of all possibilities ▫Start making the list ▫Try to recognize a pattern ▫Try to answer the question without finishing the list

Example 14.1 People enter a room one at a time and are given a name tag in one of five possible colors. The colors are given out in this order: red, blue, white, green, and yellow. What is the color of the name tag that is given to the 93 rd person who enters the room? A)RedB) BlueC) White D) GreenE) Yellow

Example 14.1 (continued) Start by making a list of the first 10 people who enter the room and the color of name tag. Person 1: RedPerson 6: Red Person 2: BluePerson 7: Blue Person 3: WhitePerson 8: White Person 4: GreenPerson 9: Green Person 5: YellowPerson 10: Yellow Notice: # divisible by 5 means YELLOW name tag What multiple of 5 is really close to 93? 90

Example 14.1 (continued) People enter a room one at a time and are given a name tag in one of five possible colors. The colors are given out in this order: red, blue, white, green, and yellow. What is the color of the name tag that is given to the 93 rd person who enters the room? A)RedB) Blue C) White D) GreenE) Yellow 91st92nd93rd90th C

Example 14.2 The product of three positive integers is 300. If one of them is 5, what is the least possible value of the sum of the other two? Start by determining the product of the other two. (A)(B)(C) = (B)(C) = 300 (B)(C) = 60 Make a list of number with a product of 60, then find the sum. 1, 60 sum = 61 2, 30sum = 32 3, 20sum = 23 4, 15sum = 19 5, 12sum = 17 6, 10sum = 16 16

Example 14.3 A palindrome is a number, such as 93539, that reads the same forward and backward. How many palindromes are there between 100 and 1000? Start by listing all of the palindromes in the 100’s =10 Recognize that the 200’s, 300’s, etc. will follow the same pattern: 202, 212, 222, etc. 100’s600’s 200’s700’s 300’s800’s 400’s900’s 500’s =9 groups of palindromes between 100 and 1000

IN CONCLUSION Many problems involving counting can be solved by making a small, organized list and then reasoning through the rest of the information.