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 ID: 782342
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Slide1
S.A.T. Math Testing Tactics
Tactic 14: Systematically Make Lists
Slide2If 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
Slide3Example 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)Red B) Blue C) White
D) Green E) Yellow
Slide4Example 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: Red Person 6: Red
Person 2: Blue Person 7: Blue
Person 3: White Person 8: White
Person 4: Green Person 9: Green
Person 5: Yellow Person 10: Yellow
Notice: # divisible by 5 means YELLOW name tag
What multiple of 5 is really close to 93?
90
Slide5Example 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)Red B) Blue C) White D) Green E) Yellow
91st
92nd93rd90th
C
Slide6Example 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) = 300
5 (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, 30 sum = 32
3, 20 sum = 234, 15 sum = 195, 12 sum = 176, 10 sum = 16
16
Slide7Example 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
101 151
111 161
121 171
131 181
141 191
=10Recognize that the 200’s, 300’s, etc. will follow the same pattern:202, 212, 222, etc.100’s 600’s
200’s 700’s
300’s 800’s
400’s 900’s
500’s
=9 groups of 10
90
palindromes between 100 and 1000
Slide8IN CONCLUSION
Many problems involving counting can be solved by making a small, organized list and then reasoning through the rest of the information.