S.A.T. Math Testing Tactics

1. S.A.T. Math Testing Tactics Tactic 6: Replace Variables with Numbers

2. Replace Variables with Numbers • Many S.A.T. questions will ask you about a generic situation using variables. Your answer choices will not be numbers. • To make these problems easier: • Replace each variable with an easy to use number • Solve the problem using those numbers • Evaluate each of the 5 choices to see which expression is equivalent to your specific answer

3. Example 6.1 If a is equal to b multiplied by c, which of the following is equal to b divided by c? A) B) C) D) E) Replace variables with numbers A = B x C 6 = 3 x 2 A=6 B =3 C =2 Solve Problem B÷C 3÷2 1.5 Test Answer Choices A) 6/(3x2) = 1 B) (6x3)/2 = 9 C) 6/2 = 3 D) 6/22 = 1.5 E) 6/(3x22) = 0.5

4. Example 6.2 If the sum of four consecutive odd integers is s, then, in terms of s, what is the greatest of these integers? A) B) C) D) E) Replace Variables with Numbers: 1 + 3+ 5 + 7 = 16 = S Largest = 7 Evaluate Answer Choices: (16-12)/4 = 1 (16-6)/4 = 2.5 (16+6)/4 = 5.5 (16+12)/4 = 7

5. Example 6.3 • If a school cafeteria needs c cans of soup each week for each student and there are exactly s students in the school, for how many weeks will x cans of soup last? A) B) C) D) E) Evaluate Answers: (4 x 80) /10 =32 (80 x 10)/4 = 200 10/(4x80) = .03125 80/(4 x 10) = 2 4x10x80 = 3200 Replace Variables with Numbers c= 4 cans each week for each student s = 10 students in school x = 80 cans of soup Answer Question: 4 x 10 = 40 cans each week 80 cans will last 2 weeks

6. In Conclusion There is no reason to deal with an abstract problem. Instead, make up your own numbers and find the solution that works! Replace Variables with Numbers!

7. S.A.T. Math Testing Tactics Tactic 7: Choose an Appropriate Number

8. Choose an Appropriate Number • Tactic 7 and Tactic 6 are very similar. In Tactic 6, we chose easy-to-substitute numbers to replace our variables. In Tactic 7, we are going to choose a nice, friendly number as a starting value. • In general: Problems dealing with fractions– choose the Least Common Denominator Problems dealing with percents – choose 100 or 1000

9. Example 7.1 • At Central High School each student studies exactly one foreign language. Three-fifths of the students take Spanish and one-fourth of the remaining students take Italian. If 300 students take French, how many students are enrolled at Central High? Notice the two fractions: 3/5 and 1/4 What is the LCD? 20 2 take Italian, 6 left 6 take French 20 students at Central HS 12 take Spanish, 8 left

10. Example 7.2 On a certain Russian-American committee, 2/3 of the members are men, and 3/8 of the men are Americans. If 3/5 of the committee members are Russians, what fraction of the members are American women?  A) 3/20 B) 11/60 C) ¼ D) 2/5 E) 5/12 LCD: 2/3 , 3/8 , 3/5 120 Start with 120 members 2/3 (120) = 80 men so 40 women 3/8 (80) = 30 USA men so 50 Russ men 3/5 (120) = 72 Russians so 48 USA 48 USA – 30 USA men = 18 USA women 18/120 = .15

11. Example 7.3 At Books, Books, Books, Inc., 40% of all books purchased are paperback. Of the paperbacks, 35% are mysteries. Of the non-mystery paperbacks, 25% are romance novels. What percent of all books purchased are either paperback mysteries or romance novels? Since we are taking a percent of a percentage, let’s start with 1000 books. • .40 (1000) = 400 paperbacks • .35 (400) = 140 mysteries, • 260 other paperbacks • .25 (260) = 65 romance 140 + 65 = 205 205/1000 = .205 20.5%

12. In Conclusion • When dealing with fractions, choose the LCD as your starting population. • When dealing with percents, choose a multiple of 100 to be your starting population.