S.A.T. Math Testing Tactics Tactic 8: Eliminate Absurd Choices and Guess

What does it mean to be an ABSURD CHOICE? Examples: Any time you can determine through logical reasoning that your answer should be… … positive, but some of the choices are negative … a ratio greater than 1, but some of the choices give you a ratio less than 1 … a small number, but some of your answers are very, very large … an obtuse angle, but some of the choices are right or acute

Example 8.1 What is the largest prime factor of 255? A) 5 B) 15 C) 17 D) 51 E) 255 I see two numbers right away that are not PRIME numbers: 15 And 255 (any number that ends in a 5 or a zero is divisible by 5) There is another, less obvious, composite number: 51 = 3 x 17 51 is not prime Now we can guess between the other two choices: 255 is obviously divisible by the prime number 5 255 ÷ 17 = 15 It is also divisible by 17.

Note: A problem like this would come with a specific diagram Note: A problem like this would come with a specific diagram. For the purpose of this tactic we are only going to think about it theoretically. Example 8.2 The region inside a semicircle of radius r is shaded. What is the area of the shaded region? A) B) C) D) E) So, we have a shaded area INSIDE a SEMICIRCLE. The area of a semicircle is half the area of a circle: Our shaded region must be LESS than So we could now guess between choice A and B.

Example 8.3 A jar contains only red and blue marbles. The ratio of the number of red marbles to the number of blue marbles is 5:3. What percent of the marbles are blue? 37.5% 50% 60% 62.5% 80% Red: Blue 5:3 Are there more red or more blue? RED So, RED must be more than 50% of the total Blue must be less than 50% of the total.

Example 8.4 4 In the figure, four semicircles are drawn, each centered at the midpoint of one of the sides of the square ABCD. Each of the four shaded “Petals” is the intersection of two semicircles. If AB = 4, what is the total area of the shaded region? 8π 32 – 8π 16 – 8π 8π –32 8π –16 4 First: What is the area of the entire square? A = 4 x 4 = 16 So, the shaded region must be LESS than 16. Next: Use your calculator to estimate your answer choices.

Example 8.4 4 In the figure, four semicircles are drawn, each centered at the midpoint of one of the sides of the square ABCD. Each of the four shaded “Petals” is the intersection of two semicircles. If AB = 4, what is the total area of the shaded region? 8π 32 – 8π 16 – 8π 8π –32 8π –16 4 = 25.12 Shaded Region < 16 = 32 – 25.12 = 6.88 = 16 – 25.12 = NEGATIVE =25.12 – 32= NEGATIVE We could now guess between choice B and E. =25.12 – 16 = 9.12

IN CONCLUSION You want to answer as many questions on the S.A.T as possible. Sources differ in opinions as to when you should guess. Some sources say to guess if you can eliminate 1 answer choice. Others say you should eliminate at least 2 choices before you guess. Regardless– you should always try and eliminate ABSURD choices! Don’t just start solving a problem. Take a few seconds and THINK about the reasonableness of your answer choices.