In many problems you can get the answer simply by trying each of the answer choices until you find the one that works.
Unless you have some intuition as to what the correct answer might be, then you should always start with choice (C) as your first guess (except for the exception below). The reason for this is simple.
Answers are usually given in increasing or decreasing order. So very often if choice (C) fails you can eliminate two of the other choices as well.
If the word LEAST appears in the problem, then start with the smallest number as your first guess. Similarly, if the word GREATEST appears in the problem, then start with the largest number as your first guess.
Sometimes the answer choices themselves cannot be substituted in for the unknown or unknowns in the problem.
But that doesn't mean you can't guess your own numbers. Try to make as reasonable a guess as possible, but don't over think it. Keep trying until you zero in on the correct value.
A problem may become much easier to understand and to solve by substituting a specific number in for a variable. Just make sure that you choose a number that satisfies the given conditions.
Here are some guidelines when picking numbers.1. Pick a number that’s simple but not too simple. In general you might want to avoid picking 0 or 1 (but 2 is usually a good choice).
2. Try to avoid picking numbers that appear in the problem.
3. When picking two or more numbers try to make them all different.
4. Most of the time picking numbers only allows you to eliminate answer choices. So don’t just choose the first answer choice that comes out to the correct answer. If multiple answers come out correct you need to pick a new number and start again. But you only have to check the answer choices that haven’t yet been eliminated.
5. If there are fractions in the question a good choice might be the least common denominator (lcd) or a multiple of the lcd.
6. In percent problems choose the number 100.
7. Don’t pick negative numbers in grid-in questions. This is a waste of time since you can’t grid a negative number.
8. If your first attempt doesn’t eliminate 4 of the 5 choices, try to choose a number that’s of a different “type.” Here are some examples of types:
A positive integer greater than 1.
A positive fraction (or decimal) between 0 and 1.
A negative integer less than -1.
A negative fraction (or decimal) between -1 and 0.
9. If you’re picking pairs of numbers try different combinations from (8). For example you can try two positive integers greater than 1, two negative integers less than -1, or one positive and one negative integer, etc.
Remember that these are just guidelines and there may be rare occasions where you might break these rules. For example sometimes it’s so quick and easy to plug in 0 and/or 1 that you might do this even though only some of the answer choices get eliminated.
Steve Warner, a Staten Island (NY) native, earned his Ph.D. at Rutgers University in Pure Mathematics in May, 2001. While a graduate student, Dr. Warner won the TA Teaching Excellence Award.
After Rutgers, Dr. Warner joined the Penn State Mathematics Department as an Assistant Professor.
In September, 2002, Dr. Warner returned to New York to accept an Assistant Professor position at Hofstra University. By September 2007, Dr. Warner had received tenure and was promoted to Associate Professor.
He has taught undergraduate and graduate courses in Precalculus, Calculus, Linear Algebra, Differential Equations, Mathematical Logic, Set Theory and Abstract Algebra.
Over that time, Dr. Warner participated in a five year NSF grant, “The MSTP Project,” to study and improve mathematics and science curriculum in poorly performing junior high schools.
He also published several articles in scholarly journals, specifically on Mathematical Logic.
Dr. Warner has over 15 years of experience in general math tutoring and over 10 years of experience in SAT math tutoring. He has tutored students both individually and in group settings.
Since the age of 4, Dr. Warner has enjoyed playing the piano—especially compositions of Chopin as well as writing his own music. He also maintains his physical fitness through weightlifting.
Currently Dr. Warner lives in Staten Island with his two cats, Achilles and Odin.
Begin with Choice (C)