![]() ![]() ![]() Then b = 1, c = 3, and therefore the ratio of a² to c² is 25 to 9, choice B. Looks scary? This ACT problem is actually pretty easy if you pick numbers. Level 4 Number Theoryįor nonzero numbers a, b, and c, if c is three times b and b is 1/5 of a, what is the ratio of a² to c² ? The following problem could appear on the ACT or GRE. Okay, so let’s try solving a math practice problem by picking numbers. For example sometimes it is 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. Remember that these are just guidelines and there may be rare occasions where you might break these rules. 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. If you are picking pairs of numbers try different combinations from (8).A negative fraction (or decimal) between -1 and 0.A positive fraction (or decimal) between 0 and 1.If your first attempt does not eliminate all choices except one, try to choose a number that is of a different “type.” Here are some examples of types:.This is a waste of time since you cannot grid a negative number. Do not pick a negative number as a possible answer to a grid-in question.In percent problems choose the number 100.If there are fractions in the question a good choice might be the least common denominator (lcd) or a multiple of the lcd.But you only have to check the answer choices that have not yet been eliminated. If multiple answers come out correct you need to pick a new number and start again. So do not just choose the first answer choice that comes out to the correct answer. Most of the time picking numbers only allows you to eliminate answer choices.When picking two or more numbers try to make them all different.Try to avoid picking numbers that appear in the problem. ![]() In general you might want to avoid picking 0 or 1 (but 2 is usually a good choice). Pick a number that is simple but not too simple.Here are some guidelines when picking numbers. The idea is simple – replace the unknowns in the problem with specific values. It can often be used to make a difficult problem much easier to understand, and if you are careful in its use, you will usually get the answer without too much trouble. The strategy of “picking numbers” works on a wide range of different math problems on standardized tests (such as the SAT, ACT and GRE) in all topics and difficulty levels. ![]()
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