In educational testing, the process of elimination is a test-taking tactic for increasing the chances of answering multiple-choice questions correctly. A test-taker is presented with several possibilities, of which only one answers the question. Even if only one is eliminated and the test-taker guesses among the rest, it is rather more probable Probability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of he will hit it; when there are only five or four the gain in luck is substantial.
Method
The method of elimination is iterative In computational mathematics, an iterative method attempts to solve a problem by finding successive approximations to the solution starting from an initial guess. This approach is in contrast to direct methods, which attempt to solve the problem by a finite sequence of operations, and, in the absence of rounding errors, would deliver an exact. One looks at the answers, determines that several answers are unfit, eliminates these, and repeats, until one cannot eliminate any more. This iteration is most effectively applied when there is logical Logic, from the Greek λογικός is the study of reasoning. Logic is used in most intellectual activity, but is studied primarily in the disciplines of philosophy, mathematics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies. It is one kind of critical thinking. In structure between the answers -- that is to say, when by eliminating an answer one can eliminate several others. In this case one can find the answers which one cannot eliminate by eliminating any other answers and test them alone -- the others are eliminated as a logical consequence. (This is the idea behind optimizations for computerized searches when the input is sorted -- as, for instance, in binary search In computer science, a binary search is an algorithm for locating the position of an element in a sorted list by checking the middle, eliminating half of the list from consideration, and then performing the search on the remaining half. If the middle element is equal to the sought value, then the position has been found; otherwise, the upper half).
Application
Here are two questions of one sort, to illustrate how this tactic is applied. In the first, elimination produces an answer almost at once - if you know how to go at it; in the other, there is no way around it -- you must try every answer.
By which of the following is the number 2135 divisible In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder: 2, 3, 4, 15, 7? Since (see divisibility rule A divisibility rule is a method that can be used to determine whether a number is evenly divisible by other numbers. Divisibility rules are a shortcut for testing a number's factors without resorting to division calculations. Although divisibility rules can be created for any base, only rules for decimal are given here for a refresher) 2135 is not divisible by 2, it is not divisible by 4; since 2 + 1 + 3 + 5 = 3 + 8 = 11 and it is not divisible by 3, it is not divisible by 15. Then only 7 is left; and, indeed: 305 times 7 is 2135.
Note that, if we had a number divisible by 2 but not by 4 (and not divisible by 7), then testing 2 would give us the answer at once. It is always worth testing answers whose exclusion eliminates possibilities, for then, as long as there is only one answer, these possibilities will not need to be tested at all; in effect we incorporate all the information found between our answers and reduce the set.
Now by which of the following is the number above divisible: 2, 3, 7, 11, 13? All of these numbers are prime; to eliminate one of them furnishes no information about the rest. We must test them all in order to find the answer.
See also
Categories: Philosophical logic | Philosophical terminology |
South Shore Now
"The furnace didn't cause the fire." Outside experts are sometimes needed to aid an investigation. "It's a process of elimination ," Mr. Swinemar added, ...
