 x Process of elimination Encyclopedia
Process of elimination is a method to identify an entity of interest among several ones by excluding all other entities.

## In education testing

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
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

he will hit it; when there are only five or four the gain in luck is substantial.

### Method

The method of elimination is iterative. 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
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

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
Binary search algorithm
In computer science, a binary search or half-interval search algorithm finds the position of a specified value within a sorted array. At each stage, the algorithm compares the input key value with the key value of the middle element of the array. If the keys match, then a matching element has been...

).

### 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: 2, 3, 4, 15, 7? Since (see divisibility rule
Divisibility rule
A divisibility rule is a shorthand way of discovering whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits...

for a refresher) 2135 is not divisible by 2, it is not divisible by 4; since 2 + 1 + 3 + 5 = 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.

## In medicine

A process of elimination can be used to reach a diagnosis of exclusion
Diagnosis of exclusion
A diagnosis of exclusion is a medical condition reached by a process of elimination, which may be necessary if presence cannot be established with complete confidence from examination or testing...

.

It is also an underlying method in performing a differential diagnosis
Differential diagnosis
A differential diagnosis is a systematic diagnostic method used to identify the presence of an entity where multiple alternatives are possible , and may also refer to any of the included candidate alternatives A differential diagnosis (sometimes abbreviated DDx, ddx, DD, D/Dx, or ΔΔ) is a...

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