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

# MethodEdit

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 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).

# ApplicationEdit

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 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 alsoEdit

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