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Elimination Strategies

Strategy-1: On hard problems, if you are asked to find the least (or greatest) number, then eliminate the least (or greatest) answer-choice.

This rule also applies to easy and medium problems. When people guess on these types of problems, they most often choose either the least or the greatest number. But if the least or the greatest number were the answer, most people would answer the problem correctly, and it therefore would not be a hard problem.

What is the maximum number of points common to the intersection of a square and a triangle if no two sides coincide?
  1. 4
  2. 5
  3. 6
  4. 8
  5. 9
By the above rule, we eliminate answer-choice (E).


Strategy-2 : On hard problems, eliminate the answer-choice “not enough information.”

When people cannot solve a problem, they most often choose the answer-choice “not enough information.” But if this were the answer, then it would not be a “hard” problem.
Strategy-3: On hard problems, eliminate answer-choices that merely repeat numbers from the problem.
If the sum of x and 20 is 8 more than the difference of 10 and y, what is the value of x + y?
  1. –2
  2. 8
  3. 9
  4. 28
  5. not enough information
By the above rule, we eliminate choice (B) since it merely repeats the number 8 from the problem. By Strategy 2, we would also eliminate choice (E).
Caution: If choice (B) contained more than the number 8, say, , then it would not be eliminated by the above rule.
Strategy-4: On hard problems, eliminate answer-choices that can be derived from elementary operations.
In the figure, what is the perimeter of parallelogram ABCD?
  1. 12
  2. 15
  3. 24
  4. not enough information
Using the above rule, we eliminate choice (D) since 24 = 8 × 3.
Further, using Strategy 2, eliminate choice (E).
Note, 12 was offered as an answer-choice because some people will interpret the drawing as a rectangle tilted halfway on its side and therefore expect it to have one-half its original area.
Strategy-5 : After you have eliminated as many answer-choices as you can, choose from the more complicated or more unusual answer-choices remaining.

Suppose you were offered the following answer-choices:

  1. 8
  2. 10
  3. 12

Then you would choose either (A) or (B).

We have been discussing hard problems but have not mentioned how to identify a hard problem. Most of the time, we have an intuitive feel for whether a problem is hard or easy. But on tricky problems (problems that appear easy but are actually hard) our intuition can fail us.

On the test, your first question will be of medium difficulty. If you answer it correctly, the next question will be a little harder. If you again answer it correctly, the next question will be harder still, and so on. If your math skills are strong and you are not making any mistakes, you should reach the medium-hard or hard problems by about the fifth problem. Although this is not very precise, it can be quite helpful. Once you have passed the fifth question, you should be alert to subtleties in any seemingly simple problems.

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