GMAT Problem Solving POE – Opposites

In this article, we will see how to use process of elimination techniques for problem solving and spot opposites in answer choices. This technique can be used mostly in questions categorized under Number Properties, and Ratio & Proportions. Let us look at an example to understand how POE Opposite technique can be applied.

Q) A competitive exam scores answers with +1 point for one correct answer and -2 for one wrong answer. The scores of the 10 students who took the exam were 10, 4, 6,-2,-4,
-6, 12, -1, -5, and -8. What is the least class median to exam score ratio?

A) -0.625
B) -0.525
C) -0.425
D)  0.525
E)   0.625

Answer

From the answer choices, it is clear that the crucial point that differentiates the answers is the nature of the median score – whether it is positive or negative. If you apply the Process of Elimination – Range technique, the answers can be grouped as:

Group 1 = {-0.625, -0.525, -0.425}
Group 2 = {0.525, 0.625}

Note: The positive and negative version of 0.625 and 0.525 is present in the answer choices, and test takers might assume that the answer choice will be one of the two. Don’t fall for the trap.

Before calculating median score, the scores should be arranged in increasing order:
-8 -6 -5 -4 -1 4 6 10 12

Since the number of scores is 10, the median will be the average of 5th and 6th elements

Median (5th + 6th)/2 = (-4+-1) /2 = - 2.5

When you know that the median is negative, all the positive numbers from the answer choice should be eliminated.  Eliminate Group 1.

Class Median/Exam Score = -2.5/ (-8), -2.5/ (-6)… -2.5/ (10), -2.5/ (12)

Since the question asks for the least Class Median to Exam Score Ratio, the score should a small positive number.

(-2.5) /4 = - (25/40) = - (25)/4 * 1/10 = -0.625

Correct Answer: A