5. Profit and Loss

Percentages, Fractions are basic concepts that appear frequently as part of the GMAT Problem Solving section. It is advised that you get a good grasp of converting percentages to equivalent fractions and fractions to equivalent percentages to able to solve questions in this topic with ease. 4GMAT's GMAT Math Lesson Book in this chapter covers the following concepts:

1. The meaning of the term percent and the need for using percentages
2. The relation between percents, fractions and decimals and the rules to convert from one form to another with illustrative examples
3. Explanation of the percentage change in values along with illustrative examples
4. 23 solved examples with detailed explanation and also the special mention of shortcuts that can be used as and when necessary
5. 29 exercise problems with answer key and explanatory answers to enhance understanding
6. An objective type speed test with around 40 questions with explanatory answers and answer key provided for the speed test

Here is an example of a typical solved example in this chapter.
Sample Question
Question
In an examination a candidate who secured 20% of the maximum marks failed by 10 marks. Another candidate who secured 30% of the maximum marks got 20 marks more than the pass mark. What is the pass mark in this examination?

Explanatory Answer
Let the pass mark in the examination be P and the maximum marks be M.

Candidate 1 secured 20% of maximum marks that was 10 marks less than pass mark
i.e., P = 20% of M + 10

Candidate 2 secured 30% of maximum marks that was 20 marks more than pass mark.
i.e., P= 30% of M - 20

Equating the two relations, we get 20% of M + 10 = 30% of M - 20 or 10% of M = 30
If 10% of the maximum marks is 30, then maximum marks, M= 300
Therefore, the pass mark is obtained by substituting for M in any one of the equations.
i.e., P = 30% of 300 - 20 = 90 - 20 = 70. Pass mark, P = 70