 # Math Book 3: Percentages

Percents and Fractions

P ercentage is the idea of expressing a fraction whose denominator is 100 to aid comparison. You could expect a couple of questions in the GMAT quant section testing concepts covered in this topic. One is expected to be adept at interchangeably expressing values as fractions, decimals and percents.

### Concepts Covered

Percentages, fractions are basic concepts that appear frequently as part of the GMAT Problem Solving section. Wizako'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. 11 illustrative examples. 23 solved examples with detailed explanation and special mention of shortcuts wherever applicable
6. An objective type test with 40 GMAT level questions in the work book. Answer key and explanatory answers for all questions are provided

Here is a typical solved example from this chapter.

### Sample 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?

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

Candidate 1 secured 20% of maximum marks, which was 10 marks less than pass mark.
i.e., 20% of M = P - 10 ... (1)

Candidate 2 secured 30% of maximum marks, which was 20 marks more than pass mark.
i.e., 30% of M = P + 20 ... (2)

Subtract equation (1) from equation (2): 10% of M = 30
If 10% of the maximum marks is 30, maximum marks, M = 300

The pass mark is obtained by substituting M = 300 in one of the two equations.
In equation (1): 20% of M = P - 10
20% of 300 = P - 10
60 = P - 10
Or P = 70. Pass mark, P = 70

### Chapterwise details of Wizako's Math Lesson Books

Math Lesson Book 1

 1 Linear Equations Details 2 Quadratic Equations Details 3 Set Theory Details 4 Sequences & Series Details 5 Number Properties & Theory Details 6 Inequalities Details 7 Functions

Math Lesson Book 2

 1 Descriptive Statistics Details 2 Ratio Proportion Details 3 Mixtures 4 Interest 5 Rates: Speed Distance Details 6 Rates: Races Details 7 Rates: Work Time Details

Math Lesson Book 3

 1 Percents Details 2 Profits Details 3 Permutation Combination Details 4 Probability Details 5 Geometry Details 6 Solid Geometry 7 Coordinate Geometry Details