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Math Book 1 : Sets

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Set Language Theory is a topic from which you could expect 4 to 7 questions in the GMAT quant section. The topic is an important one.

Set Theory
Book 1

Concepts Covered

Basics of set language theory such as union of sets, intersection of sets are tested in the GMAT in both variants - problem solving and data sufficiency. With a good grasp of the basic formulae governing set language, one should be able to attempt these questions with ease. 4GMAT's GMAT Math Lesson Book in this chapter covers the following concepts

  1. Introduction to the concept of sets and methods to represent sets.
  2. Different types of sets explained with illustrative examples.
  3. Cardinal number of sets, power sets, number of subsets for a set.
  4. The De-Morgan's Law.
  5. Using Venn Diagrams to solve set language questions explained with illustrative examples.
  6. 9 solved examples, including Venn Diagram representation.
  7. 5 Comprehensive exercise problems with answer key and explanatory answers.
  8. An objective type speed test with 32 questions along with explanatory answers and answer key are provided for the speed test.
Here is an example of a typical solved example in this chapter.


Sample Question

In a room of 50 people who have a red book or a white book, 30 have a red book and 16 have both a red book and a white book. How many among the 50 in the room have only a white book?

Explanatory Answer
Venn Diagram Number of people having a red book = 30
i.e., n(R) = 30

Number of people having a red and a white book = 16
i.e., n (R Intersection W) = 16

The total number of people in the room = number of people who have a red book or a white book = n (R Union W) = 50.

We know,
n (R Union W) = n(R) + n(W) - n(R Intersection W)
50 = 30 + n(W) - 16
50 - 14 = n(W) - 16
n(W) = 36
i.e., the number of people who have a white color = 36.

Therefore, number of people who have only a white book = n(W) - n(R Intersection W) = 36 - 16 = 20

Chapterwise details of 4GMAT's Math Lesson Books

Math Lesson Book 1
  1. Linear Equations
  2. Quadratic Equations
  3. Set Theory
  4. Sequences & Series
    Details | Quiz
  5. Number Theory
  6. Inequalities
    Details | Quiz
  7. Functions
Math Lesson Book 2
  1. Descriptive Statistics
  2. Ratio Proportion
  3. Mixtures
  4. Interest
  5. Rates : Speed Distance
  6. Rates : Races
  7. Rates : Pipes Cisterns
  8. Rates : Work Time
Math Lesson Book 3
  1. Percents
  2. Profits
  3. Permutation
  4. Probability
  5. Geometry
  6. Solid Geometry
  7. Coordinate Geometry