9. Inequalities

Inequalities is an important topic in the GMAT problem solving and GMAT data sufficiency sections. One can expect quite a few questions from this topic. Once the basics are understood and mastered, solving these questions is quite easy. 4GMAT's GMAT Math Lesson Book in this chapter covers the following concepts

1. Explanation to the basic concept of inequalities.
2. Various basic rules governing inequalities such as multiplying both sides of an inequality with a negative number, inequalities with algebraic equations such as quadratic expressions, inequalities with exponents, inequalities with modulus.
3. 16 solved examples, which also contain additional notes that help solve questions in inequalities quickly.
4. 17 exercise problems with the answer key and also explanatory answers.
5. An objective type speed test with around 35 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
Question
Find the range of values for x for which 1 / (x - 2) > -2?

Explanatory Answer
As there is a linear term in 'x' in the denominator, we can eliminate the x terms in the denominator by multiplying both sides of the inequality by (x - 2)2 in the numerator

(x - 2) > -2(x - 2)2
=> (x - 2) > -2(x2 - 4x + 4)
=> (x - 2) > -2(2x2 + 8x - 8)
=> 0 > -2x2 + 7x - 6
=> 2x2 - 4x - 3x + 6 > 0
=> (2x - 3) (x - 2) > 0
The range of values of x that satisfy the above inequality are
In other words, x does not lie between 3 / 2 and 2.