# Guide to GMAT Inequalities

The GMAT exam syllabus for Quant covers topics like Algebra, Arithmetic, Geometry, and word problems.

In the GMAT Quant section, there are two types of questions – Problem-solving and Data sufficiency. The inequalities are mostly tested in Data sufficiency type questions, especially in Yes/No data sufficiency questions. You may get around 3 to 4 questions in a test from inequalities, tested directly or indirectly in a question.

Before getting into GMAT questions we will discuss the basic rules about inequalities. Equalities and inequalities are almost the same except for one important rule about inequalities. To solve equalities, we do the same operations on both sides of the equalities, such as addition, subtraction, multiplication, division, etc. We can do the same in inequalities, but when you multiply and divide by negative numbers we need to flip the inequality sign. Examples of solving equalities and inequalities are given below,

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GMAC uses this rule effectively to create traps. Let us look at some examples.

When we try to solve the equation 2x/y = z for x, we can easily solve it as x = y*z/2. Similarly, let’s look at the case of inequalities, 2x/y > z, shall we solve for x as x > y*z/2? Certainly, not, though it appears as if it is correct.

Yes, we have missed the case of multiplying or dividing the inequality by a negative number. Let us look at the step by step approach to solve a basic inequality question for a better understanding.

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What we did in the first step is correct, because we have divided both sides by a positive value ‘2’. But in the next step, we have divided both sides of the inequality by ‘y’. This step is wrong because we don’t know whether the ‘y’ is positive or negative. If the value of y is negative, we need to flip the inequality sign.

This is the usual mistake that the students do while solving inequality questions. We can easily avoid this mistake by carefully applying the inequality rules while solving through a step by step approach. Or we can simply try some numbers that satisfy the inequalities, better to try negative and positive numbers when you have inequalities.

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