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Inequalities describe relationships in which one quantity is greater than, less than, greater-than-or-equal-to, or less-than-or-equal-to another, usually requiring us to figure out the ranges of possible values rather than a single fixed answer. They play an important role in many algebraic problems on GMAT and are tested in abundance on the exam. Therefore, full coverage of inequalities is an essential part of any comprehensive GMAT preparation course. This page offers you an organized subtopic wise playlist, along with a few worked examples, for efficient preparation of this concept.
Modulus based or absolute value inequalities appear frequently on the GMAT. The central idea is that every modulus expression naturally splits into two separate cases, one positive and one negative. If you overlook either branch, you quietly lose a part of the solution set. For instance, to solve |x – 2| > 3, you must work through both x – 2 > 3 and x – 2 < -3. Many test takers skip the second inequality, and that is where avoidable errors enter. In the same way, for expressions like |x + 5| < 10, the logic changes shape and the variable must lie between two boundary values, -10 to 10. The following short video breaks down the approach, demonstrates it in detail, and prepares you to apply it in GMAT drills, sectional tests, and full-length GMAT mock tests.
Polynomial inequalities can appear daunting at first because the expressions look large, but the underlying idea is logical and highly structured. The GMAT rarely tests very bulky polynomials, yet building clarity on such examples ensures that even the most demanding cases feel manageable. The heart of the method lies in factorization and in studying how the polynomial behaves around its critical points. In your GMAT prep, once you learn to mark these points, plot them on a number line, and see how the signs change across intervals, the question turns into a graceful exercise in reasoning rather than a heavy calculation. This approach is known as the wavy curve method and is remarkably effective for solving factorization based inequalities on the GMAT. The following short video unpacks this concept and demonstrates its typical GMAT question forms.
Understanding how positive and negative numbers behave under multiplication and powers is one of the most basic yet powerful ideas in mathematics. In the GMAT Quant section, this knowledge becomes crucial in inequality questions and number property problems. A single slip with a sign can flip the entire answer, which makes such questions feel delicate. The core rules may seem straightforward at first: positive times positive stays positive, negative times negative becomes positive, and so on. However, once powers and inequalities enter together, the scenarios grow more layered. For instance, raising a negative number to an odd power versus an even power leads to completely different outcomes, and recognizing this difference makes all the impact. This quick video lesson presents the concept and shows how the GMAT is likely to test it.
Many GMAT questions on inequalities and functions require a very fine sense of how numbers behave across different ranges. Patterns that feel obvious for large values can completely reverse when you test numbers between −1 and 1. For instance, we usually expect 1/x to become smaller as x increases, but the exact reverse occurs when x lies between 0 and 1. In the same way, squaring a small fraction makes it even smaller, while taking its square root makes it larger. Similar reversals appear with negative numbers, where the behavior shifts once again. These subtle changes form the backbone of several higher level inequality problems. Without a firm grasp of these ranges, many students walk into traps, especially on advanced questions. In this short clip, the concept is explained step by step, along with how it can appear on the GMAT.
Some of the most challenging GMAT questions are those that use phrases such as “may be true,” “can be true,” or “must be true.” These are less about routine equation solving and more about testing conditions logically, deciding whether a statement works in at least one scenario or whether it holds in every possible case. In may be true or can be true problems, your goal is not to prove a rule forever but simply to find a single example that satisfies the statement; if one case fits, that option is acceptable. In contrast, must be true or always true questions reverse the requirement: if you can uncover even one situation where the statement does not hold, you must discard that choice. This brief video breaks down the idea and illustrates how GMAT questions can be built around it.
Real practice for Inequalities problems begins when you work on them through a software simulation that closely mirrors the official GMAT interface. You need a platform that presents the question stem and the inequality information in a GMAT like layout, lets you interact with the conditions and answer choices naturally, and provides all the on screen tools and functionalities that you will see on the actual exam. Without this kind of environment, it is difficult to feel fully prepared for test day. High quality Inequalities questions are not available in large numbers. Among the limited, genuinely strong sources are the official practice materials released by GMAC and the Experts’ Global GMAT course.
Within the Experts’ Global GMAT online preparation course, every Inequalities problem appears on an exact GMAT like user interface that includes all the real exam tools and features. You work through more than 100 Inequalities questions in quizzes and also take 15 full-length GMAT mock tests that include several Inequalities questions in roughly the same spread and proportion in which they appear on the actual GMAT.
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