Considered as one of the most coveted entrance exams, the Graduate Management Admission Test (GMAT) examines the basic analytical, quantitative and verbal skills of the candidates. Although every section has its own significance, the quantitative section of GMAT is the trickiest one. Quantitative Aptitude examines your basic knowledge of mathematics concepts. One such key topic of the Quants section is Inequalities Questions. Since the questions asked from this topic carry significant weightage in the exam, it becomes important to understand this concept thoroughly. Here is a comprehensive blog detailing Inequality questions, how you can solve them by following some basic rules as well as various sample questions to help you grasp the basics of this concept.
What are Inequalities?
Before moving on to the fundamental formulas for inequality questions, it is pivotal to simplify the concept of inequalities. They are defined as the functions which determine a relationship between distinct values and expressions. This crucial feature differentiates inequalities from equations. While equations represent the relationship between equal values, inequalities compare unequal quantities. The symbols which represent inequalities are : ‘>’, ‘<‘, ‘≥’, ‘≤’ and ‘≠’.
X ≠ Y
Here, ‘≠’ is called as the ‘unequal’ sign. We may not know which variable out of X or Y has a higher or a lower value but they are certainly not equal.
X > Y
The inequality is referred to as the ‘greater than’ sign. As per the above equation, X is greater than Y.
X < Y
This symbol is the opposite of greater than and is called as ‘less than’. Thus, X is less than Y.
X ≥ Y
The combination of greater than and equal to sign shows that the variable X is greater than Y but can also be equal.
X ≤ Y
This is the opposite of greater than equal to sign. Thus, variable Y can be greater than or equal to X.
Types of Inequality Questions
Generally, the inequality questions for GMAT are of two types, i.e.
1. Direct Inequalities
The questions on direct inequalities are comprised of the relationship between variables which is indicated in the symbol form.
2. Indirect Inequalities
When it comes to question on indirect inequalities, the relationship between variables is defined in a coded form. Different symbols like @, #, %, $ etc. are used to represent this relationship.
Rules For Solving Inequality Questions
Inequalities can seem tricky and complex if you don’t know about the basic rules of solving them. Here is a list of some key rules and tips you can follow to simplify inequality questions:
1. When you divide or multiply an inequality by a negative number, the inequality sign flips.
Example: 12 > – 5
On multiplying both sides with -5, we get the equation as -60 > 25. But, – 60 cannot be greater than 25. Thus, it becomes important to reverse the symbol.
2. In Inequality Questions where symbols are opposite, no conclusion can be drawn.
Example: in P>Q<R, it cannot be concluded whether P is greater than R or vice versa.
3. In complementary pairs, the relationship cannot be established if the relation between common elements is not defined.
Example: In P ≥ Q, Q ≤ R, Q is less than or equal to both P and R. Thus, the relationship between P and R cannot be established.
4. The inequality direction does not change if we add or subtract numbers on both sides.
Example: On adding 2 to both sides of 10 < 15 we get 12 < 17. Which stands true in both the cases.
5. Dividing the inequality with a variable whose sign is unknown does not yield the right answer.
Example: PX < 3P. On dividing the inequality with P on both sides we get, X < 3.
But if we divide it with -P then we get -X < -3.
Thus, it is advisable to not divide the inequality with a variable whose sign remains unknown.
Sample Inequality Questions for GMAT
By now, you must have understood the basics of Inequalities and its different concepts. Here are some sample Inequality Questions which you can practice to strengthen the basics:
1. If 3 < x < 8 and 5 < y < 11, which of the following represents all of the possible values of xy?
(A) 3 < xy < 11
(B) 8 < xy < 19
(C) 15 < xy , 88
(D) 24 < xy < 55
2. Consider three distinct positive integers a, b, c all less than 100. If |a – b| + |b – c| = |c – a|, what is the maximum value possible for b?
3. Consider integers p, q, r such that |p| < |q| < |r| < 40. P + q + r = 20. What is the maximum possible value of pqr?
4. If −1 < x < 5, which is the following could be true?
(A) 2x > 10
(B) x > 17/3
(C) x^2 > 27
(D) 2x – x^2 < 0
5. If |(x – 3)2 + 2| < |x – 7| , which of the following expresses the allowable range for x?
(A) 1 < x < 4
(B) 1 < x < 7
(C) – 1 < x < 4 and 7 < x
(D) x < – 1 and 4 < x < 7
(E) – 7 < x < 4 and 7 < x
We hope that this blog helped you gain better clarity about the Inequality questions for GMAT. If you are appearing for GMAT and need more tips and tricks for solving other sections, our Leverage Edu experts can guide you throughout the preparation process and helping you ace every section on this exam and successfully clearing it with high scores.