How to Solve Mathematical Inequality in Reasoning

Mathematical Inequality is a topic that appears often in Reasoning section of competitive exams. It forms the basis for the more complex Coded Inequality questions. Following are the operators used in Mathematical Inequalities in Logical Reasoning. These questions appear for up to 5-10 marks in IBPS Clerk, SBI Clerk, SSC CGL, SBI PO, IBPS PO and other exams. Learn how to quickly solve Mathematical Inequality in Reasoning.

Let us start with the basics.

Symbols & Meanings of Mathematical Inequalities

Symbol	Its meaning	Example
>	Greater than	A > B → A is greater than B
<	Less than	A < B → A is less than B
≥	Greater than or equal to	A ≥ B → A is greater than or equal to B
≤	Less than or equal to	A ≤ B → A is greater than or equal to B
=	Equal to	A = B → A is equal to B

There are a few negative operative as shown below:

Symbol	Its meaning	Equivalent Operation
	Not greater than	≤
	Not less than	≥
	Not greater than  or equal to	<
	Not less than or equal to	>
≠	Not equal to	< or >

Solving Mathematical Inequality in Reasoning With Examples

To solve regular problems of mathematical inequality problems, here are a few tips:

1. A > B ≥ C → A > C

2. A ≥ B > C → A > C

3. A > B = C → A > C

4. A = B > C → A >

5. A < B ≤ C = D → A < D and B ≤ D

6. A < B ≤ C > D = E → A < C and C > E
In this case, the relations between AD, AE, BD and BE cannot be established.
For e.g. A < C and C > D so we get A < C > D. That means C is greater than both A and D. But we don’t know which is greater – A or D; or if they are both equal. Thus the relation between A and D cannot be established.

7. A > B ≤ C D ≤ E → A > B ≤ C < D ≤ E
→ B < E, C < E, B < D.
But the relations between AC, AD, and AE cannot be established.

8. A < B = C < D > E, C > P < F
→ A < D, A < C, B <D, B > P, D > P
Relations between AE BE, CE, AP, AF, BF, CF, DF, EP and EF cannot be established.

9. A B > C = D ≥ E, M ≥ B T → A > B > C = D ≥ E, M ≥ B ≥ T
→ A > C, A > D, A > E, B > D, B > E, C ≥ E , A > T, M > C, M > D, M > E
Relations between AM, CT, DT, ET cannot be established.