# Study Notes on the basics of Inequality

By Gaurav Mohanty|Updated : December 17th, 2021

As you all are well aware, Inequality, whether coded or direct forms an important topic of the Reasoning Ability section. 2 questions can be asked from Direct inequality in the BBA & IPM Entrance Exam. Through This article, we are sharing important basics of Inequality.

Dear Aspirants,

Under this topic, a few statements are provided which provide the relationship between some variables, followed by some conclusions and you need to figure out which of the conclusions provided are in accordance with the statements and answer accordingly.
Before moving on to the types of questions that you may encounter under this topic, first, let us have a quick look over the meaning of different symbols.

Now, you may come across a number of conditions under this topic such as -

1. When the signs face in the same direction for all the given variables. For instance, for 3 variables, the following cases are possible -

• A > B > C - Here, A > B, B > C and A > C hold true
• A > B ≥ C - Here, A > B, B > C, B = C and A > C hold true (A ≥ C would be wrong)
• A ≥ B > C - Here A > B, A = B, A > C and B > C hold true
• A ≥ B ≥ C - Here A > B, A > C, B > C, A = B, B = C and A = C hold true
• A > B = C - Here A > B, A > C and B = C hold true
• A ≥ B = C - Here, A > B, A > C, B = C and A = C hold true
• A = B > C - Here, A = B, A > C and B > C hold true
• A = B ≥ C - Here, A > C, A = B, A = C, B > C and B = C hold true

2. When the sign among the given variables changes. A number of cases may be formed in this case. For instance,

• A > B < C - Here, A > B and C > B hold true. No relationship can be established between A and C.
• A ≥ B < C - Here following conclusions may be drawn -
(a) A > B and C > B hold true. No relationship can be established between A and C.
(b) C > B and C > A when  A = B hold true.
• A ≥ B ≤ C - Here, following conclusions may be drawn -
(a) A > B, C > B and no relationship can be established between A and C.
(b) A = C when B = C
(c) A > B and A > C when  B = C
(d) C > B and C > A when A = B
• A > B ≤ C - Here following are possible -
(a) A > B, C > B and no relationship can be established between A and C.
(b) A > B and A > C when B = C
• A < B > C - Here B > A and B > C hold true. No relationship can be established between A and C.
• A ≤ B > C - here following are possible -
(a) B > A and B > C hold true. No relationship can be established between A and C.
(b) B > C and A > C when A = B
• A < B ≥ C - here following are possible -
(a) B > A and B > C hold true. No relationship can be established between A and C.
(b) B > A and C > A when B = C
• A ≤ B ≥ C - here following are possible -
(a) B > A and B > C hold true. No relationship can be established between A and C.
(b) B > A and C > A when B = C
(c) B > C and A > C when A = B

3. The case of either/or -

Consider the following statement - A > B < C = D ≤ E. For such case, no relationship can be established between A and E directly. However if conclusions are provided as -
Conclusion I . A > E
Conclusion II D < B
Conclusion III. A ≤ E
For this case, clearly, Conclusion II is wrong. However for I and III, either of the two will follow because for two given variables, either one of the following will be true -
(a) A > E
(b) A < E
(c) A = E
Hence either I or III will follow.

Key takeaways of the topic -

• If the similar sign is present between the variables, the relationship can be established between them. For instance, A > B > C ≥ D  ≥ E, here relationship can be determined for all the given variables.
• However, make sure that the similar sign does not break while drawing answers from the conclusions provided. Take the above example, A > B > C ≥ D  ≥ E, Here A > D or A > E would be correct but A ≥ D or A ≥ E would be wrong because the sign > breaks the continuity and is replaced by ≥ in the given statement.
• Whenever the signs between the variables change for a given statement, the relationship cannot be established unless a case of either/ or is given in the conclusion.

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