Inequality Reasoning refer to expressions that contain inequality signs such as <, >, =, etc. To understand the questions based on mathematical inequalities, candidates must know about various signs, which are used in such types of questions. There are also various types of inequalities, which are discussed in this article.

Questions of Inequality Reasoning are usually easy in nature. In this article, we are going to cover the key Inequality Logical Reasoning concepts with the solved examples, practice questions,  tips and inequality reasoning tricks, and other important details. Read the article to clear all your doubts regarding the same. 

What is Inequality?

As mentioned above, Inequality refers to expressions that contain inequality signs such as <, >, =, etc. To understand the questions based on mathematical inequalities, candidates must know about various signs, which are used in such types of questions. The same is given below:

Symbol	Meaning
A > B	A is greater than B
A < B	A is less than B
A = B	A is equal to B
A ≥ B	A is either greater than or equal to B
A ≤ B	A is either less than or equal to B
A ≠ B	A is either greater than or less than B

Types of Inequality

As now we know what consists of the questions related to the Inequality reasoning section. Let us see the various types of questions that may come one by one from below: 

1. Basic Inequality

In these type of Inequality reasoning questions, expressions consisting of comparison between different elements will be given and a defined relation between any 2 elements will be asked. 

2. Either  – or Case 

In these type of Inequality reasoning questions, a definite relation between two elements cannot be determined. In this type of question there will be given 2 relations only from which either relation 1 or 2 can be true. 

3. Coded Inequality

In these type of Inequality reasoning questions, codes will be assigned to inequality symbols and the expression will be given using those codes. Candidates need to decode the symbols and find the relation between the elements.

How to Solve Inequality Reasoning Questions – Tips and Tricks 

Candidates can find various tips and inequality reasoning tricks from below for solving the questions related to the Inequality reasoning section.

Tip # 1: Candidates can consider the symbols by trick to find the answers quickly such as > as Father,  ≥ as Mother, = as Servant, the priority for solving any questions will be given on the basis of seniority such as Father is senior than Mother and Mother is senior than Servant, and so on. 

Tip # 2: Some of the rules for Basic Inequalities are as follows. 

Statement	Conclusion
P > Q >R	P > R
P > Q ≥ R
P ≥ Q > R
P = Q > R
P > Q = R
P < Q < R	P < R
P < Q ≤ R
P ≤ Q < R
P = Q < R
P < Q = R
P ≥ Q ≥ R	P > R or P = R
P = Q ≥ R
P ≥ Q = R
P ≤ Q ≤ R	P < R or P = R
P = Q ≤ R
P ≤ Q = R
P < Q > R	No conclusion can be inferred
P ≤ Q > R
P < Q ≥ R
P > Q < R
P > Q ≤ R
P ≥ Q < R

Tip # 3: Candidates need to follow the below mentioned rules for solving the either or case inequalities reasoning section:

Complementary Pair	Conditions
> + =	Elements in both conclusions should be the same. Both are individually false.  Combination of the relation should be true.
< + =
> + < + =
≤ + >	Elements in all conclusions should be the same.  The relation between the elements in all the cases should be “can’t say”
> +  ≤

Check more details on Order and Ranking Reasoning

Inequality Sample Questions 

Question 1: In the question, assuming the given statements to be true, find which of the conclusions among given two conclusions is/are definitely true, and then give your answer according to it. 

Statement: 

H < A < T = G > U ≥ V ≥ B 

Conclusion:

I. T > B

II. G > H

(1) Only conclusion I follow 

(2) Either conclusion I or II follow 

(3) Only conclusion II follow

(4) None Follows 

(5) Both conclusion I and II follow

Solution: 

Given Statement: H < A < T = G > U ≥ V ≥ B

I. T > B = True (as T = G > U ≥ V ≥ B)

II. G > H = True (as H < A < T = G)

If we analyse the given statements, then we get the answer both conclusion I and II follows. 

Question 2 : In the question, assuming the given statements to be true, find which of the conclusions among given two conclusions is/are definitely true, and then give your answer according to it. 

Statement: 

F > Y  ≥ X < Z, C ≤ X < W 

Conclusion:

I. Z > C

II. F > W

(1) Only conclusion I follow 

(2) Either conclusion I or II follow 

(3) Only conclusion II follow

(4) None Follows 

(5) Both conclusion I and II follow

Solution: 

Given Statement: F > Y ≥ X < Z, C ≤ X < W

On combining we will get F > Y ≥ X ≥ C and F > Y ≥ X < W

Conclusions:

I. Z > C = True (F > Y ≥ X ≥ C)

II. F > W = False (F > Y ≥ X < W, relationship between F and W cannot be determined.)

Hence, the only conclusion I follow. 

Get more details on Input-Output Reasoning

Question 3 : In the question, assuming the given statements to be true, find which of the conclusions among given two conclusions is/are definitely true, and then give your answer according to it. 

Statement: 

B = K  ≥ H = T > U ≤ I

Conclusion:

I. H > I

II. H ≤ I

(1) Only conclusion I follow 

(2) Either conclusion I or II follow 

(3) Only conclusion II follow

(4) None Follows 

(5) Both conclusion I and II follow

Solution: 

Given Statement: B = K  ≥ H = T > U ≤ I

I. H > I = False (as H = T > U ≤ I)

II. H ≤ I = False (as H = T > U ≤ I)

Hence, Either conclusion I or II follows. 

Check out Statement & Conclusion Reasoning

Question 4 : In the question, assuming the given statements to be true, find which of the conclusions among given two conclusions is/are definitely true, and then give your answer according to it. 

Statement:

1. O < L > P > M ≤ N ≤ B

2. L = K, M ≥ R

Conclusion:

I. K > M

II. O = M

III. R < B

IV. R = B

(1) Only conclusion II follow 

 

(2) Either conclusion I or III follow 

(3) Only conclusion I and IV follow

(4) Either conclusion III or IV follow

(5) Only conclusion I and Either conclusion III or IV follow

Solution: 

Given Statement:

1. O < L > P > M ≤ N ≤ B

2. L = K, M ≥ R

I. K > M = True (as L = K, so L replaced by K then K > P > M)

II. O = M = False (as O < L > P > M)

III. R < B = False (as M ≥ R then R ≤ M ≤ N ≤ B gives either R < B or R = B)

IV. R = B = False (as M ≥ R then R ≤ M ≤ N ≤ B gives either R < B or R = B)

Hence, Only conclusion I and Either Conclusion III or IV follow. 

Question 5 : In the question, assuming the given statements to be true, find which of the conclusions among given two conclusions is/are definitely true, and then give your answer according to it. 

Statement: 

C = T ≥ V ≥ U

Conclusion:

I. C > U

II. T = U

(1) Only conclusion I follow 

(2) Either conclusion I or II follow 

(3) Only conclusion II follow

(4) None Follows 

(5) Both conclusion I and II follow

Solution:

Given Statement: C = T ≥ V ≥ U

I. C > U  = False (as C = T ≥ V ≥ U)

II. T = U = False (as T ≥ V ≥ U)

As we can see either I or II is true as we can see C = T, Hence it is the correct answer. 

Also check out Missing Number Reasoning

Sample Inequality Reasoning Questions

Given below are sample inequality reasoning questions that will help improve your understanding:

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.

Statement: 

L > M > C ≥ Q < P = E < F

Conclusion:

1. L > Q
2. F > C

(1). Only I follow

(2). Only II follow

(3). Both I and II follow

(4). Either I or II follow

(5). Neither I nor II follows

Solution:

 

Given statement:

1. L > M > C ≥ Q < P = E < F
2. L > Q ⇾ True (As L > M > C ≥ Q)
3. F > C ⇾ False (As C ≥ Q < P = E < F)

Conclusion II is false as there is an inequality symbol change between Q and C.

Hence, Only I follow.

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.

Statement: 

9 > 7 < 6 = 5 ≥ 4

Conclusion:

1. 9 > 5
2. 6 > 4

(1). Only I follow

(2). Only II follow

(3). Both I and II follow

(4). Either I or II follow

(5). Neither I nor II follows

Solution: 

Given Statement:

1. 9 > 7 < 6 = 5 ≥ 4
2. 9 > 5 ⇾ False (As 9 > 7 < 6 = 5)
3. 6 > 4 ⇾ True (As 6 = 5 ≥ 4)

Hence, Only II follow.

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.

Statement:

H > I < J = K

Conclusion:

1. H > J
2. J < H
3. I > K

(1). Either I or II follow

(2). Only II follow

(3). Both I, II, and III follow

(4). Only I follow

(5). Neither I, II, nor III follow

Solution:

Statement:

1. H > I < J = K
2. H > J ⇾ False (as H > I < J)
3. J < H ⇾ False (as H > I < J)

III. I > K ⇾ False (as I < J = K)

Here, J and H elements are the same but the meaning is different so they will not form a complementary pair.

Hence, Neither I, II, nor III follow.

Exams where Inequality Reasoning is Part of Syllabus

Questions based on the Inequality reasoning section come up often in various prestigious government exams, some of them are as follows: 

• Bank (PO & Clerk) Exams 
• SSC (CGL, 10+2, Steno, FCI, CPO, Multitasking)
• LIC (AAO & ADO)
• RRB
• UPSC 
• State PSC Exams 

Get to know more details on other Reasoning Topics:

Syllogisms	Venn Diagrams
Analogy	Classification
Puzzles	Alphabet Test

We hope you found this article regarding the Inequality reasoning section was informative and helpful, and please do not hesitate to contact us for any doubts or queries regarding the same. You can also download the Testbook App, which is absolutely free and start preparing for any government competitive examination by taking the mock tests before the examination to boost your preparation.