Inequality: Meaning, Reasoning Questions with Answers, Tricks, Examples

What are Inequality Reasoning Questions?

Inequality reasoning questions test your ability to compare elements based on given statements using symbols like >, <, ≥, ≤, and =. Common in inequality reasoning questions for bank exams and inequality questions for SSC CGL, they may also involve the inequality either or case, where only one of two statements can be true. Regular practice of inequalities reasoning questions with answers improves both accuracy and speed.

Importance of Inequalities in Competitive Exams

In exams like SBI PO, IBPS Clerk, SSC CGL, and RRB NTPC, inequalities reasoning questions are a scoring topic because they are quick to solve and highly reliable if approached methodically. They often appear in sets, making them valuable for maximizing marks in minimal time.

Symbols and Notations Used in Inequality Questions

Key symbols include: > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), = (equal to), and ≠ (not equal to). In some cases, especially in coded inequality questions for bank exams, these are replaced with special characters that must be decoded before solving.

Inequality Reasoning: Symbols and Their Meanings

Approach and Inequality Reasoning Tricks to Solve the Questions Based on Inequality Reasoning

To find the answers to such questions, firstly, aspirants need to know the meaning of different symbols used in inequalities and be able to determine the relation between given elements.

Types of Inequality Reasoning

There are the following types of inequality.

1. Basic Inequality

2. Either Or Case

3. Coded Inequality

4. Fillers Inequality

Let’s understand these types of inequalities in detail -

1. Basic Inequality

In this type of inequality, in question expression contains elements and different inequality symbols are given, and an aspirant has to compare these elements to determine the conclusion.

Example:

Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: A < H = F > S ≥ P < T < L

Conclusions:

I. F < L

II. H > L

1) Only conclusion I is true

2) Neither conclusion I nor II is true

3) Only conclusion II is true

4) Both conclusions I and II are true

Solution

Given:

Statement: A < H = F > S ≥ P < T < L

Conclusion (I): F < L→; F > S ≥ P < T < L; There is no definite relation between F and L. Therefore, F < L is a false conclusion.

Conclusion (II): H > L→H = F > S ≥ P < T < L; There is no definite relation between H and L. Therefore, H > L is a false conclusion.

So, neither conclusion I nor II is true. Hence, the second option is correct.

2. Either Or Case

If a definite relation between elements can not be determined and we have either case 1 or case 2 is true, then this is called either or case of inequality.

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

Example:
Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: L = K ≥ P = T > U ≤ I

Conclusion:

I. P > I

II. P ≤ I

1) Only conclusion I follow

2) Either conclusion I or II follow

3) Only conclusion II follow

4) None Follows

Solution:

Given Statement: L = K ≥ P = T > U ≤ I

I. P > I = False (as H = T > U ≤ I)

II. P ≤ I = False (as H = T > U ≤ I)

Therefore, Either conclusion I or II follows. Hence, the second option is correct.

3. Coded Inequality

In this type of inequality, codes are assigned instead of symbols and an aspirant has to decode the code according to the instructions to determine the conclusion.

Example:

Directions: In the following questions, the symbols @, *, #, &, % are used. All the symbols define the following meanings.

A @ B means that ‘A is smaller than B’

A * B means that ‘A is less than or equal to B’

A # B means that ‘A is equal to B’

A & B means that ‘A is greater than B’

A % B means that ‘A is either greater than or equal to B’

Statements: A % B, C % D, B # D.

Conclusions:

I) B @ C

II) B # C

1) If only conclusion I is true.

2) Only conclusion II is true.

3) If either I or II is true.

4) Neither I nor II is true.

Solution:

Symbols @ * # & %

Meaning < ≤ = > ≥

After decoding the statement and conclusions, we get -

A < B, C ≥ D and B = D

Conclusion I: B < C; False, because C ≥ B.

Conclusion II: B = C; False, because C ≥ B

We can conclude that it can be either C > B or C = B.

Therefore, either conclusion I or conclusion II follows. Hence, the third option is correct.

4. Fillers Inequality

In this type of inequality, some relation or all relations between given elements are not given, and in place of symbols blank spaces are given, and an aspirant has to fill in these blanks based on certain conditions.

Example:

Directions: Which of the following symbols should replace the blank spaces in the expression to make J > K true?

J __ P > L __ H __ K

1) =, >, ≥

2) =, <, >

3) >, <, >

4) <, =, <

Solution:

Let’s check each option -

First option: =, >, ≥; J = P > L > H ≥ K, makes J > K true.

Second option: =, <, >; J = P > L < H > K, False, there is no definite relation between J and K.

Third option: >, <, >; J > P > L < H > K, False, there is no definite relation between J and K.

Fourth option: <, =, <; J < P > L = H < L, False, there is no definite relation between J and K.

Tips and Tricks to Solve Inequality Questions Faster

Mastering inequality reasoning questions requires both accuracy and speed, especially in time-bound competitive exams. Below are some effective tips and tricks to help you solve these questions faster and with greater confidence.

Shortcut Methods for Direct Comparison

When solving inequality reasoning questions, scan the statements to connect the two required elements directly. If a direct link exists, compare immediately without processing unnecessary parts. For example, in inequalities reasoning questions for bank exams, skipping intermediate steps when symbols are clear can save valuable seconds.

How to Identify Either/Or Cases Quickly

The inequality either or case applies when two conclusions cannot be true together, but one of them must be correct. To spot this quickly, check if both conclusions are false individually, but one becomes true when the other is considered wrong. This method is especially useful in inequality questions with answers for SSC CGL and SBI PO.

Avoiding Common Mistakes in Inequality Reasoning

A frequent error in equality and inequality reasoning is assuming relationships without sufficient information. Always verify that the comparison path exists in the statements before concluding. Another mistake is overlooking coded symbols in coded inequality questions for bank exams, which can lead to wrong answers. Careful attention to the given symbols ensures accuracy.

Verbal Reasoning Topics

Verbal reasoning covers a wide range of topics that test logical thinking, problem-solving, and analytical skills. Below are the important verbal reasoning topics that frequently appear in competitive exams and are essential for strong exam performance. The important verbal reasoning topics below:

Question Weightage of Inequality Reasoning in Competitive Exams

The number of questions based on inequality reasoning varies depending on the exam.

1. Banking Exams (SBI PO, IBPS, etc.) – 1 to 5 questions.

2. SSC Exams (SSC MTS, SSC CGL, SSC CHSL, SSC CPO, Stenographer) – 1 to 2 questions.

3. RRB Exams (Group D, NTPC, JE, ALP, etc.) – 1 to 2 questions.

4. College Entrance Exams (CUET, NPAT, and others) – 1 to 2 questions.

Practice and Resources

The following are the recommended sources for the practice of the questions of inequality -

• A Modern Approach to Verbal & Non-Verbal Reasoning – R.S. Aggarwal

• Analytical Reasoning – M.K. Pandey

• Logical and Analytical Reasoning – A.K. Gupta

• Test of Reasoning – Edgar Thorpe

• Reasoning Ability for Competitive Examinations – Nishit K. Sinha

• Reasoning for SSC & Banking Exams – Kiran Prakashan

The candidates must practice banking inequality reasoning questions PDF, mathematical inequality reasoning questions PDF as there are many PDFs available online. The candidates must solve the e-book of inequality reasoning questions with the answers PDF given below:
Inequality Questions with Solutions PDF

Inequality Reasoning Questions for Practice

The candidates must practice several questions on inequality reasoning to excel in the topic as it is an important topic from an examination point of view.

1. Directions: If G = E < D < R and E = Y > K > Q, then which of the following options is NOT correct?

1) G < Q

2) R > Q

3) G < R

4) Y < R

Solution

Given:

(I) G = E < D < R

(II) E = Y > K > Q

By comparing the equations (I) and (II), we get→R > D > G = E = Y > K > Q

Let's check each option –

First option: G < Q

From the equation, it is evident that G = E and E is greater than Q which means G is greater than Q. So, this is incorrect.

Second option: R > Q

From the equation, it is evident that G = E, R is greater than G and E is greater than Q. So, R is greater than Q is correct.

Third option: G < R

From the equation, it is evident that G = E and R is greater than G. So, this is correct.

Fourth option: Y < R

From the equation, it is evident that G = E and Y and R is greater than G. So, R is greater than Y is correct.

So, only the first option doesn't satisfy the equation. Hence, the first option is correct.

2. Direction: If Z = Y > R = M and G > H = Z = Q, then which of the following options is NOT correct?

1) H = Y

2) G > Q

3) R > Z

4) Q > R

Solution

Given:

Z = Y > R = M and G > H = Z = Q,

After combining the statements: G > H = Z = Q = Z = Y > R = M

Let's check each option –

First option: H = Y; True, as H = Z = Q = Z = Y makes H = Z.

Second option: G > Q; True, as G > H = Z = Q makes G > Q.

Third option: R > Z; False, as Z = Y > R makes Z > R.

Fourth option: Q > R; True, as Q = Z = Y > R makes Q > R.

Therefore, the conclusion given in the third option is NOT correct. Hence, the third option is correct.

3. Directions: If Z = U = R < Q < G = D > H > A, then which of the following options is NOT correct?

1) A < G

2) G > H

3) Z = Q

4) Q > U

Solution

Given:

Z = U = R < Q < G = D > H > A

Let's check each option –

First option: A < G; True, G = D > H > A makes G > A.

Second option: G > H; True, G = D > H > A makes G > H.

Third option: Z = Q; False; Z = U = R < Q makes Z < Q.

Fourth option: Q > U; True, U = R < Q, make Q > U.

Therefore, the conclusion given in the third option is not correct. Hence, the third option is correct.

4. Directions: If H < E = D < P and C = E > Z = Q, then which of the following options is NOT correct?

1) D > H

2) P > Z

3) P = Q

4) D = C

Solution

Given:

H < E = D < P and C = E > Z = Q

After combining the above-given equation, we get – H < E = D = C > Z = Q, D < P

Let's check each option –

First option: D > H; True, as H < E = D makes D > H.

Second option: P > Z; True, as Z < D < P makes P > Z.

Third option: P = Q; False, as there is no direct relation between P and Q.

Fourth option: D = C, True, as D = C is given.

So, only the equation in the third option is incorrect. Hence, the third option is correct.

5. Directions: If U = M > J = R and J = S < T, then which of the following options is NOT correct?

1) M > T

2) J < U

3) J < T

4) R = S

Solution

Given:

U = M > J = R and J = S < T

After combining the statements – U = M > J = R = S < T

Let's check each option –

First option: M > T; False, M > J = R = S < T, as there is no definite relation between M and T.

Second option: J < U; True, U = M > J, make U > J

Third option: J < T; True, J = R = S < T, make J < T

Fourth option: R = S; True, as given in the statement.

Therefore, the conclusion given in the first option is not correct. Hence, the first option is correct.

6. Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: A ≤ D < C = B > E ≥ F < G

Conclusions:

I. B > A

II. C < F

1) Neither conclusion I nor II is true

2) Both conclusions I and II are true

3) Only conclusion II is true

4) Only conclusion I is true

Solution:

Given:

Statement: A ≤ D < C = B > E ≥ F < G

Conclusion (I): B > A→A ≤ D < C = B makes A < B. Therefore, B > A is true.

Conclusion (II): C < F→C = B > E ≥ F makes C > F. Therefore C < F is false.

So, the only conclusion I follows. Hence, the fourth option is correct.

7. Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: P > D < R > A = X ≤ P = T

Conclusions:

I. A = T

II. R > X

1) Neither conclusion I nor II is true

2) Only conclusion II is true

3) Only conclusion I is true

4) Both conclusions I and II are true

Solution:

Given:

Statement: P > D < R > A = X ≤ P = T

Conclusion (I): A = T→A = X ≤ P = T, makes A ≤ T. Therefore, A = T is a false conclusion.

Conclusion (II): R > X→R > A = X, which makes R > X. Therefore, this conclusion is true.

So, only conclusion II follows. Hence, the second option is correct.

8. Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: X < U = F > R ≥ P < T < W

Conclusions:

I. X < T

II. R > W

1) Only conclusion I is true

2) Neither conclusion I nor II is true

3) Only conclusion II is true

4) Both conclusions I and II are true

Solution

Given:

Statement: X < U = F > R ≥ P < T < W

Conclusion (I): X < T→X < U = F > R ≥ P < T; There is no definite relation between X and T. Therefore, X < T is a false conclusion.

Conclusion (II): R > W→R ≥ P < T < W; There is no definite relation between R and W. Therefore, R > W is a false conclusion.

So, neither conclusion I nor II is true. Hence, the second option is correct.

9. Directions: In the following coded inequality reasoning questions, the symbols %, *, #, &, @ are used. All the symbols define the following meanings.

A % B means that ‘A is smaller than B’

A * B means that ‘A is less than or equal to B’

A # B means that ‘A is equal to B’

A & B means that ‘A is greater than B’

A @ B means that ‘A is either greater than or equal to B’

Statements: K % B, C & D, B * D

Conclusions:

I) B @ C

II) B # C

1) If only conclusion I is true.

2) Only conclusion II is true.

3) If either I or II is true.

4) Neither I nor II is true.

Solution:

Symbols % * # & @

Meaning < ≤ = > ≥

After decoding the statement and conclusions, we get -

K < C, C > D, B ≤ D

Conclusion I: B < C; True, because C > D ≥ B makes C > D.

Conclusion II: B = C; False, because C > D ≥ B makes C > D.

Therefore, the only conclusion I follows. Hence, the first option is correct.

10. Directions: Select the symbol from the given alternatives that will replace the question mark in the expression and make R > S true.

S < O ? L < J = R
1) >

2) <

3) ≥

4) Either ≥ or >

Solution:
Let’s check each option -

First option: >; S < O > L < J = R→False
Second option: <; S < O < L < J = R→True
Third option: ≥; S < O ≥ L < J = R→False
Fourth option: ≥ or > ; S < O ≥ / > L < J = R→False

Hence, the second option is correct.

11. Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: K > F ≤ C = D < E

Conclusion I: K > E

Conclusion II: F < E

1) Only conclusion I is true

2) Only conclusion II is true

3) Both conclusion I and II are true

4) Neither conclusion I nor II is true

Either conclusion I or II is true

Solution:
Statement: K > F ≤ C = D < E

Conclusion I: K > E; False, as there is no definite relation between them.

Conclusion II: F < E; True, as F ≤ C = D < E, makes E > F.

Therefore, only conclusion II follows. Hence, the second option is correct.

12. Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: W > Q, X ≤ R < T, T > W

Conclusion I: W ≤ R

Conclusion II: X > T

1) Only conclusion I is true

2) Only conclusion II is true

3) Both conclusion I and II are true

4) Neither conclusion I nor II is true

Solution:

Statement: W > Q, X ≤ R < T, T > W

Conclusion I: W ≤ R; False, as there is no definite relation between them.

Conclusion II: X > T; False, as X ≤ R < T makes T > X.

Therefore, neither conclusion I nor II follow. Hence, the third option is correct.

13. Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: P ≤ H > K ≤ U = F > O

Conclusion I: K < F

Conclusion II: K = F

1) Only conclusion I is true

2) Only conclusion II is true

3) Both conclusions I and II are true

4) Either conclusion I or II is true

Solution:

Statement: P ≤ H > K ≤ U = F > O

Conclusion I: K < F; False, as K ≤ F.

Conclusion II: K = F; False, as K ≤ F.

Therefore, either conclusion I or conclusion II follows Hence, the fourth option is correct.

14. Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: E = B ≥ A ≤ D = F

Conclusion I: E = D

Conclusion II: E < D

1) Only conclusion I is true

2) Only conclusion II is true

3) Either conclusion I or II is true

4) Neither conclusion I nor II is true

Solution:

Statement: E = B ≥ A ≤ D = F

Conclusion I: E = D; False, as there is no definite relation between them.

Conclusion II: E < D; False, as there is no definite relation between them.

Therefore, either conclusion I or II follows. Hence, the third option is correct.

15. Directions: In the following questions, the symbols %, ^, !, &, @ are used. All the symbols define the following meanings.

A % B means that ‘A is smaller than B’

A ^ B means that ‘A is less than or equal to B’

A ! B means that ‘A is equal to B’

A & B means that ‘A is greater than B’

A @ B means that ‘A is either greater than or equal to B’

Statements: X ! Y, Y & K, X @ P

Conclusions:

I) X % P

II) K & P

1) If only conclusion I is true.

2) Only conclusion II is true.

3) If either I or II is true.

4) Neither I nor II is true.

Solution

Symbols % ^ ! & @

Meaning < ≤ = > ≥

After decoding the statement and conclusions, we get -

X = Y, Y > K, X ≥ P

Conclusion I: X < P; False, because X ≥ P.

Conclusion II: K > P; False, P ≤ X = Y > K, there is no definite relation between K and P.

Therefore, neither conclusion I nor II follow. Hence, the fourth option is correct.

Inequality Reasoning Practice Questions for BITSAT/ CUET

1) Directions: If U = M > J = R and J = S < T, then which of the following options is NOT correct?

1) M > T

2) J < U

3) J < T

4) R = S

Hint: Combine the statements and compare them with the given conclusions.

Solution

Given:

U = M > J = R and J = S < T

After combining the statements – U = M > J = R = S < T

Let's check each option –

First option: M > T; False, M > J = R = S < T, as there is no definite relation between M and T.

Second option: J < U; True, U = M > J, make U > J

Third option: J < T; True, J = R = S < T, make J < T

Fourth option: R = S; True, as given in the statement.

Therefore, the conclusion given in the first option is not correct. Hence, the first option is correct.

2) Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: S ≤ P = U < T > V ≥ X > W

Conclusions:

I. T > S

II. W < V

1) Only conclusion I is true

2) Both conclusions I and II are true

3) Neither conclusion I nor II is true

4) Only conclusion II is true

Hint: Examine the statement and determine the conclusion that follows.

Solution

Given:

Statement: S ≤ P = U < T > V ≥ X > W

Let's check the conclusions –

Conclusion (I): T > S→True; S ≤ P = U < T ⇒ S < T

Conclusion (II): W < V→True; V ≥ X > W ⇒ V > W

So, both conclusions I and II are true. Hence, the second option is correct.

Inequality Reasoning Practice Questions for SSC CHSL/SSC CGL/ SSC CPO exams

3) Directions: If G = E < D < R and E = Y > K > Q, then which of the following options is NOT correct?

1) G < Q

2) R > Q

3) G < R

4) Y < R

Hint: Identify the options that do not satisfy the given equations.

Solution

Given:

(I) G = E < D < R

(II) E = Y > K > Q

By comparing the equations (I) and (II), we get→R > D > G = E = Y > K > Q

Let's check each option –

First option: G < Q

From the equation, it is evident that G = E and E is greater than Q, which means G is greater than Q. So, this is incorrect.

Second option: R > Q

From the equation, it is evident that G = E, R is greater than G, and E is greater than Q. So, R is greater than Q is correct.

Third option: G < R

From the equation, it is evident that G = E and R is greater than G. So, this is correct.

Fourth option: Y < R

From the equation, it is evident that G = E and Y and R are greater than G. So, R is greater than Y is correct.

So, only the first option doesn't satisfy the equation. Hence, the first option is correct.

Inequality Reasoning Questions for Bank exams such as IBPS CWE Clerical/ IBPS RRB Assistant/ SBI Assistant/ Insurance exams

4) Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: A ≤ D < C = B > E ≥ F < G

Conclusions:

I. B > A

II. C < F

1) Neither conclusion I nor II is true

2) Both conclusions I and II are true

3) Only conclusion II is true

4) Only conclusion I is true

Hint: Examine the statement and determine the conclusion that follows.

Solution

Given:

Statement: A ≤ D < C = B > E ≥ F < G

Conclusion (I): B > A→A ≤ D < C = B makes A < B. Therefore, B > A is true.

Conclusion (II): C < F→C = B > E ≥ F makes C > F. Therefore, C < F is false.

So, the only conclusion I follow. Hence, the fourth option is correct.

5) Directions: In this question, the statement is followed by two conclusions. Which of the two conclusions is/are true?

Statement: P > D < R > A = X ≤ P = T

Conclusions:

I. A = T

II. R > X

1) Neither conclusion I nor II is true

2) Only conclusion II is true

3) Only conclusion I is true

4) Both conclusions I and II are true

Hint: Examine the statement and determine the conclusion that follows.

Solution

Given:

Statement: P > D < R > A = X ≤ P = T

Conclusion (I): A = T→A = X ≤ P = T, makes A ≤ T. Therefore, A = T is a false conclusion.

Conclusion (II): R > X→R > A = X, makes R > X. Therefore, this conclusion is true.

So, only conclusion II follows. Hence, the second option is correct.

Non-Verbal Topics

Non-verbal reasoning evaluates the ability to analyze and interpret visual information without using words or numbers. For effective preparation, read through the important non-verbal reasoning topics listed below. For Non-Verbal reasoning, read the topics below:

About the Faculty
Tanu Gupta, with over a decade of experience as a reasoning faculty, specializes in preparing students for various entrance examinations and career development. Her extensive work with multiple educational platforms and institutions has honed her expertise in logical and analytical thinking. Her dedication to innovative teaching methods ensures these articles provide practical insights and expert guidance.