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

In inequality, we have expressions containing symbols such as >, <, =, etc. In a statement or expression, there is a combination of symbols with numbers or letters and conclusions follow this statement. An aspirant has to determine which of the following conclusion(s) follows. Inequality is one of the most important and common topics seen in many Government exams like Banking, SSC, Railway, Insurance, Defence and other competitive exams. An aspirant should know about the symbols used in mathematical inequality to understand this topic.

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This Story also Contains

1. Inequality: Symbols and their meanings
2. Approach to Solve the Questions Based on Inequality
3. Types of Inequality
4. Question Weightage of Inequality in Competitive Exams
5. Practice and Resources
6. Practice Questions for Inequality
7. Inequality Questions for BITSAT/ CUET
8. Inequality Questions for SSC CHSL/SSC CGL/ SSC CPO exams
9. Inequality Questions for Banking IBPS CWE Clerical/ IBPS RRB Assistant/ SBI Assistant/ Insurance exams

Inequality: Symbols and their meanings

Approach to Solve the Questions Based on Inequality

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

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 given two 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.

Question Weightage of Inequality in Competitive Exams

The number of questions based on inequality varies from exam to exam -

1) Inequality questions asked in Banking exams i.e. SBI, IBPS etc. - 1 to 5 questions.

2) Inequality questions asked in SSC exams i.e. SSC MTS, SSC CGL, SSC CHSL, SSC CPO, Steno - 1 to 2 questions.

2) Inequality questions asked in the Railways exam i.e. Group D, NTPC, JE, ALP etc - 1 to 2 questions.

3) Inequality questions asked in CUET, NPAT and other college entrance exams - 1 to 2 questions.

Practice and Resources

Following are the recommended sources for the practice of the questions of inequality -
a) A Modern Approach to Verbal & Non-Verbal Reasoning by R.S. Aggarwal

b) Analytical Reasoning by M.K. Pandey

c) Logical and Analytical Reasoning by A.K. Gupta

d) Test of Reasoning by Edgar Thorpe

Practice Questions for Inequality

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 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 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 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 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.

Inequality Questions for Banking 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 follows. 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.

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.