# Inequality Questions for Bank and SSC Exams

*The questions of Inequality chapters are considered as important questions in the Logical Reasoning section of various Bank PO, Clerk, SSC, and Railways exams. In this article, we will discuss and solve the basic Inequality questions (Level 1 and Level 2); and for Advanced-level Inequality Questions and Answer visit our Advanced Level Inequality Chapter.*

**Level 1:**

**Directions (1-2): In these questions, the relationship between different elements is shown in the statements. These statements are followed by two conclusions. **

**Mark the answer as:**

a) If only conclusion I follows.

b) If only conclusion II follows.

c) If either conclusion I or II follows.

d) If neither conclusion I nor II follows.

e) If both conclusions I and II follow.

**Q1. Statements:**

Q≤B<M, Z>Q, S>B≤T,

Conclusions:

I. Q ≤ T

II. M > S

**Ans: a**

**Solution:**

Only conclusion I follows.

Conclusions:

I. Q ≤ T (True) (Q≤B≤T)

II. M > S (False) (M>B<S)

**Q2. Statements: **

T>Z≥W, B>Q>W>O < M

Conclusions:

I. T > O

II. B > O

**Ans: e**

**Solution:**

Both conclusions I and II follow.

Conclusions:

I. T > O (True) (T>Z≥W>O)

II. B > O (True) (B>Q>W>O)

**Directions (3-4): In these questions, relationship between different elements is shown in the statements. The statements are followed by conclusions. Give answer.**

a) If only conclusion I is true

b) If only conclusion II is true

c) If either conclusion I or II is true

d) If neither conclusion I nor II is true

e) If both conclusions I and II are true

**Q3. Statements:**

Q > A ≥ K ≤ J; N ≥ R ≥ B = Q < P

Conclusion:

I. B > K

II. A > R

**Ans: a**

**Solution:**

Only conclusion I is true.

After arranging, we get;

N ≥ R ≥ B = Q > A ≥ K ≤ J

Conclusion:

I. B > K (True)

II. A > R (False)

**Q4. Statements:**

M > K ≥ O = E; A = B ≤ F ≥ K

Conclusion:

I. F > E

II. F ≥ E

**Ans: b**

**Solution:**

Only conclusion II is true.

After arranging the series, we get;

A = B ≤ F ≥ K ≥ O = E

Conclusion:

I. F > E (False)

II. F ≥ E (True)

**Directions (5-6): In each of the following questions assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true. Give answer **

1) If only conclusions I is true.

2) If only conclusions II is true.

3) If either conclusions I or conclusion II is true.

4) If neither conclusions I nor conclusions II is true.

5) If both conclusions I and II are true.

**Q5. Statement: **

M < P < Q < R < S; M < B < N < D < E = F < G

Conclusion:

I. F > Q

II. S < G

**Ans: 4**

**Solution:**

Neither conclusions I nor conclusions II is true.

Conclusion:

I. F > Q (False) (F = E > D > N > B > M < P < Q)

II. S < G (False) (S ≥ R > Q > P > M < B < N < D < E = F < G)

**Q6. Statement: **

Y > W ≤ M < N < O < E < F ≤ G, P ≤ Q < R < S ≤ T < W

Conclusion:

I. F < T

II. R < E

**Ans: 2**

**Solution: **

Conclusions II is true.

Conclusion:

I. F < T (False) (F > E > O > N > M ≥ W > T)

II. R < E (True) (R < S ≤ T < W ≤ M < N < O < E)

**Q7. Directions: In these questions relationship between different elements is shown in the statements. These statements are followed by conclusions. You have to find out which of the following conclusion follow or not from the given statements. **

**Statements:**

R > H = I > J ≥ K, X > Z < J ≥ C > E < D

Conclusions:

I. H > E

II. Z > I

1) Only I is true

2) Only II is true

3) Either I or II is true

4) Both I and II are true

5) Neither I nor II is true

**Ans: 1**

**Solution:**

Only I is true.

Conclusion:

I. H > E (True) (H = I > J ≥ C > E)

II. Z > I (False) (Z < J < I)

**Directions (8-10): In each of the following questions assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true. Give answer.**

1) If only conclusions I is true.

2) If only conclusions II is true.

3) If either conclusions I or conclusion II is true.

4) If neither conclusions I nor conclusions II is true.

5) If both conclusions I and II are true.

**Q8. Statements:**

8 > 1; 5 < 6 < 9 < 7, 1 = 2 < 6,

Conclusion:

I. 9 > 1

II. 8 > 5

**Ans: 1**

**Solution:**

Conclusions I is true.

Conclusion:

I. 9 > 1 (True) (1 = 2 < 6 < 9)

II. 8 > 5 (False) (8 > 1 = 2 < 6 > 5)

**Q9. Statements:**

M < Q = U < B < P, T = B, M > O > S;

Conclusion:

I. B > O

II. M < T

**Ans: 5**

**Solution:**

Both conclusions I and II are true.

I. B > O (True) (B > U = Q > M > O)

II. M < T (True) (M < Q = U < B = T)

**Q10. Statements:**

M > P > F; E > D > B = A; R > Y = E > F ;

Conclusion:

I. M > D

II. R > B

**Ans: 2**

**Solution:**

Conclusions II is true.

Conclusion:

I. M > D (False) (M > P > F < E > D)

II. R > B (True) (R > Y = E > D > B)

**Q11. Directions: In these questions relationship between different elements is shown in the statements. These statements are followed by conclusions. You have to find out which of the conclusions follow or not from the given statements.**

**Statements:**

N = L ≤ M, P > Q = O, Q > S ≤ Y = L.

Conclusions:

I. O < M

II. N > O

1) If only conclusion I is true

2) If only conclusion II is true

3) If either conclusion I or II is true

4) If neither conclusion I nor II is true

5) If both conclusions I and II are true

**Ans: 4**

**Solution:**

Neither conclusion I nor II is true.

Conclusions:

I. O < M (False) (O = Q > S ≤ Y = L ≤ M)

II. N > O (False) (N = L = Y ≥ S < Q = O)

**Q12. Directions: In these questions relationship between different elements is shown in the statements. These statements are followed by conclusions. You have to find out which of the conclusions follow or not from the given statements. **

**Statement: **

M < R < T < Q = K; T < E = A; M > B = O > G

Conclusion:

I. O < A

II. G < K

1) If only conclusion I is true

2) If only conclusion II is true

3) If either conclusion I or II is true

4) If neither conclusion I nor II is true

5) If both conclusions I and II are true

**Ans: 5**

**Solution:**

Both conclusions I and II are true.

Conclusion:

I. O < A (True) (O = B < M < R < T < E = A)

II. G < K (True) (G < O = B < M < R < T < Q = K)

**Q13. Directions: In these questions relationship between different elements is shown in the statements. These statements are followed by conclusions. You have to find out which of the conclusions follow or not from the given statements. **

**Statement: **

A < B ≤ Q = K; T > O = W; A < O = F

Conclusion:

I. Q ≤ F

II. O < K

1) If only conclusion I is true

2) If only conclusion II is true

3) If either conclusion I or II is true

4) If neither conclusion I nor II is true

5) If both conclusions I and II are true

**Ans: 3**

**Solution:**

Either conclusion I or II is true.

Conclusion:

I. Q ≤ F (False) (K = Q ≥ B > A < O = F)

II. O < K (False) ((K = Q ≥ B > A < O = F)

**Q14. Directions: In these questions relationship between different elements is shown in the statements. These statements are followed by conclusions. You have to find out which of the conclusions follow or not from the given statements. **

**Statements:**

M < O > F > T, J < K = L < Z < N, P > Z = M

Conclusion :

I. O > K

II. J < P

1) If only conclusion I is true

2) If only conclusion II is true

3) If either conclusion I or II is true

4) If neither conclusion I nor II is true

5) If both conclusions I and II are true

**Ans: 5**

**Solution:**

Both conclusions I and II are true.

Conclusion :

I. O > K (True) (O > M = Z ≥ L = K)

II. J < P (True) (J < K = L < Z ≤ P)

**Q15. Directions: In these questions relationship between different elements is shown in the statements. These statements are followed by conclusions. You have to find out which of the conclusions follow or not from the given statements. **

**Statements:**

A > B > C = D; T < X = Y < Z; D = T > H = O

Conclusion:

I. Z > C

II. A > Y

1) If only conclusion I is true

2) If only conclusion II is true

3) If either conclusion I or II is true

4) If neither conclusion I nor II is true

5) If both conclusions I and II are true

**Ans: 1**

**Solution:**

Only conclusion I is true.

Conclusion:

I. Z > C (True) (Z > Y = X ≥ T = D = C)

II. A > Y (False) (A > B > C = D = T < X = Y)

**Q16. Directions: In these questions relationship between different elements is shown in the statements. These statements are followed by conclusions. You have to find out which of the conclusions follow or not from the given statements. **

**Statement: M ≠ N = O**

Conclusion:

I. M > O

II. M < O

1) Only I

2) Only II

3) Both I and II

4) None follows

5) None of the above

**Ans: 5**

Either conclusion I or conclusion II follows

**Q17. Directions: In these questions relationship between different elements is shown in the statements. These statements are followed by conclusions. You have to find out which of the conclusions follow or not from the given statements. **

**Statement: **

P < F = B > E = N, O < S < D = F,

Conclusion:

I. N < D

II. B < O

1) If either conclusion I or II is true.

2) If only conclusion I is true.

3) If neither conclusion I nor II is true.

4) If only conclusion II is true.

5) If both conclusions are true.

**Ans: 2**

**Solution:**

Conclusion:

I. N < D (True) (N = E < B = F = D)

II. B < O (False) (B = F = D > S > O)

Only conclusion I is true.

**Q18. Directions: In these questions relationship between different elements is shown in the statements. These statements are followed by conclusions. You have to find out which of the conclusions follow or not from the given statements. **

**Statement: **

M < S ≤ Q = K; T > E = W; M < E = P

Conclusion:

I. S < T

II. E < K

1) If either conclusion I or II is true.

2) If only conclusion I is true.

3) If neither conclusion I nor II is true.

4) If only conclusion II is true.

5) If both conclusions are true.

**Ans: 3**

**Neither conclusion I nor II is true.**

Conclusion:

I. S < T (False) (S > M < E < T)

II. E < K (False) (E > M < S ≤ Q = K)

**Q19. Which of the following expressions will be true if the given expression ‘R < H ≥ S = T ≤ P’ is definitely true? **

1) R < S

2) H ≥ P

3) T < H

4) H = T

5) None of these

**Ans: 5**

None of the above conclusions is true.

**Q20. In which of the following expressions will the expression ‘R < Y’ be definitely true?**

1) R ≥ P > Q < Y

2) R > P ≥ Q = Y

3) P < R ≥ Q = Y

4) Y = Q ≥ P > R

5) None of these

**Ans: 4**

**Solution:**

Only 4 is true.

## Level 2:

**Directions (1-5): In these question, relationship between different elements is shown in the statements. These statements are followed by two conclusions.**

**Given answer**

1. If only conclusion I follows

2. If only conclusion II follows

3. If either conclusion I or II follows

4. If neither conclusion I nor II follows

5. If both conclusion I and II follow

**Q1. Statement:**

D < N < E, Z > B = D, M > J > Z

Conclusion:

I. N > Z II. E > J

**Ans: 4**

**Solution:**

Conclusions:

I. N > Z → False (Z > B = D < N)

II. E > J → False (J > Z > B = D < N < E)

Hence, neither Conclusion I nor II follows.

**Q2. Statement:**

M ≠ I = L, M > H > K, T < H < R,

Conclusion:

I. M > T II. K < R

**Ans: 5**

**Solution:**

Conclusions:

I. M > T → True (M > H > T)

II. K < R → True (K < H < R)

Hence, both conclusions I and II follow.

**Q3. Statement:**

M≠J≠S; H < L = P > S > I,

Conclusion:

I. L > J II. H < S

**Ans: 4**

**Solution:**

Conclusions:

I. L > J → False (L = P > S ≠ J ) (≠ means either > or <)

II. H < S → False (H < L = P > S)

Hence, neither conclusion I nor II follows.

**Q4. Statement:**

G > K > H = O, H > S, A < K< X

Conclusion:

I. S < O II. G ≤ K

**Ans: 1**

**Solution:**

Conclusions:

I. S < O → True (S< H = O)

II. G ≤ S → False (G > K > H > S)

Hence, only conclusion I follows

**Q5. Statement:**

H < M < A; R = M < E, U ≠ A = I

Conclusion:

I. H < E II. R < I

**Ans: 5**

**Solution:**

Conclusions:

I. H < E → True (H < M < E)

II. R < I → True (R = M < A = I)

Hence, both conclusions I and II follow.

**Directions (6-10): In the given questions, assuming the given statements to be true. Find which of the given four conclusions numbered I, II, III and IV is/are definitely true and give your answer accordingly.**

**6. Statement:**

A > B ≥ C > D ≤ E ≤ F < G

Conclusion:

I. A > D

II. G > D

III. E < G

IV. B > F

- Only I, II and III are true
- Only II is true
- Only I and II are true
- Only I and either II or IV are true
- All I, II, III and IV are true

**Ans: 1**

**Solution:**

I. A > D (true)

II. G > D (true)

III. E < G (true)

IV. B > F (false)

**Q7. Statement: R > S > T ≤ V; T ≥ Z > Y**

Conclusion:

I. Z < V

II. R > V

III. V = Z

IV. R > Y

- Only either II or III is true.
- Only IV and either I or III are true.
- Only IV is true.
- Only II is true.
- Only III is true.

**Ans: 2**

**Solution:**

I. Z < V (false)

II. R > V (false)

III. V = Z (false)

IV. R > Y (true)

**Q8. Statement: I ≥ R > K = U; V < R < X**

Conclusion:

I. X < I

II. I > V

III. K > V

IV. U < X

- Only II is true.
- Only I and III are true.
- None is true.
- Only II and IV are true.
- Only I and II are true.

**Ans: 4**

**Solution:**

Conclusion:

I. X < I (false)

II. I > V (true)

III. K > V (false)

IV. U < X (true)

**Q9. Statement: A > C ≤ B ≤ E; C ≥ D < F**

Conclusion:

I. A > E

II. F < C

III. B > F

IV. E < D

- Only I is true.
- Only II is true.
- Only III is true.
- None is true.
- Only I and IV are true.

**Ans: 4**

**Solution:**

Conclusion:

I. A > E (false)

II. F < C (false)

III. B > F (false)

IV. E < D (false)

**Q10. Statement: M ≥ N > O = P; Q ≥ P > N**

Conclusion:

I. M < P

II. M > Q

III. O > Q

IV. P < M

- Only IV is true.
- Only I and III are true.
- None is true.
- Only II and IV are true.
- Only I and II are true.

Ans: 1

Solution:

I. M < P (false)

II. M > Q (false)

III. O > Q (false)

IV. P < M (true)

**Q11. Which of the following symbol should replace the sign (@) and (#) in the given expression. **

**In order to make the expression Z > D and M > D is definitely true.**

**Z ≥ R @ Q > T ≤ Y, X < M = T # A > D**

a) > , ≤

b) = , <

c) < , ≥

d) > , ≥

e) < , ≤

Ans: d

Option ‘d’ is true.

**Q12. Which of the following expressions will be true if the given expression ‘G = P ≤ M = D ≥ E’ is definitely true? **

1) G < M

2) P ≥ E

3) D < P

4) D = P

5) None of these

**Ans: 5**

**Solution:**

None of the above is true.

**Directions (13-15): Study the following information carefully to answer the given questions.**

A % B – A is neither greater than nor equal to B

A & B – A is neither smaller than nor equal to B

A # B – A is not greater than B

A $ B – A is not smaller than B

A @ B- A is neither smaller than nor greater than B

**Q13. Statements: **

S$T, G$Y, T@G, Y%V

Conclusions:

I. S$Y

II. V%T

1) Only conclusion I follows

2) Only conclusion II follows

3) Either conclusion I or II follows

4) Neither conclusion I nor II follow

5) Both conclusion I and II follows

**Ans: 1**

**Solution:**

I. S$Y (true)

II. V%T (false)

First we will decode the information given,

A % B – A is neither greater than nor equal to B i.e., A < B

A & B – A is neither smaller than nor equal to B i.e., A > B

A # B – A is not greater than B i.e., A ≤ B

A $ B – A is not smaller than B i.e., A ≥ B

A @ B- A is neither smaller than nor greater than B i.e., A = B

By decoding the statement and arranging it, we get;

S ≥ T = G ≥ Y < V

I. S$Y (true)

II. V%T (false)

**Q14. Statements: **

**A&B, C$E, D%B, D@C**

**Conclusions: **

I. A&C

II. E%B

1) Only conclusion I follows

2) Only conclusion II follows

3) Either conclusion I or II follows

4) Neither conclusion I nor II follow

5) Both conclusion I and II follows

**Ans: 5**

**Solution:**

I. A&C (true)

II. E%B (true)

By decoding the statement and arranging it, we get;

A > B > D = C ≥ E

I. A&C (true)

II. E%B (true)

**Q15. Statements: **

M%Y, W$P, Y&X, X@W,

Conclusions:

I. Y&P

II. M&P

1) Only conclusion I follows

2) Only conclusion II follows

3) Either conclusion I or II follows

4) Neither conclusion I nor II follow

5) Both conclusion I and II follows

**Ans: 1**

**Solution:**

I. Y&P (true)

II. M&P (false)

By decoding the statement and arranging it, we get;

M < Y > X = W ≥ P

I. Y&P (true)

II. M&P (false)

**(16-20) Direction: In the following question, some statements are coded in a certain coded language and those statement are followed by two conclusions (I and II). Assuming the given statements to be true, find which of the two conclusions follow(s) the given statements and choose appropriate answer choice:**

A 9 B means A is not smaller than B;

A 4 B means A neither greater nor equal to B;

A 3 B means A neither smaller nor equal to B;

A 6 B means A is not greater than B; and

A 8 B means A neither greater nor smaller than B.

**Options:**

a) Only conclusion II is true

b) Either conclusion I or II is true

c) Both conclusions I and II are true

d) Neither conclusion I nor II is true

e) Only conclusion I is true

**16. Statements:**

T 3 U 3 V 4 W; V 3 X 3 Y

Conclusions:

I.T 3 Y

II. U 3 W

**Ans: e**

After decode the given statements:

T > U > V < W; V > X > Y

Conclusions:

I. T 3 Y (True)

II. U 3 W (false)

Only conclusion I is true.

**17. Statements:**

P 9 Q 8 R 9 S 4 T 8 U; V 8 S 3 W 3 X 8 Y

Conclusions:

I. V 6 P

II. U 3 X

**Ans: c**

After decode the given statements:

P ≥ Q = R ≥ S < T = U; V = S > W > X = Y

Conclusions: I. V 6 P(True)

II. U 3 X(True)

Both conclusions I and II are true

**18. Statements:**

A 8 C 4 I 6 J 8 K; R 3 P 8 I 9 Y 6 Z; Q 3 T 9 V 4 P

Conclusions:

I. V 4 Y

II. K 9 Y

**Ans: a**

After decode the given statements:

A = C < I ≤ J = K; R > P = I ≥ Y ≤ Z; Q > T ≥ V < P

Conclusions: I. V 4 Y (False)

II. K 9 Y (True)

Only conclusion II is true.

**19. Statements:**

A 8 B 4 F 6 H 8 I; J 3 L 8 F 9 M 6 N; I 3 P 9 R 4 T

Conclusions:

I. J 3 A

II. I 3 N

**Ans: e**

After decode the given statements:

A = B < F ≤ H = I; J > L = F ≥ M ≤ N; I > P ≥ R < T

Conclusions: I. J 3 A (True)

II. I 3 N (False)

Only conclusion I is true.

**20. Statements:**

A 8 B 9 D 9 F, G 6 H 8 F 9 J, K 6 L 4 H 9 M

Conclusions:

I. A 3 K

II. K 8 A

**Ans: e**

After decode the given statements:

A= B ≥ D ≥ F, G ≤ H = F ≥ J, K ≤ L < H ≥ M

Conclusions:

I. A 3 K (True)

II. K 8 A (False)

Only conclusion I is true.