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Advanced Level Inequality Questions for Bank and SSC Exams

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  • Last Updated : 08 Sep, 2022
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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 Advanced-level Inequality questions in two parts level-3 and Previous years Questions; and for Basic-level Inequality Questions and Answer visit our Basic-level Inequality Chapter.

Level 3:

Q1. Which of the following symbols should be placed in the blank spaces respectively (in the same order from left to right) in order to complete the given expression in such a manner that both ‘U ≤ P’ as well as ‘P ≥ D’ definitely holds true?  

P _ R _ D _ U _ E

A) ≥, ≥, ≤,≤

B) >, >, ≥, <

C) >, ≥, <, = 

D) ≥, =, ≥,<

E) None of the above

Ans: D

Solution:

A) P ≥ R ≥ D ≤ U ≤ E; Here ‘U ≤ P’ is false.

B) P > R > D ≥ U < E; Here ‘U ≤ P’ is false

C) P > R ≥ D < U = E; Here ‘U ≤ P’ is false

D) P ≥ R = D ≥ U < E; Here ‘U ≤ P’ and ‘P ≥ D’ definitely holds true.

Q2. Which of the following symbols should be placed in the blank spaces respectively (in the same order from left to right) in order to complete the given expression in such a manner that both ‘G≤R’ as well as ‘A≥C’ definitely holds true?  

R _ X _ C _ G _ A

A) >, ≥, <, =

B) >, >, ≥, <

C) ≥, ≥, =, ≤

D) ≥, =, =,<

E) None of the above

Ans: C

Solution:

A) R > X ≥ C < G =A; Here, ‘G≤R’ is false.

B) R > X > C ≥ G < A; Here, ‘G≤R’ is false.

C) R ≥ X ≥ C = G ≤ A; Here, ‘G≤R’ as well as ‘A≥C’ definitely holds true.

D) R ≥ X = C = G < A; Here, ‘G≤R’ is true, but ‘A≥C’ is false.

Q3. Which of the following order of letters (from left to right) in the blanks makes the expression, P < Q is definitely holds false?

____ > ____ ≥ ____ = ____< ___

A) R Q, L, P, G

B) R, L, P, G, Q

C) Q, L, G, P, R

D) G, L, Q, R, P

E) More than one options are correct  

Ans: D

Solution:

A) R > Q ≥ L = P < G; here, P < Q is possibly true

B) R > L ≥ P = G < Q; here P < Q is true

C) Q > L ≥ G = P < R; here P < Q is true

D) G > L ≥ Q = R < P; here P < Q is definitely hold false

Hence, option D showed that P < Q, is definitely false.

Q4. Which of the following order of letters (from left to right) in the blanks makes the expression, R < W definitely true?

____    ____  =  ____    ____  <  _____

1) R, U, V, W, Q

2) V, W, Y, Q, R

3) R, Y, W, Q, V

4) Both 2) and 3)

5) None of the above

Ans: 5

Solution:

1) R ≤ U = V ≤ W < Q; here, R < W is possibly true

2) V ≤ W = Y ≤ Q < R; here, R < W is definitely false

3) R ≤ Y = W ≤ Q < V; here, R < W is possibly true

Hence, none of the options showed that R < W definitely true.

Q5. Which of the following order of letters (from left to right) in the blanks makes the expression, W > F definitely False?

____ < ____ = ____ > ____>____  

1) G, W, N, P, F

2) W, G, P, F, Z

3) G, F, N, H, W

4) F, H W, Z, T

5) None

Ans: 3

Solution:

1) G < W = N > P > F; Here W > F is definitely true

2) W < G = P > F > Z; Here no relation found between W and F.

3) G < F = N > H > W; Here W > F is definitely false

4) F < H = W > Z > T; Here W > F is definitely true

Hence, option 3 showed that W > F is definitely false.

Q6. Which of the following order of letters (from left to right) in the blanks makes the expression, S > W definitely false?

____ = ____ < ____ = ____>____  

1) W, Q, H, S, P

2) P, Q, H, S, W

3) S, H, Q, W, P

4) Q, P, S, H, W

5) None  

Ans: 3

Q7. Which of the following order of letters (from left to right) in the blanks makes the expression, P < B definitely false?

____ = ____ ≥ ____ > ____=___

1) B, R, W, U, P

2) P, W, R, B, U

3) U, W, B, R, P

4) B, W, R, P, U

5) W, B, P, U, R

Ans: 2

Conclusion:

1) B = R ≥ W > U = P; Here P < B is definitely true.

2) P = W ≥ R > B = U; Here P < B is definitely false.

3) U = W ≥ B > R = P; Here P < B is definitely true.

4) B = W ≥ R > P = U; Here P < B is definitely true.

5) W = B ≥ P > U = R; Here P < B is possibly true.

Hence, option 2 is true.

Directions (8-9): Study the following information carefully to answer the given questions.

O $ Q – O is not smaller than Q

O # Q – O is not greater than Q

O % Q – O is neither greater than nor equal to Q

O & Q – O is neither smaller than nor equal to Q

O @ Q- O is neither smaller than nor greater than Q

Q8. Statements:  

T&P, W%R, P#U, M@U, 

Conclusions:  

I. U$T

II. M%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: 4

Solution:

By decoding the statement and after rearranged, we get;

T > P ≤ U = M > W

I. U$T (false)  

II. M%T (false)

Q9. Statements:  

G@H, H$C, C#D, D%E,

Conclusions:  

I. H&D

II. C%E

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: 2

Solution:

By decoding the statement and arranging it, we get;

G = H ≥ C ≤ D < E

I. H&D (False)  

II. C%E (True)

Directions (10-12): In the given question, assuming the given statements to be true. Find which of the given four conclusions numbered I, II, and III is/are definitely true and give your answer accordingly.

Q10. Statements:

S < Q = U < D < P; A < Y = D; S > O > G

Conclusion:  

I. D > O  

II. G > P

III. S < Y  

1) Conclusion I is true.

2) Both conclusions I and III are true.

3) All conclusions I, II and III are true

4) None is true.

5) None of these.

Ans: 2

Solution:

I. D > O (True)

II. G > P (False)

III. S < Y  (True)

Hence, both conclusions I and III are true.

Q11. Statements:

U ≥ O > S = K; M ≥ N = Z > O ; Z ≥ Q > F;

Conclusion:  

I. U > Q  

II. M > F

III. N > K

1) Conclusion II is true

2) Both conclusions I and III are true

3) All conclusions I, II and III are true

4) None is true

5) None of the above given option is follows

Ans: 5

Solution:

I. U > Q  (False)

II. M > F (True)

III. N > K (True)

Hence, both conclusions II and III are true.

Q12. Statements:

O < H ≤ K; G < H ≤ M < Q = R; P = B ≤ O = T

Conclusion:  

I. R > T    

II. T < G

III. K > P

1) Both conclusions I and II are true

2) Both conclusions I and III are true

3) All conclusions I, II and III are true

4) None is true

5) None of the above given option is follows

Ans: 1

Solution:

I. R > T (True)   

II. T < G (False)

III. K > P (True)

Hence, both conclusions I and III are true.

Q13. Which of the following expressions is true if the expressions G≤N=S and R=T≥B>S are definitely true?

1) B < R

2) S < R

3) N > R

4) G < B

5) More than one options are true

Ans: 5

Solution:

1) B < R — False

2) S < R — True

3) N > R — False

4) G < B — True

Hence, more than one options are true.

Q14. In which of the following expressions does the expression ‘O≤D’ to definitely hold true?  

1) H ≥ O ≤ R = Q < S ≤ D

2) Z ≥ D ≥ E = N ≤ A ≥ O

3) O ≥ Q > Y ≥ B = U ≤ D

4) G ≥ O = R = E ≤ S ≤ D

5) D ≥ W = G ≥ X > Z ≥ O

Ans: 4

Q15. In which of the following expressions does the expression ‘A>G’ be definitely false?  

1) A > U ≥ Q = X ≥ R > G

2) A > U > F ≤ Z; G > F  

3) G ≤ Z ≤ Y = R < A

4) A > T = U ≥ P; G < X = U

5) X < U ≤ A ≤ T; G ≥ O > T

Ans: 5

Some previous years Memory Based Questions of various Exams:

Directions (1-3): In these questions, relationship between different elements is shown in the statements. These statements are followed by two conclusions. Mark answer as. (IBPS PO Pre 2020)

(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 = E, D < M < P < Q; W ≥ D

Conclusions: I. D < E II. Q < W  

Q2. Statements: S < C, H ≥ M > F < Q = C

Conclusions: I. H > S II. F >C

Q3. Statements: W ≥ T ≥ K; J = R < K

Conclusions: I. W ≥ R II. T > J

Solution (1-3):

1. Ans.(a)

2. Ans.(d)

3. Ans.(b)

Directions (4-8): In the following questions, the symbols &, %, #, * and @ are used with the following meaning as illustrated below: (SBI Clerk Mains 2019).

‘P#Q’ means ‘P is not greater than Q’

‘P*Q’ means ‘P is neither equal to nor smaller than Q’

‘P%Q’ means ‘P is not smaller than Q’

‘P@Q’ means ‘P is neither smaller than nor greater than Q’

‘P&Q’ means ‘P is neither greater than nor equal to Q’

Now in each of the following questions assuming the given statement to be true, find which of the conclusions given below them is/are definitely true and give your answer accordingly.

(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.

Q4. Statements: T * W % R % Q & P @ M

Conclusions: I. T % Q II. Q & M

Q5. Statements: M # B * C * U & E

Conclusions: I. M * U II. U & B

Q6. Statements: H * S % T; W % J * H % G;

Conclusions: I. H & W II. T * J

Q7. Statements: K # D @ F # R * H % C

Conclusions: I. K & R II. R @ K

Q8. Statements: Y * P @ M; Q % Y & K # L

Conclusions: I. M & L II. Q * M

Solution: (4-8)

Answer 4. Ans.(b)

Sol. I. T % Q (False) II. Q & M (True)

Answer 5. Ans.(b)

Sol. I. M * U (False) II. U & B (True)

Answer 6. Ans. (a)

Sol. I. H & W (True) II. T * J (False)

Answer 7. Ans.(c)

Sol. I. K & R (False) II. R @ K (False)

Answer 8. Ans.(e)

Sol. I. M & L (True) II. Q * M (True)

Directions (9-11): In these questions, relationship between different elements is show in the statements. The statements are followed by conclusions. Study the conclusions based on the given statements and select the appropriate answer: 

(SBI PO Pre 2020)

(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.

Q9. Statements:  J=Q; Y=B>K≥M; Q>R=V>B;

Conclusion I: R>K II: J<B

Q10. Statements: Q=T<I; X≥G>P=Z<O; I<X

Conclusion I: Z≤I II: O>G

Q11. Statements: E=P≤L>K; W>G≥B=D≤P; 

Conclusion I: E>B II: B=E

Solutions (9-11):

S9. Ans.(a)

Sol. I: R>K (True) II: J<B (False)

S10. Ans.(d)

Sol. I: Z≤I (False) II: O>G (False)

S11. Ans.(c)

Sol. I: E>B (False) II: B=E (False)

Direction: (12-14): In each of the following questions, the relationship between different elements is shown in the statements followed by two conclusions. Find the conclusion which is definitely true. (RRB PO Prelims 2020)

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.

12. Statements:

M = O > F; R ≥ T = L ≤ F , 

Conclusion:

I). M < L

II). O > R

13. Statements:

D ≥ C = Y ≥ Z ; X > H = C ≤ W = R < T

Conclusion:

I). T > Z

II). H ≤ D

14. Statements:

D ≤ W < L ≤ Q = C > T = V; A = B ≥ C

Conclusion:

I). A ≥ L

II). T > D

Solution: (12-14)

12. Answer: d)

I). M < L ( M = O >F ≥ L) False

II). O > R (O > F ≥ L = T ≤ R) False

Hence, none follows.

13. Answer: e)

I). T > Z (Z ≤ Y = C ≤ W = R < T) True

II). H ≤ D ( D ≥ C = H) True

Hence, both conclusions I and II follow

14. Answer: a)

I). A ≥ L (L ≤ Q = C ≤ B = A) True

II). T > D ( D ≤ W < L ≤ Q = C > T) False

Hence, only conclusion I follows.


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