A Complete Guide on Reasoning Ability for Banking Examinations

However,
Either (a) or (b) is definitely true; either x > y or x = y, It is just like saying x ≥ y.
Complicated case of “Either or”
Statement: H≥M≤V=K
Find the what is relation between H and K?
Conclusion: (i) H < K
(ii) H ≥ K
In the above statement we cannot find relation between H and K, But there are three relationship possibilities between

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H and K.
(i) H > K (ii) H = K and (iii) H < K
And all three possibilities are given in the above conclusion.

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So, this case are also “Either or”
H ≥ K or H < K
Example of direct inequalities:
Statement Conclusion
Statement (1) A=B ≥ C < D=E ≤ F (i) F > B (ii) B ≥ D

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Here, conclusion (i) as well as conclusion (ii) does not follow
Statement (2) P > M > Q, Q > Z > N (i) M ≥ Z (ii) N < P
Solution: P > M > Q > Z > N (i) Not follow (ii) Follow
Statement (3) X > Y, Y ≥ Z, Z = V, V < W (i) Y = V (ii) Y > V
Solution: X > Y ≥ Z = V < W (i) Not follow (ii) Not follow, but either (i) or (ii) follow
Example of coded Inequalities
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Directions (1-5): In these questions, symbols ©, #, %, $ and @ are used with different meanings as follows:
‘A©B’ Means ‘A’ is smaller than ‘B’
‘A#B’ Means ‘A’ is greater than B
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‘A%B’ Means ‘A’ is either smaller than or equal to ‘B’
‘A$B’ Means ‘A’ is either greater than or equal to ‘B’
‘A@B’ means ‘A’ is neither smaller than nor greater than ‘B’
1. Statement: V#S, S©L, L©J
Conclusion: I. V©L II. S©J
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2. Statement: M#R, R©J, J#H

Conclusion: I. M#H II. R©H
3. Statement: M$F, F@G, G%M
Conclusion: I. F$H II. F@M
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4. Statement: T#L, L%W, W@V

Conclusion: I. L%V II. T%W
5. Statement: K%L, L%T, I$T
Conclusion: I. L%I II. L#I
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Solutions:

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1. V > S < L < J (i) Not follow (ii) Follow
2. M > R < J > H (i) Not follow (ii) Not follow
3. H ≥ F = G ≤ M (i) Not follow (ii) Not follow
4. T > L ≤ W = V (i) Follow (ii) Not follow
5. K ≤ L ≤ I ≥ T (i) Follow (ii) Not follow

Some common examples asked in mains exam-

Directions (1-3): In the following questions, the symbols @, #, $, % and & are used with the following meaning as

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illustrated below-
‘M@N’ means ‘N is smaller than or equal to M’

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‘M#N’ means ‘N is greater than or equal to M’
‘M$N’ means ‘N is equal to M’
‘M%N’ means ‘N is greater than M’
‘M&N’ means ‘N is smaller than M’
Now in each of the following questions assuming the given statements to be true, find which of the three conclusions
I, II and III given below them is/are definitely true and give your answer accordingly.

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Example 1: Statements: U & V @ W%X; P# W$ Q; R&X
Conclusions: I. P%U II. R&W III. Q&X
(a) Only I is true
(b) Only II is true
(c) Both I and II are true
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(d) Both III and II are true
(e) All are true
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Solution. (c): I. P%U (True) II. R&W (True) III. Q&X (False)

Example 2: Statements: A # B$ C&D; E % B@ F; G & D&X

Conclusions: I. F#A II. G&B III. B&X
(a) Only III is true
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(b) Only II is true

(c) Only I is true
(d) Both I and II are true
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(e) All are true

Solution (a): I. F#A (False) II. G&B (False) III. B&X (True)

Example 3: Statements: F $G #S &T ; Q@ S #R ; B$ T

Conclusions: I. F#Q II. G%R III. B%G
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(a) Only I is true

(b) Only II is true
(c) Only III is true
(d) Both I and II are true
(e) All are true
Solution (a): I. F#Q (True) II. G%R (False) III. B%G (False)

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Directions (4-6): In the following questions, the symbols @, &, $, µ and© are used with the following meaning as
illustrated below-
‘P&Q’ means ‘Q is smaller than or equal to P’
‘P$Q’ means ‘Q is greater than or equal to P’
‘PµQ’ means ‘Q is equal to P’
‘P@Q’ means ‘Q is greater than P’
‘P©Q’ means ‘Q is smaller than P’
Now in each of the following questions assuming the given statements to be true, find which of the three conclusions

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I, II and III given below them is/are definitely true and give your answer accordingly.

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Example 4: Statements: A©B&CµD ; F&CµE ; G&D
Conclusions: I. B&E II. G$B III. E$G
(a) Only I is true
(b) Only II is true
(c) Both I and II are true

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(d) Both I and III are true
(e) All are true
Solution (d): I. B&E (True) II. G$B (False) III. E$G (True)

Example 5: Statements: I& J ©K ; L@KµM ; N©J

Conclusions: I. N© K II. I© L
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III. L@J
(a) Only I is true
(b) Only II is true
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(c) Only III is true
(d) Both I and II are true
(e) All are true
Solution (e): I. N© K (True) II. I© L (True) III. L@J(True)
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Example 6: Statements: U©V&W@X ; Y @VµZ ; X © Y

Conclusions: I. Y@W II. W©Y III. U©W
(a) Only I is true
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(b) Only II is true

(c) Only III is true
(d) Both I and II are true
(e) All are true
Solution (c): I. Y@W (False) II. W©Y (False) III. U©W(True)
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Points to Remember:
(1) In chapter of Inequalities, you should give proper attention to sign of inequalities.
(2) Be careful about "either-or" case which has been clearly described in concept part.
(3) In case of coded inequalities, you should read the directions and decode them properly.
(4) Use the tabular form for coded inequlities, which will help you to solve questions in less time.
(5) Relate the conclusion from the given statements carefully.

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Directions (1-10): In each of the following questions 17. Statements: Z = N, N ≥ K, K > M, M < D
assuming the given statements to be true, find which of Conclusions: I. D = N II. Z = M
the two conclusions I and II given below is/are definitely 18. Statements: F ≥ K, K > T, D = T, V ≥ D
true and give your answer accordingly. Conclusions: I. T ≥ F II. D = K
(a) If, I is true (b) If, II is true 19. Statements: H > J, J < Y, Y ≥ K, K = W
(c) If either I or II is true (d) If, neither I nor II is true Conclusions: I. W = Y II. K < J
(e) If, Both I and II are true. 20. Statements: F ≥ K, K > T, D = T, V ≥ D

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1. Statements: J > M, N ≤ R, R < M Conclusions: I. D < F II. V = K
Conclusions: I. N < J II. N < M Directions (21-30): In each of the following questions

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2. Statements: F < N, N = D, D > T assuming the given statements to be true, find which of
Conclusions: I. F > T II. N > T the following conclusion I and II given below is/are
3. Statements: Z ≥ H, B < H, K < B definitely true and give your answer accordingly.
Conclusions: I. K > Z II. K = Z (a) If, I is true. (b) If, II is true.
4. Statements: F < N, N = D, D > T (c) If, either I or II is true (d) If, neither I nor II is true
Conclusions: I. F = D II. F < D (e) If, Both I and II is true

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5. Statements: J > M, N ≤ R, R < M 21. Statements: M < D, D = K, K ≤ R, R = F
Conclusions: I. J > R II. N = R Conclusions: I. F < K II. D = F
6. Statements: Z ≥ H, B < H, K < B 22. Statements: B ≥ K, K > T, T = F, H < F
Conclusions: I. K > H II. Z > B Conclusions: I. B > T II. T < B
7. Statements: H ≤ R, R< M, M = J 23. Statements: W = B, B ≤ F, F < R, R > F
Conclusions:
8. Statements:
I. H < J
B ≤ K, K> M, C ≤ M
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II. H ≤ J Conclusions:
24. Statements:
I. W = F II. W < F
E ≤ K, K > T, T < N, B ≥ N
Conclusions: I. B < C II. K > C Conclusions: I. T ≥ E II. K < N
9. Statements: H ≤ R, R < M, M = J 25. Statements: Z > B, B ≥ M, M < F, F ≤ R
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Conclusions: I. M > H II. H = J Conclusions: I. Z = M II. F = B
10. Statements: B ≤ K, K > M, C ≤ M 26. Statements: M < D, D = K, K ≤ R, R = F
Conclusions: I. B = C II. K = C Conclusions: I. M < R II. D = R
Directions (11-20): In each of the following questions 27. Statements: B ≥ K, K > T, T = F, H < F
assuming the given statements to be true, find which of Conclusions: I. H < K II. F < B
the following, conclusion I and II given below is/are 28. Statements: W = B, B ≤ F, F < R, R > F
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definitely true and give your answer accordingly: Conclusions: I. R = B II. B < R
(a) If, I is true (b) If, II is true 29. Statements: H ≤ T, T > N, F < N, B ≥ F
(c) If, either I or II is true (d) If, neither I nor II is true Conclusions: I. F ≤ H II. F < T
(e) If, Both I and II are true. 30. Statements: H ≤ T, T > N, F < N, B ≥ F
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11. Statements: B ≤ K, K > M, C ≤ M Conclusions: I. B = T II. B ≥ H

Conclusions: I. B > K II. K > C Direction (31-35): In each of the questions below are
12. Statements: B ≤ K, K > M, C ≤ M given some statements followed by two conclusions. You
Conclusions: I. B ≤ C II. K ≥ C have to take the given statements to be true even if they
13. Statements: B ≤ K, K > M, C ≤ M seem to be at variance with commonly known facts. Read
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Conclusions: I. B = C II. K > C all the conclusions and then decide which of the given
14. Statements: F < W, W > V, V = B, B ≥ D conclusions logically follows from the given statements
Conclusions: I. F < B II. D < V disregarding commonly known facts.
15. Statements: Z = N, N ≥ K, K > M, M < D (a) If only conclusion I follows.
Conclusions: I. M > N II. M = N (b) If only conclusion II follows.
16. Statements: F < W, W > V, V = B, B ≥ D (c) If either conclusion I or II follows.
Conclusions: I. V = F II. W = D (d) If neither conclusion I nor II follows.
(e) If both conclusions I and II follow.

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31. Statements: S > D = F ≥ G ≥ H ≤ K, Y ≤ H = T Directions (44-48): In these questions, relationship
Conclusions: I. S > Y II. S > T between different elements is shown in the statements.
32. Statements: W ≥ E > R < T ≤ Y, Y ≤ U = I ≥ O These statements are followed by two conclusions. Give
Conclusions: I. R < I II. E > O answer-
33. Statements: X < C < V = B ≤ N, V > L = O ≥ U (a) If only conclusion I follows.
Conclusions: I. B ≤ O II. B < O (b) If only conclusion II follows.
(c) If either conclusion I or II follows.
34. Statements: X = F < Y > H = I ? O, F ? E = R
(d) If neither conclusion I nor II follows.
Conclusions: I. Y > R II. Y ≥ R

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(e) If both conclusion I and II follow.
35. Statements: M > K > L = O ≥ P, K < B = G ≤ Y≤ T
44. Statements: G≥F>E=D≥C>B
Conclusions: I. L > Y II. O < G
Conclusions: I. G ≥ B II. B < G
Directions (36-39): In the given questions, assuming the

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45. Statements: J > I = H < G ≤ F < E; L > G ≤ K
given statements to be true. Find which of the given two Conclusions: I. I < L II. K ≤ H
conclusions numbered I, and II is/are definitely true and 46. Statements: N < M = L ≥ K ≤ J = I; O > P = K
give your answer accordingly. Conclusions: I. O < M II. M ≤ O
(a) If only conclusion I is true 47. Statements: N > F > O ≤ M; O ≤ B > A
(b) If only conclusion II is true Conclusions: I. M ≥ B II. N > A

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(c) If either conclusion I or II is true 48. Statements: B ≥ A > D = E; C < A < F
(d) If neither conclusion I nor II is true Conclusions: I. F < B II. B ≥ C
(e) If both conclusions I and II are true Direction (49-53): In each of the questions below are
36. Statements: T>N≥E>I≤S≤U<X given a statement followed by two conclusions. You
have to take the given statements to be true even if they
Conclusions: I. T > I
37. Statements:
II. X > I
N > V > M ≤ O; M ≥ Z > B
Conclusions: I. Z ≤ O II. N > O
m seem to be at variance with commonly known facts. Read
all the conclusions and then decide which of the given
conclusions logically follows from the given statements
38. Statements: K ≥ B > E = F; M < B < N
disregarding commonly known facts.
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Conclusions: I. N < K II. K > M
(a) If only conclusion I follows.
39. Statements: Z > G ≤ P ≤ Q; G ≥ V < U
(b) If only conclusion II follows.
Conclusions: I. Z > Q II. P < G (c) If either conclusion I or II follows.
Direction (40-43): In this question, relationship between (d) If neither conclusion I nor II follows.
different elements is shown in the statements. The (e) If both conclusions I and II follow.
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statements are followed by conclusions. Study the 49. Statements: K>M<P≤L≤U=Y>D

conclusions based on the given statement and select the Conclusions: I. Y < M II. M < Y
appropriate answer. 50. Statements: H≥G≥R≤W≤A<O≤L
(a) Only conclusion I is true. Conclusions: I. R ≤ A II. L < W
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(b) Only conclusion II is true. 51. Statements: T>R=E>W<Q=S≤A<Y

(c) Either conclusion I or II is true. Conclusions: I. T > S II. W < Y
(d) Neither conclusion I nor II is true. 52. Statements: S > D = R < W ≥ F ≤ G; B > D ≥ X
(e) Both conclusions I and conclusion II are true. Conclusions: I. X < W II. B > R
40. Statements: D ≥ E = T ≤ S < M ≤ B; C ≥ D > A; D < P 53. Statements: E>H>G=D<L<O=P
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Conclusions: I. D < E II. P < G

Conclusions: I. E < B II. A ? M
Direction (54-58): In each of the questions below are
41. Statements: P > D ≥ E = T; C ≥ D > A; T ≤ S < M ≤ B
given some statements followed by two conclusions. You
Conclusions: I. C = T II. C > T
have to take the given statements to be true even if they
42. Statements: W < U; A < J < U = D ≤ V
seem to be at variance with commonly known facts. Read
Conclusions: I. J < V II. V > W all the conclusions and then decide which of the given
43. Statements: P < N ≤ L > Q; G ≥ S; L ≥ F; S = X< P conclusions logically follows from the given statements
Conclusions: I. P < F II. Q > X disregarding commonly known facts.

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(a) If only conclusion I follows. Direction (59-60): In these questions, relationship
(b) If only conclusion II follows. between different elements is show in the statements.
(c) If either conclusion I or II follows. The statements are followed by conclusions. Study the
(d) If neither conclusion I nor II follows. conclusions based on the given statements and select the
(e) If both conclusions I and II follow. appropriate answer:
54. Statements: A<B≤L≤U>R=S>T (a) If only conclusion I follows.
Conclusions: I. A < U II. B < R (b) If only conclusion II follows.
55. Statements: C>D=H≥G<S≤N<M (c) If either conclusion I or II follows.

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Conclusions: I. D > S II. S < M
(d) If neither conclusion I nor II follows.
56. Statements: X≤Y<A>W=H≥G>J
(e) If both conclusions I and II follow.
Conclusions: I. Y < W II. W < J

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59. Statements: G>R≥E≥W=S>D≤F
57. Statements: V>D>E=K<Q>F≥H
Conclusions: I. R > D II. R = W
Conclusions: I. V > K II. Q > H
60. Statements: G=N<S≤L≤O<Q=W
58. Statements: G≤O<R≤Y<P=K<L
Conclusions: I. S > Q II. S = Q
Conclusions: I. G < Y II. G ≤ Y

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Direction (1-25): In each of the following questions 7. Statements: V % B, B $ D, D © E
assuming the given statements to be true, find out which Conclusions: I. E d B II. D @ V
of the two conclusions I and II given below them is/ are Directions (8–13): In the following questions, the
definitely true symbols @, ©, %, d and # are used with the following
Give answer (a) If only Conclusion I is true.
Give answer (b) if only Conclusion II is true.
m meaning as illustrated below:
‘P % Q’ means ‘P is not greater than Q’.
Give answer (c) if either Conclusion I or II is true. ‘P d Q’ means ‘P is neither greater than nor smaller than
Give answer (d) if neither Conclusion I nor II is true. Q’.
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Give answer (e) if both Conclusion I and II are true. ‘P # Q’ means ‘P is neither greater than nor equal to Q’.
Directions (1–7): In the following questions, the symbols ‘P © Q’ means ‘P is not smaller than Q’.
@, ©, %, $ and d are used with the following meanings ‘P @ Q’ means ‘P is neither smaller than nor equal to Q’.
illustrated. 8. Statements: R © T, T @ M, M δ D
‘P % Q’ means ‘P is greater than Q’. Conclusions: I. D # T II. M # T
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‘P d Q’ means ‘P is neither greater than nor smaller than 9. Statements: B @ N, N % R, R © F

Q’. Conclusions: I. B @ F II. N # F
‘P @ Q’ means ‘P is smaller than Q’. 10. Statements: D # T, T @ R, R © M
‘P © Q’ means ‘P is either smaller than or equal to Q’. Conclusions: I. M # D II. M # T
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‘P $ Q’ means ‘P is either greater than or equal to Q’. 11. Statements: K δ H, H % F, F # J

1. Statements: M @ J, J © R, R d K Conclusions: I. F © K II. J © H
Conclusions: I. K d J II. K % J 12. Statements: W @ G, N © G, N % V
2. Statements: N $ T, T d H, N @ W Conclusions: I. W @ N II. V © G
Conclusions: I. W % T II. H © N 13. Statements: T © Y, Y % M, M @ R
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3. Statements: F @ R, R © V, V $ T Conclusions: I. R # Y II. T δ M

Conclusions: I. V % F II. F @ T Directions (14-18): In the following questions, the
4. Statements: W © D, D $ B, B @ H symbols @, ©, #, $ and % are used with the following
Conclusions: I. H % D II. W @ B meaning as illustrated below:
5. Statements: F d T, T $ M, M © R ‘P © Q’ means ‘P’ is either greater than or equal to Q’.
Conclusions: I. R $ F II. M © F ‘P%Q’ means ‘P is either smaller than or equal to Q’.
6. Statements: H $ N, N % R, R @ J ‘P@ Q’ means ‘P is neither greater than nor smaller than
Conclusions: I. R @ H II. J % H Q’.

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‘P#Q’ means ‘P is smaller than Q’. Direction (26-40): In each of the following questions
‘P $ Q’ means ‘P is greater than Q’. assuming the given statements to be true, find out which
Now in each of the following questions assuming the of the two conclusions I and II given below them is/ are
given statements to be true, find which of the two definitely true
conclusions I and II given below them is / are definitely Give answer (a) If only Conclusion I is true.
true? Give answer (b) if only Conclusion II is true.
14. Statements: K© R, R $ F, F # B Give answer (c) if either Conclusion I or II is true.
Conclusions: I. B $ R II. F # K Give answer (d) if neither Conclusion I nor II is true.

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15. Statements: J $ M, M © K, K # N Give answer (e) if both Conclusion I and II are true.
Conclusions: I. J $ K II. N $ M Direction: (26-30)
16. Statements: F # T, T @ W, W $ H ‘P © Q’ means ‘P is neither smaller than nor greater than

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Conclusions: I. F # H II. F © H Q’.
17. Statements: M % T, T # R,R @ D ‘P # Q’ means ‘P is neither greater than nor equal to Q.
Conclusions: I. D $ T II. R $ T ‘P $ Q’ means ‘P is neither smaller than nor equal to Q’.
18. Statements: D $ N, N # F, F © T ‘P @ Q’ means ‘P is either greater than or equal to Q’.
Conclusions: I. T # N II. D $ F ‘P % Q’ means ‘P is either smaller than or equal to Q’.
Directions (19–23): In the following questions, the 26. Statements: M $ N, N $ O, O % P

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symbols #, $, %, * and @ are used with the following
Conclusions: I. O # M II. P © N
meaning as illustrated below:
27. Statements: 5 @ 7, 7 # 8, 8 $ 9
‘A # B’ means ‘A is not greater than B’.
Conclusions: I. 9 # 7 II. 8 $ 5
‘A $ B’ means ‘A is neither smaller nor equal to B’.
28. Statements: X # Y, Y @ Z, Z @ D
‘A % B’ means ‘A is neither smaller nor greater than B’.
‘A * B’ means ‘A is neither greater nor equal to B’.
‘A @ B’ means ‘A is not smaller than B’.
m Conclusions:
29. Statements:
I. D % Y
P @ Q, Q $ R, R # S
II. Z @ X

Conclusions: I. S $ Q II. R # P
19. Statements: A # B, B % C, C * D
30. Statements: C © B, B % D, D $ E
Conclusions: I. C @ A II. A # D
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Conclusions: I. D $ C II. D © C
20. Statements: P $ Q, Q @ S, S % R
Conclusions: I. P @ R II. R $ Q Direction (31-35): In each of the following questions
21. Statements: W * X, X # Y, Y $ Z assuming the given statements to be true, find out which
Conclusions: I. W * Z II. W @ Z of the two conclusions I and II given below them is/ are
22. Statements: G @ H, H $ J, J % K definitely true
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Conclusions: I. K * G II. J * G Give answer (a) If only Conclusion I is true.

23. Statements: N @ M, M $ P, P # T Give answer (b) if only Conclusion II is true.
Conclusions: I. T # N II. P * N Give answer (c) if either Conclusion I or II is true.
Directions (24-25): In these questions, relationship Give answer (d) if neither Conclusion I nor II is true.
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between different elements is shown in the statements. Give answer (e) if both Conclusion I and II are true.
These statements are followed by two conclusions. ‘A © B’ means ‘A is smaller than B’
Mark answer (a) if only conclusion I follows. ‘A # B’ means ‘A is either smaller than or equal to B’
Mark answer (b) if only conclusion II follows. ‘A _ B’ means ‘A is greater than B’
Mark answer (c) if either conclusion I or conclusion II ‘A $ B’ means ‘A is either greater than or equal to B’
‘A @ B’ means ‘A is neither smaller than nor greater than
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follows.
Mark answer (d) if neither conclusion I nor conclusion II B’
follows. 31. Statements: V#S, S©L, L©J
Mark answer (e) if both conclusions I and II follow. Conclusions: I. V © L II. S © J
24. Statements: A=B≥C<D=E≤F 32. Statements: M#R, R©J, J#H
Conclusions: I. F > B II. B ≥ D Conclusions: I. M #H II. R © H
25. Statements: P > M > Q, Q > Z > N 33. Statements: H$F, F@G, G_M
Conclusions: I. M ≥ Z II. N < P Conclusions: I. H_M II. H_G

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34. Statements: R©J, J _T,,T # L (a) Only I is true (b) Only II is true
Conclusions: I. R @ T II. J @ L (c) Both I and II is true (d) Either I or III is true
35. Statements: W@T, T$K, K _F (e) None is true
Conclusions: I. W $ K II. W @ K Directions (44-48) : In the following questions, the
Directions (36-40): symbols @, #, %, $ and © are used with the following
‘P © Q’, means ‘P is not greater than Q’. meaning as illustrated below-
‘P * Q’, means ‘P is not smaller than Q’. 'P#Q' means 'P is neither greater than nor equal to Q'
‘P @ Q’, means ‘P is neither greater than nor smaller than 'P©Q' means 'P is neither equal to nor smaller than Q'

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Q’. 'P%Q' means 'P is neither smaller than nor greater than
‘P $ Q’, means ‘P is neither smaller than nor equal to Q’. Q'
‘P % Q’, means ‘P is neither greater than nor equal to Q’. 'P$Q' means 'P is not smaller than Q'

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36. Statements: M % T, T $ K, K © D 'P@Q' means 'P is not greater than Q'
Conclusions: I. T $ D II. D $ M Now in each of the following questions assuming the
37. Statements: F @ B, B % N, N © H given statement to be true, find which of the three
Conclusions: I. N $ F II. H $ F conclusions I, II and III given below them is/are true and
38. Statements: R * M, M @ K, K © J give your answer accordingly.
Conclusions: I. J $ M II. J @ M 44. Statements: J@M©L$H%R

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39. Statements: B $ N, N * R, R @ K Conclusions: I. J©R II. M$H III. H#J
Conclusions: I. K © N II. B $ K (a) None is true (b) Only I is true
40. Statements: J © K, K $ N, N * D. (c) Only I and II is true (d) Only III is true
Conclusions: I. J % N II. D % K (e) Only II is true
Directions (41-43): In the following questions, the 45. Statements: A#B$C©D#E
symbols @, #, %, $ and © are used with the following
meaning as illustrated below-
m Conclusions: I. A$C
(a) Only I is true
II. A#C III. B©E

'P#Q' means 'P is neither greater than nor equal to Q' (b) Only II is true
'P©Q' means 'P is neither equal to nor smaller than Q' (c) Either I or II is true
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'P%Q' means 'P is neither smaller than nor greater than (d) III and either I or II is true
Q' (e) None is true
'P$Q' means 'P is not smaller than Q' 46. Statements: R%G$H%J@K
'P@Q' means 'P is not greater than Q' Conclusions: I. R©H II. R$K III. G©J
Now in each of the following questions assuming the (a) Only I is true (b) Only III is true
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given statement to be true, find which of the three (c) None is true (d) Both I and II is true
conclusions I, II and III given below them is/are true and (e) Only II is true
give your answer accordingly. 47. Statements: A#B$C©D%E
41. Statements: J%L, T@L, L#M Conclusions: I. E#B II. C@B III. C©E
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Conclusions: I. M©L II. T#J III. T%J (a) Only I is true (b) Only II is true
(a) Only I is true (c) Both I and II is true (d) Only III is true
(b) Either II or III are true (e) All are true
(c) None is true 48. Statements: R%G#H@J©K
(d) I and either II or III are true Conclusions: I. R#J II. G@J III. K©G
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(e) None of these (a) Only II is true (b) Only III is true
42. Statements: K@T, L#M, K$L, L©R (c) Both I and III is true (d) Only I is true
Conclusions: I. T©M II. L©T III. T#R (e) Both II and III is true
(a) None is true (b) Only I is true Directions (49-53) : In the following questions, the
(c) Only II is true (d) Either I or II is true symbols @, ^, *, # and © used with the following
(e) Only III is true meaning as illustrated below:
43. Statements: G©R%H@N©J 'A & B' means 'A is not greater than B'
Conclusions: I. H#N II. J#G III. R$J 'A $ B' means 'A is not smaller than B'

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'A @ B' means 'A is neither smaller than nor equal to B' 54. Statements: R$S, S*L, L$Q
'A # B' means 'A is neither greater than nor equal to B' Conclusions: I. R*Q II. S$Q
'A % B' means "A is neither greater than nor smaller than (a) None is true (b) Only I is true
B' (c) Only II is true (d) Either I or II are true
Now, in each of the following questions assuming the (e) Both are true
given statements to be true, find which of the three 55. Statements: B%J, J&M, M@V
conclusions I, II and III is/are definitely true and give Conclusions: I. J@V II. B*M
your answer accordingly. (a) Only I is true (b) Only II is true
(c) Either I and II are true (d) Both are true

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49. Statements: N & M, M $ J, J # K, K @ L
Conclusions: I. N @ K II. K $ N III. J & L (e) None is true
(a) Either I or II is true (b) None is true 56. Statements: C*X, G$X, Y%G
Conclusions: I. Y*X II. Y$X

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(c) Only II is true (d) Only III is true
(e) Only I and III are true (a) None is true (b) Only I is true
50. Statements: H $ G, G @ D, D % E, E # F (c) Only II is true (d) Both II and I are true
Conclusions: I. D # F II. H $ E III. G % F (e) Either I or II is true
(a) Only I and II are true (b) Only I is true 57. Statements: A$D, D%V, V*Z
(c) Only III and II are true (d) Only III is true Conclusions: I. D*Z II. V@A

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(e) Only I and III are true (a) None is true (b) Only I is true
51. Statements: A%B$C@D#E (c) Only II is true (d) Either I or III is true
(e) Both are true
Conclusions: I. B @ D II. A @ E III. A & E
58. Statements: Q@T, T&K, K%E
(a) Only I is true (b) Only III is true
Conclusions: I. T$E II. T*E
(c) Only II is true (d) Only either III or I is true
(e) Only either III or II and I are true
52. Statements: V & Z, Z $ W, W # X, X @ Y
m (a) Either I or II are true
(c) Both I and II are true
(b) Only I is true
(d) Only II true
(e) None is true
Conclusions: I. Y # W II. Z % X III. V # X
Directions (59-63): In the following questions, the
(a) None is true (b) Only I is true
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symbols @, !, %, $ and & are used with the following
(c) Only II is true (d) Only III is true
meaning as illustrated below:
(e) Only I and II are true
'A & B' means 'A is not smaller than B'
53. Statements: N&O$P@Q#M
'A $ B' means 'A is neither smaller than nor equal to B'
Conclusions: I. P & O II. Q # P III. P @ M
'A ! B' means 'A is neither smaller than nor greater than
(a) Only I is true B'
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(b) Only I and II are true 'A % B' means 'A is not greater than B'
(c) Only II and III are true 'A @ B' means 'A is neither greater than nor equal to B'
(d) Only I and III are true (a) If only conclusion I is true
(e) All I, II, III are true (b) If only conclusion II is true
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Directions (54-58) : In the following questions, the (c) If either conclusion I or II is true
symbols @, &, %, $ and * are used with the following (d) If neither conclusion I nor II is true
meaning as illustrated below- (e) If both conclusions I and II are true
'P&Q' means 'P is neither greater than nor equal to Q' 59. Statements: N ! M, M & L, L $ K, P & K
'P*Q' means 'P is neither equal to nor smaller than Q' Conclusions: I. N ! L II. L @ N
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'P$Q' means 'P is neither smaller than nor greater than Q' 60. Statements: X ! W, V $ U, Z @ X, W % V
'P%Q' means 'P is not smaller than Q' Conclusions: I. Z @ V II. W % U
'P@Q' means 'P is not greater than Q' 61. Statements: M % N, K @ L, L ! M, J @ K
Now in each of the following questions assuming the Conclusions: I. L @ N II. M $ J
given statement to be true, find which of the two 62. Statements: C % B, E & D, F $ E, D $ C
conclusions I and II given below them is/are definitely Conclusions: I. F & C II. C ! E
true and give your answer accordingly. 63. Statements: E ! F, F & G, G % H, D $ E
Conclusions: I. E % H II. G @ D

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Directions (64-69): In each of the following questions, 70. Statements: M © T, T @ J, J # D
assuming the given statements to be true, find which of Conclusions: I. D # T II. D % T III. D % M
the following two conclusions I and II is/are definitely (a) All are true (b) Only I is true
true. Give answer: (c) Only II is true (d) Only either I or II true
(a) if only conclusion I is true.
(e) Only either I or II & III are true
(b) if only conclusion II is true.
71. Statements: H $ J, J © M, M @ T
(c) if either I or II is true.
(d) if neither I nor II is true. Conclusions: I. H % M II. H $ T III. T % J
(a) Only I is true (b) Only III is true

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(e) if both I and II are true.
‘P b Q’ means ‘P is not smaller than Q’. (c) Only II is true (d) Only I and II are true
‘P + Q’ means ‘P is neither greater nor smaller than Q’. (e) None of these

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‘P $ Q’ means ‘P is not greater than Q’. 72. Statements: R @ N, N % E, E # K
‘P a Q’ means ‘P is neither smaller than nor equal to Q’. Conclusions: I. R © K II. K % N III. E % R
‘P * Q’ means ‘P is neither greater than nor equal to Q.
(a) None is true (b) Only I is true
64. Statements: M b N, H $ Q, Q b M
(c) Only II is true (d) Only III is true
Conclusions: I. H + M II. Q b N
65. Statements: C α B, L * S, S $ C (e) Only II and III are true

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Conclusions: I. B α S II. C α L 73. Statements: M © K, K % T, T $ R
66. Statements: I b H, E a F, I + F Conclusions: I. R © K II. R © M III. T © M
Conclusions: I. E α I II. H * E (a) Only I is true (b) Only II is true
67. Statements: V + O, R + V, O b B (c) Only III is true (d) Only I and II are true
Conclusions: I. R + B II. R a B
68. Statements:
Conclusions:
L α U, T + V, U * V
I. T a L
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II. U + T
(e) None of these
74. Statements: D # W, W $ Z, Z % M
Conclusions: I. Z @ D II. M © D III. D $ M
69. Statements: A * B, A b Z, Y * Z
Conclusions: I. Y * B II. A b Y (a) Only I and II are true (b) Only II and III are true
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Directions (70-76): In the following questions, the (c) Only I & III are true (d) All are true
symbols $, @, ©, % and # are used with the following (e) None of these
meaning as illustrated below: 75. Statements: K % N, N $ B, B © D
‘P $ Q’ means ‘P is not smaller than Q’. Conclusions: I. D % N II. K % D III. B © K
‘P @ Q’ means ‘P is not greater than Q’. (a) None is true (b) Only II is true
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‘P © Q’ means ‘P is neither greater than nor equal to Q’.

(c) Only III is true (d) Only I is true
‘P % Q’ means ‘P is neither smaller than nor equal to Q’.
(e) Only II and III are true
‘P # Q’ means ‘P is neither greater than nor smaller than
76. Statements: T # A, A $ B, B @ D
Q’.
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Now in each of the following questions assuming the Conclusions: I. D # A II. D # T III. B @ T
given statements to be true, find which of the (a) None is true (b) Only I is true
conclusions I, II and III given below them is / are (c) Only II is true (d) Only III is true
definitely true and give your answer accordingly. (e) Only II and III are true
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Directions (1-5): In these questions, relationship 1. Statements: L = P ≤ W < V ≤ K ≥ Q; B < L; K = M

between different elements is shown in the statements. Conclusions: I. B < V II. M > P
(a) Only conclusion I is true
The statements are followed by conclusions. Study the
(b) Only conclusion II is true
conclusions based on the give statements and select the (c) Either conclusion I or II are true
appropriate answer: (d) Both conclusion I and II are true
(e) Neither conclusion I nor II is true

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2. Statements: L = P ≤ W < V ≤ K ≥ Q; B < L; K = M 8. Statements: Z=M<T≥F>U
Conclusions: I. L > Q II. W = M Conclusions: I. Z < F II. U < M
(a) Either conclcusion I or II is true (a) Only conclusion I is true
(b) Neither conclusion I nor II is true (b) Both conclusion I and II is true
(c) Only conclusion I is true (c) Only conclusion II is true
(d) Only conclusion II is true (d) Either conclusion I or II is true
(e) Both conclusion I and II are true (e) Neither conclusion I nor II is true
3. Statements: R ≤ U = B < S; B ≤ X 9. Statements: S < T ≥ O = R; T < T

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Conclusions: I. X > R II. X = R Conclusions: I. V > S II. R < V
(a) Both conclusion I and II are true (a) Either conclusion I or II is true
(b) Either conclcusion I or II is true (b) Neither conclusion I nor II is true

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(c) Only conclusion I is true (c) Only conclusion II is true
(d) Neither conclusion I nor II is true (d) Only conclusion I is true
(e) Only conclusion II is true (e) Both conclusion I and II are true
4. Statements: C > U ≤ S < T = O > D ≥ Y; Z = O ≤ P 10. Statements: M<A≤L=V<B≥V
Conclusions: I. U > D II. S < P Conclusions: I. B > A II. T ≤ M
(a) Neither conclusion I nor II is true (a) Only conclusion I is true

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(b) Both conclusion I and II are true (b) Only conclusion II is true
(c) Only conclusion I is true (c) Both conclusion I and II are true
(d) Either conclusion I or II is true (d) Either conclusion I or II is true
(e) Only conclusion II is true (e) Neither conclusion I nor II is true
5. Statements:
Conclusions: I. Z > Y II. C < O
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C > U ≤ S < T = O > D ≥ Y; Z = O ≤ P Directions (11-15): In these questions, relationship
between different elements is shown in the statements.
(a) Only conclusion I is true The statements are followed by conclusion. Study the
(b) Both conclusion I and II are true conclusions based on the given statement(s) and select
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(c) Only conclusion II is true the appropriate answer.
(d) Either conclusion I or II is true 11. Statements: P<L≤A>M=K≥E
(e) Neither conclusion I nor II is true Conclusions: I. K ≤ L II. P < E
Directions (6-10): In each question, a relationship (a) Only conclusion II is true
between different elements is shown in the statements. (b) Either conclusion I or II is true.
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The statements are followed by conclusions. Study the (c) Both conclusion I and II are true.
conclusion based on the given statements and select the (d) Neither conclusion I nor II is true.
appropriate answer. (e) Only conclusion I is true.
6. Statements: C<O≥M>P=T>S 12. Statements: P > R = A < Y; D < A
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Conclusions: I. S < O II. T < C Conclusions: I. P > D II. D < Y

(a) Either conclusion I or II is true (a) Both conclusion I and II are true.
(b) Both conclusion I and II are true (b) Only conclusion I is true.
(c) Neither conclusion I nor II is true (c) Neither conclusion I nor II is true.
(d) Only conclusion I is true (d) Either conclusion I or II is true.
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(e) Only conclusion II is true (e) Only conclusion II is true.

7. Statements: S < T ≥ O = R; T < V 13. Statements: P > R = A < Y; D < A
Conclusions: I. R < S II. T ≥ R Conclusions: I. P < Y II. R ≤ D
(a) Either conclusion I or II is true (a) Both conclusions I and II are true.
(b) Both conclusion I is true (b) Neither conclusion I nor II is true.
(c) Only conclusion I is true (c) Only conclusion I is true.
(d) Only conclusion II is true (d) Only conclusion II is true.
(e) Neither conclusion I nor II is true (e) Either conclusion I or II is true.

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14. Statements: C ≥ R > A = S ≤ H; R < P < Q 20. Statements: H#G; H#I&J; M#F%I
Conclusions: I. C > S II. P < C Conclusions: I. G%J II. F@H III. I@M
(a) Either conclusion I or II is true. (a) Both I and II (b) Only I
(b) Both conclusion I and II are true. (c) Only III (d) Both I and III
(c) Only conclusion II is true (e) Only II
(d) Neither conclusion I nor II is true. Direction (21-25): In each of the questions below are
(e) Only conclusion I is true. given some statements followed by two conclusions. You
15. Statements: C ≤ R > A = S ≤ H; R < P < Q have to take the given statements to be true even if they

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Conclusions: I. H ≥ R II. R < Q seem to be at variance with commonly known facts. Read
(a) Both conclusions I and II are true. all the conclusions and then decide which of the given
(b) Only conclusion II is true. conclusions logically follows from the given statements

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(c) Only conclusion I is true. disregarding commonly known facts.
(d) Either conclusion I or II is true (a) If only conclusion I follows.
(e) Neither conclusion I nor II is true. (b) If only conclusion II follows.
Directions (16-20): In the following questions, the (c) If either conclusion I or II follows.
symbols @, #, $, % and & are used with the following (d) If neither conclusion I nor II follows.

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meaning as illustrated below- (e) If both conclusions I and II follow.
'P@Q' means 'P is neither smaller than nor equal to Q' 21. Statements: J>Z ≥ R<Q=P, R>S<J
'P#Q' means 'P is neither greater than nor equal to Q' Conclusions: I. Z < R II. J>P
'P$Q' means 'P is neither smaller than nor greater than Q' 22. Statements: M≤B=C>D, A≥B<K
'P%Q' means 'P is not greater than Q' Conclusions: I. M < K II. D < A
'P&Q' means 'P is not smaller than Q'
Now in each of the following questions assuming the
m 23. Statements: E>F=G≥S, T≤G≥H
Conclusions: I. E < S II. T < F
given statements to be true, find which of the three 24. Statements: P>Q≤R<S≤T=U>V=W
conclusions I, II and III given below them is/are Conclusions: I. R < P II. Q < T
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definitely true and give your answer accordingly. 25. Statements: J>K≤L<M≤N=O>P=Q
16. Statements: N@V$W, W%K#L, L%R Conclusions: I. J < L II. M > J
Conclusions: I. L@N II. K#R III. V%R Directions (26-30): In these questions, relationship
(a) Only I (b) Both II and III between different elements is shown in the statements.
(c) Only I and II (d) Only II These statements are followed by two conclusions.
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(e) All I, II, III Mark answer as:

17. Statements: J#K&L, L@M$O, O@N%G (a) If only conclusion I follows.
Conclusions: I. G&M II. K@O III. M@G (b) If only conclusion II follows.
(a) Either I or III (b) II and Either I or III (c) If either conclusion I or II follows.
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(c) Only I (d) I and Either II or III (d) If neither conclusion I nor II follows.
(e) Both I and II (e) If both conclusions I and II follow.
18. Statements: N#M&L; L#J&O; O&V 26. Statements: A≥M≥H≥K≥L<N≤B
Conclusions: I. M@N II. J#V III. L%N Conclusions: I. A > L II. B ≥ K
(a) Only I (b) Only II 27. Statements: A≥M≥H≥K≥L>N≥B
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(c) Both I and II (d) Both II and III Conclusions: I. A ≥ B II. B < K
(e) None of these 28. Statements: P < A ≤ R = K, S ≤ R ≤ N,
19. Statements: A@B&D; D%E#F; H@G&D Conclusions: I. N > P II. K ≤ N
Conclusions: I. D#A II. F@D III. H%E 29. Statements: M ≤ E ≤ L ≤ T > S, L > V
(a) Both I and II (b) Only II Conclusions: I. V ≥ S II. S > V
(c) Both II and III (d) Only I 30. Statements: P < A ≤ R = K, S ≤ R ≤ N
(e) All I, II, III Conclusions: I. K > A II. A ≤ K

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Direction (31-33): In each of the questions below are 38. Statements: J>K≥H=U≥B≤T<F≤R
given some statements followed by two conclusions. You Conclusions: I. J>B II. H<R
have to take the given statements to be true even if they (a) if only conclusion II is true.
seem to be at variance with commonly known facts. Read (b) if either conclusion I or II is true.
all the conclusions and then decide which of the given (c) if neither conclusion I nor II is true.
conclusions logically follows from the given statements (d) if only conclusion I is true.
disregarding commonly known facts. (e) if both conclusions I and II are true.
(a) If only conclusion I follows. Directions (39-41): In these questions, relationship
(b) If only conclusion II follows. between different elements is shown in the statements.

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(c) If either conclusion I or II follows. Two conclusions follow these statements:
(d) If neither conclusion I nor II follows. Give answer,
(e) If both conclusions I and II follow. (a) If only conclusion I follows.

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31. Statements: V>B≥G=H>F<D≤T, Q<W=E≤F (b) If only conclusion II follows.
Conclusions: I. B>W II. E≥B (c) If either conclusion I or II follows.
32. Statements: II: M<N=B≤V>C, L>K≥J=H≥B (d) If neither conclusion I nor II follows.
Conclusions: I. N?H II. B>J (e) If both conclusion I and II follow.
33. Statements: P=L>O≥K>U>M, N<H≤M=B<K 39. Statements: B<W≤A<D≤K<I
Conclusions: I. L>B II. N<U Conclusions: I. W < I II. K ≥ W

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Directions (34-38): In these questions, a relationship 40. Statements: L=K≥R>D≥M<N
between different elements is shown in the statements. Conclusions: I. N < R II. R > M
The statements are followed by two conclusions. Give 41. Statements: L < K, N ≤ M < R, K = N
answer Conclusions: I. N < R II. R > L
34. Statements: L ≤ T ≤ I ≥ M < X, W < P ≤ L ≥ B ≥ K Directions (42-46): In these questions, relationship
Conclusions: I. K<X II. W>M
(a) if only conclusion II is true.
m between different elements is shown in the statements.
The statements are followed by conclusions.
Give answer
(b) if only conclusion I is true.
(a) If only conclusion I is true
(c) if neither conclusion I nor II is true.
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(b) If only conclusion II is true
(d) if either conclusion I or II is true.
(c) If either conclusion I or II is true
(e) if both conclusions I and II are true.
(d) If neither conclusion I nor II is true
35. Statements: Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G
(e) If both conclusions I and II are true
Conclusions: I. Z<Y II. S>Q
42. Statements: X ≥ G = H; G > J ≥ L; J ≥ K < Y
(a) if both conclusion I and II are true.
Conclusions: I. X > L II. K < G
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(b) if only conclusion I is true.

43. Statements: A > B = R ≥ S ≥ T; X < J ≤ K < T
(c) if neither conclusion I nor II is true.
Conclusions: I. A > X II. R ≥ T
(d) if either conclusion I or II is true.
44. Statements: M > L ≥ K ≤ J; N ≥ R ≥ S = M
(e) if only conclusion II is true.
Conclusions: I. R > J II. J ≥ R
36. Statements: L≤T≤I≥M<X,W<P≤L≥B≥K
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45. Statements: C ≥ D = E; A = B ≤ S ≥ C
Conclusions: I. K≥M II. P>M
Conclusions: I. C < A II. D ≤ B
(a) if only conclusion II is true.
46. Statements: X ≥ G > H ≥ I; M > H ≥ L
(b) if either conclusion I or II is true. Conclusions: I. X > M II. X > L
(c) if neither conclusion I nor II is true. Directions (47-50): In these questions, relationship
(d) if only conclusion I is true. between different elements is shown in the statements.
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(e) if both conclusions I and II are true. The statements are followed by conclusions.
37. Statements: Z < U ≤ D ≤ A ≤ M < S, Q > A ≤ Y < G Give answer
Conclusions: I. M≥U II. G>Z (a) If only conclusion I is true
(a) if only conclusion II is true. (b) If only conclusion II is true
(b) if only conclusion I is true. (c) If either conclusion I or II is true
(c) if neither conclusion I nor II is true. (d) If neither conclusion I nor II is true
(d) if either conclusion I or II is true. (e) If both conclusions I and II are true
(e) if both conclusions I and II are true. Year: 2020 IBPS Clerk Pre

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47. Statements: F>R≥T=E>W≤Q 56. Statements: P=L>O≥K>U>M, N<H≤M=B<K
Conclusions: I. E < F II. Q ≥ T Conclusion I. L>B II. N<U
48. Statements: W=G≥H≥T=C≤V≤B Directions (57-60): In these questions, relationships
Conclusions: I. T < G II. C = G
between different elements are shown in the statements.
49. Statements: K>I≥G>F≤T<R
These statements are followed by two conclusions. Give
Conclusions: I. K > T II. R > F
50. Statements: K<G≤D<C>R≤Y answer
Conclusions: I. C > G II. K < D (a) If only conclusion I follows.
Directions (51-53): In these questions, relationships (b) If only conclusion II follows.

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between different elements are shown in the statements. (c) If either conclusion I or II follows
These statements are followed by two conclusions. Give (d) If neither conclusion I nor II follows.
answer

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(e) If both conclusions I and II follow.
(a) if only conclusion I is true
Year: 2020 RRB PO Pre
(b) if only conclusion II is true
57. Statements: Z>O=G<IS>P
(c) if either conclusion I or conclusion II is true
(d) if neither conclusion I nor conclusion II is true Conclusions: I. S > O II. P > G
(e) if both conclusions I and II are true 58. Statements: K  M > W  T  Y< Q

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Year: 2020 IBPS PO Pre Conclusions: I. T < Q II. T < K
51. Statement: D > G ≤ H = J; J > F ≥ L; K = L 59. Statement: J  V < R > M, L> M = I  H
Conclusions: I. H > F II. K ≤ G Conclusions: I. V  H II. H  M
52. Statement: V < Q ≤ R; W = R > M; W > P ≥ X
60. Statement: I=HBN<D>L
Conclusions: I. P > Q II. Q ≥ X
53. Statement: W > S = Q; S ≤ N = O ≥ Y
Conclusions: I. Q ≤ N II. W ≥ O
m Conclusions: I. B < N II. L > H
Directions (61-63): In each of the question, relationships
between some elements are shown in the statements.
Direction (54-56): In each of the questions below are
given some statements followed by two conclusions. You These statements are followed by conclusions numbered
xa
have to take the given statements to be true even if they I and II. Read the statements and give the answer.
seem to be at variance with commonly known facts. Read (a) If only conclusion I follows.
all the conclusions and then decide which of the given
(b) If only conclusion II follows.
conclusions logically follows from the given statements
(c) If either conclusion I or II follows.
disregarding commonly known facts.
(a) If only conclusion I follows. (d) If neither conclusion I nor II follows.
te

(b) If only conclusion II follows. (e) If both conclusion I and II follows.

(c) If either conclusion I or II follows. Year: 2020 SBI Clerk Pre
(d) If neither conclusion I nor II follows. 61. Statements: P>Q≥R=S<T=U
(e) If both conclusions I and II follow. Conclusions: I. Q > S II. S = Q
ce

Year: 2020 RBI Assistant Pre 62. Statements: J<D=L≤K≤Q≥R

54. Statements: V>B≥G=H>F<D≤T, Q<W=E≤F
Conclusions: I. J < Q II. L ≤ R
Conclusion I. B>W II. E≥B
55. Statements: M<N=B≤V>C, L>K≥J=H≥B 63. Statements: O>P=G>B≥X=M≤H
Conclusion I. N≤H II. B>J Conclusions: I. G > X II. O > M
@

Solutions

Directions (1-10) 4. (b): F < N = D > T, only II is true.

1. (e): J > M > R ≥ N, Both are true. 5. (a): J>M>R≥N
2. (b): F < N = D > T, only II is true. 6. (b): Z ≥ H > B < K, only II is true.
3. (d): Z ≥ H > B < K, none is true. 7. (a): H ≤ R < M = J, only I is true.

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