Reasoning: Inequalities Questions for Upcoming Exam – Set 23

In these following questions the symbols @, #, $, & and % are used with the following meanings.

P @ Q means P is neither greater than nor equal to Q.
P # Q means P is not lesser than Q.
P $ Q means P is neither greater than nor lesser than Q.
P & Q means P is not greater than Q.
P % Q means P is neither lesser than nor equal to Q.
In each of the following questions four statements followed by three conclusions marked I, II and III are given. Assuming the statements to be true, find which of the three conclusions follow(s) the given statements.

1. Statements: A % B, B # C, C @ D, D % E
   Conclusions:
   I. A % C
   II. D @ A
   III. B # E
   Only I follows
   Only II follows
   Only III follows
   Either I or II follows
   All follows
   Option A
   A % B → A > B
   B # C → B ≥ C
   C @ D → C < D
   D % E → D > E
   On combining the given statements:
   A > B ≥ C < D > E
   Conclusions:
   I. A % C → A > C (True as A > B ≥ C)
   II. D @ A → D < A (False as A > B ≥ C < D. There is no relation between A and D)
   III. B # E → B ≥ E (False as B ≥ C < D > E. There is no relation between B and E)
   Hence, only I follows.

    

2. Statements: J % M, J & R, S $ R, S & T
   Conclusions:
   I. J @ S
   II. T % J
   III. J $ T
   Only I follows
   Only II follows
   Only III follows
   Either II or III follows
   None follows
   Option E
   J % M → J > M
   J & R → J ≤ R
   S $ R → S = R
   S & T → S ≤ T
   On combining given statements:
   M < J ≤ R = S ≤ T
   Conclusions:
   I. J @ S → J < S (False as J ≤ R = S and J ≤ S)
   II. T % J → T > J (False as J ≤ R = S ≤ T and T ≥ J)
   III. J $ T → J = T (False as J ≤ R = S ≤ T and J ≤ T)
   Hence, no conclusion follows.

    

3. Statements: T $ X, X # W, W @ Y, Y % Z
   Conclusions:
   I. T % W
   II. X @ Y
   III. Z % W
   None follows
   Both II and III follow
   Both I and III follow
   Either I or III follows
   All follows
   Option A
   T $ X → T = X
   X # W → X ≥ W
   W @ Y → W < Y
   Y % Z → Y ≥ Z
   On combining these statements:
   T = X ≥ W < Y ≥ Z
   Conclusions:
   I. T % W → T > W (False as T = X ≥ W and T ≥ W)
   II. X @ Y → X < Y (False as X ≥ W < Y. There is no relation between X and Y)
   III. Z % W → Z > W (False as W < Y ≥ Z. There is no direct relation between Z and W)
   Hence, no conclusion follows.

    

4. Statements: F @ G, G # J, H @ J, H $ I
   Conclusions:
   I. F % J
   II. I @ G
   III. J % I
   Both I and II follows
   Both II and III follow
   Both I and III follow
   Either I or III follows
   All followsAll follows
   Option B
   F @ G → F < G
   G # J → G ≥ J
   H @ J → H < J
   H $ I → H = I
   On combining these statements:
   F < G ≥ J > H = I
   Conclusions:
   I. F % J → F > J (False as F < G ≥ J. There is no relation between F and J)
   II. I @ G → I < G (True as G ≥ J > H = I)
   III. J % I → J > I (True as J > H = I)
   Hence, both conclusions II and III follows.

    

5. Statements: M # N, O @ N, P & O, P # Q
   Conclusions:
   I. O @ M
   II. N % Q
   III. O # Q
   Both I and II follows
   Both II and III follow
   Both I and III follow
   None follows
   All follows
   Option E
   M # N → M ≥ N
   O @ N → O < N
   P & O → P ≤ O
   P # Q → P ≥ Q
   On combining these statements:
   M ≥ N > O ≥ P ≥ Q
   Conclusions:
   I. O @ M → O < M (True as M ≥ N > O)
   II. N % Q → N > Q (True as N > O ≥ P ≥ Q)
   III. O # Q → O ≥ Q (True as O ≥ P ≥ Q)
   Hence, all conclusions follow.

    

In these questions, a relationship between different elements is shown in the statements. The statements are followed by two conclusions.

6. Statements:A < B < C = D, E = B < F, G > F
   Conclusions:
   I. A > F
   II. G > D
   If only conclusion I is true.
   If only conclusion II is true.
   If either conclusion I or II is true.
   If neither conclusion I nor II is true.
   If both conclusions I and II are true.
   Option D

    

7. Statements: A ≥ B < C; D = B; A < E; F < D < E
   Conclusions:
   I. D > C
   II. A < C
   If only conclusion I is true.
   If only conclusion II is true.
   If either conclusion I or II is true.
   If neither conclusion I nor II is true.
   If both conclusions I and II are true.
   Option D
   

    

8. Statements: P ≤ Q > R = S; S < T; T = P > U; V < U
   Conclusions:
   I. Q = P
   II. Q > P
   If only conclusion I is true.
   If only conclusion II is true.
   If either conclusion I or II is true.
   If neither conclusion I nor II is true.
   If both conclusions I and II are true.
   Option C
   

    

9. Statements:
   A ≥ B = C , C ≤ D ≤ E , F = G > D
   Conclusions:
   I. F < A
   II. E > A
   If only conclusion I is true.
   If only conclusion II is true.
   If either conclusion I or II is true.
   If neither conclusion I nor II is true.
   If both conclusions I and II are true.
   Option D
   

    

10. Statements:
    A ≥ P = S > T, V < B = T > X
    Conclusions:
    I. A > X
    II. P < B
    If only conclusion I is true.
    If only conclusion II is true.
    If either conclusion I or II is true.
    If neither conclusion I nor II is true.
    If both conclusions I and II are true.
    Option A