Reasoning: Inequalities Set 1

Directions (1 – 5): In the following questions, the symbols %, @, #, $ and & are used with the following meaning as illustrated below:
‘P%Q’ means ‘P is neither smaller than nor equal to Q’.
‘P@Q’ means ‘P is neither greater than nor equal to Q’.
‘P#Q’ means ‘P is not greater than Q’.
‘P$Q’ means ‘P is not smaller than Q’.
‘P&Q’ means ‘P is neither smaller than nor greater than Q’.
Now in each of the following questions, assuming the given statements to be true, find which of the four conclusions I, II, and III given below them is/are definitely true and give your answer accordingly.

1. Statements: A%S, S$W, W&F, F@X
   Conclusions:
   I. S%F
   II. W@A
   III. X%W
   A) Only I
   B) Only II
   C) Both II and III
   D) All I, II and III
   E) Only I and II
   
   View Answer

   Option C
   A > S ≥ W = F < X, so S ≥ F, A > W and W < X
   
2. Statements: R&W, W#C, C%A, A$V
   Conclusions:
   I. C&R
   II. A%W
   III. V@C
   A) Only II
   B) Only I
   C) Only I and III
   D) Only III
   E) None of these
   
   View Answer

   Option D
   R = W ≤ C > A ≥ V, so R≤ C, no relation between A and W, C > V
   
3. Statements: A@D, D$M, M#S, S&J
   Conclusions:
   I. A$M
   II. J&D
   III. A@M
   A) Either I or III
   B) Only I
   C) Only II and III
   D) All I, II and III
   E) Either I or III and II
   
   View Answer

   Option A
   A < D ≥ M ≤ S = J, so no relation between D and J and no relation between M and A
   In I and III we see subject predicate same and since no relation and I is A ≥ M and III is A < M so either or
   
4. Statements: C#A, X%A, R$X, R@S
   Conclusions:
   I. R%A
   II. R$A
   III. C@S
   A) Both I and II
   B) Both I and III
   C) Both II and III
   D) Either I or II and III
   E) Only I
   
   View Answer

   Option B
   C ≤ A < X ≤ R < S, so R > A, C < S
   
5. Statements: X$E, E%W, W&Q, Q@A
   Conclusions:
   I. A@W
   II. X%Q
   III. E&A
   A) Only III
   B) Both I and II
   C) All I, II and III
   D) Both II and III
   E) None of these
   
   View Answer

   Option E
   X ≥ E > W = Q < A, so A > W, X > Q and no relation between E and A
   

Direction (6-10): Relationship between different elements is shown in the statements. Find if the conclusions also follow or not.

1. Statements: W > S ≤ Q, D ≤ S, I ≤ B = D
   Conclusions:
   I. Q ≥ I
   II. Q = I
   A) only I follows
   B) only II follows
   C) either I or II follows
   D) neither I nor II follow
   E) both I and II follow
   
   View Answer

   Option A
   Q ≥ S ≥ D ≥ I.
   So Q ≥ I
   
2. Statements: Q < D ≤ A, C > A < K, D ≥ S Conclusions: I. K > D
   II. C > S
   A) only I follows
   B) only II follows
   C) either I or II follows
   D) neither I nor II follow
   E) both I and II follow
   
   View Answer

   Option E
   K > A ≥ D , so K > D
   C > A ≥ D ≥ S so C > S
   
3. Statements: S > N ≥ F, P = N, E > S
   Conclusions:
   I. E > P
   II. F < E
   A) only I follows
   B) only II follows
   C) either I or II follows
   D) neither I nor II follow
   E) both I and II follow
   
   View Answer

   Option E
   E > S > N = P, so E > P
   F ≤ N < S < E, so F < E
4. Statements: E ≥ L > K, L > F < D, P > E
   Conclusions:
   I. P > D
   II. E > F
   A) only I follows
   B) only II follows
   C) either I or II follows
   D) neither I nor II follow
   E) both I and II follow
   
   View Answer

   Option B
   P > E ≥ L > F < D, so relation cant be determined between P and D E ≥ L > F, so E > F
   
5. Statements: Q ≥ X ≥ S, S < A, A > E
   Conclusions:
   I. E > X
   II. X ≥ E
   A) only I follows
   B) only II follows
   C) either I or II follows
   D) neither I nor II follow
   E) both I and II follow
   Explanation:
   
   View Answer

   Option C
   E < A > S ≤ X, so relation cant be determined between E and X, but is for sure that either E is greater than X or is less than equal to X, so either or between the two