Inequalities Concepts and its Application:
(i) A > B ≥ C
> is common
A > C
(ii) A ≥ B > C
A > C
Table:
Answer Options:
(1) Only 1 is true
(2) If only 2 is true
(3) Either 1 or 2 true
(4) Neither 1 nor 2 is true
(5) Both 1 and 2 are true
Examples:
1) P > Q > R < S ≥ T
A) (i) P > R (T)
(ii) R < P (T) - (5)
B) (i) P > S (F)
(ii) R > P (F) - (4)
C) (i) R = T (F)
(ii) R > T (F) - (4)
2) P < Q ≤ R < S > T > U≠Z
A) (i) P < S
(ii) Q ≤ S
B) (i) R > T
(ii) S > U
C) (i) S > Z
(ii) R > P
D) (i) P ≤R
(ii) Q ≤ S
E) (i) P > T
(ii) P ≤ S
F) (i) P = Z
(ii) U ≤ R
Answers:
A) (i) T
(ii) F (1)
B) (i) F
(ii) T (2)
C) (i) F
(ii) T (2)
D) (i) F
(ii) F (4)
E) (i) F
(ii) F (4)
F) (i) F
(ii) F (4)
3) M≤ N≤ O< P; K = L≥ O > C
A) (i) M < O
(ii) M ≤ P
B) (i) K ≥ N
(ii) M ≤ O
C) (i) P ≥ K
(ii) P ≤ M
D) (i) M = C
(ii) N > C
E) (i) C > P
(ii) P = C
F) (i) D = O
(ii) D ≤ M
Answers:
A) (i) F
(ii) F-(4)
B) (i) T
(ii) T-(5)
C) (i) F
(ii) F-(4)
D) (i) F
(ii) F-(4)
E) (i) F
(ii) F-(4)
F) (i) F
(ii) F-(4)
4)T < P≤ U ; L> U≤K ; P≥ R
A) (i) K≥ R
(ii) L> R
B) (i) L > U ≥ P
(ii) R ≤ U
C) (i) T < K
(ii) L > T
D) (i) R > L
(ii) R ≤ L
E) (i) U ≤ R
(ii) T < R
Answers:
A) (i) T
(ii) T (5)
B) (i) T
(ii) T (5)
C) (i) T
(ii) T (5)
D) (i) F
(ii) F (4)
E) (i) F
(ii) F (4)
5) A≥B≠ C≥ F ; Z < C ≤ D < E
A) (i) A ≥ B > C
(ii) D ≥ C ≥ F
B) (i) A > E
(ii) D < B
C) (i) B > C
(ii) B < D
4) (i) F > E
(ii) F < E
5) (i) B < C ≥ F
(ii) E ≥ C > B
Answers:
A) (i) F
(ii) F (4)
B) (i) F
(ii) F (4)
C) (i) F
(ii) F (4)
D) (i) F
(ii) T (2)
E) (i) F
(ii) F (4)
Either or condition
1)Subject and predicate of the 2 conclusions should be same (may not be in the same order)
2)Individually both conclusions should be false
3)Both conclusions should cover maximum solutions according to the given statement.
5)A ≥ B≥ C
A) (i) A > C
(ii) A = C
B) (i) C < A
(ii) C = A
C) (i) C ≠ A
(ii) A = C
D) (i) A > C
(ii) A < C
E) (i) A > C
(ii) A ≤ C
Answers:
A) (i) F
(ii) F (3)
2) (i) F
(ii) F (3)
3) (i) F
(ii) F (4)
4) (i) F
(ii) F (4)
5) (i) F
(ii) F (4)
Exceptions to Either Or
6) P > Q > R < S
A) (i) P≤ S
(ii) P≥ S
B) (i) P ≠ S
(ii) S = P
C) (i) U ≤ V
(ii) U ≥ V
D) (i) S>P
(ii) S≤P
E) (i) P≠ T (> ,<)
(ii) P = T
F) (i) U≤ V
(ii) V ≥ U
G) (i) P ≤ T
(ii) P ≥ R
H) (i) P ≤ T
(ii) P > R
Note: Even though T is not there in the statement, but if there is no definite relation between the ‘2’ letters and covers 3 maximum relations, then it is not false.
Answers:
A) (i) F
(ii) F (3)
B) (i) F
(ii) F (3)
C) (i) F
(ii) F (3)
D) (i) F
v (ii) F (3)
E) (i) F
(ii) F (3)
F) (i) F
(ii) F (4)
G) (i) F
(ii) F (4)
H) (i) F
(ii) T (2)
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