Inequality concepts

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

  1. 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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