Inequalities rules - simple tricks and techniques

Symbols - Type 1
symbol 1: ">" means Greater than
symbol 2: "<" means Less than
symbol 3: "=" means Is equal to

Inequalities Rules:
1) >  >  gives  >
2) >  =  gives  >
3) > <   Cannot be determined
4) < < gives  <
5) < = gives  <
6) = = gives =
7) <  >  Cannot be determined

Point No 1:  
A>B>C → A>B and B>C and A>C  (As '>' and '>' → ">")
A=B>C → A=B and  B>C and A>C  (As  '=' and '>' → "> ")
A>B=C → A>B and  B=C and A>C (As '> ' and  '='  → "> ")
A>B<C → A>B and  B<C and Relation between A and C cannot be determined (Because A and C have opposite signs between them )

Point No 2:
Sponsored links
A<B>C → A<B and B>C and relation between A and C cannot be determined (Because A and C have opposite signs between them)
A<B<C → A<B and B<C and A<C  (As '<' and '<' → "<")
A<B=C → A<B and B=C and A<C  (As '< ' and  '='  → "< ")
A=B <C → A=B and B<C and A<C (As  '=' and'<'    → "< ")


Symbols - Type 2
Symbol 4 :  " ≤ " which  means Less than or Equal to
Symbol 5 : " ≥ " Which means Greater than or Equal to 

Inequalities Rules :
1) ≥  ≥ gives  >
2) ≥ = gives ≥
3) > ≥ gives >
4) ≥ > gives >
5) ≥ ≤  Cannot be determined 
6) ≤ ≤ gives <
7)≤ < gives <

Point No 3:
A≥B≥C →  A≥B and B≥C and A>C 
A=B≥C → A=B and B≥C and A≥C 
A>B≥ C → A>B and B≥C and A>C
A≥B<C →A≥B and B<C and Relation between A and C cannot be determined (Because A and C have opposite signs between them)
Point No 4:
A≤B≤C → A≤B and B≤C and A<C 
A=B≤C →A=B and B≤C and A≤C
A<B≤C → A<B and B≤C and A<C
A≤B≥C → A≤B  and B≥C and Relation between A and C cannot be determined ( Because and A and C have opposite signs between them)


Let's see some examples and apply above points

Question 1

Statement:   A ≤ B = C > D >E
Conclusions: I. A < E    II. E < B

   A) Only conclusion I follows

   B) Only conclusion II follows

   C) Either conclusion I or II follows

   D) Neither conclusion I nor II follows

Solution:

First see conclusion no 1 .  we have to check relation between A and E .

So check for all symbols between A and E  . Now we can write relation between A and E as

A  ≤ = > > E . we can see  < and > symbols between them . So relation cannot be determined.

Next see conclusion no II.  We have to check relation between E and B

So check for all symbols between  E and B . Now  we can write  relation between E and B as

B = > > E  . We can easy say  E is definitely less than  B . So Conclusion II  follows

Correct answer: B  

Questions 2

Statement:   M ≤ N < O > P = Q

Conclusion: I. Q <O   II. P< N

   A) Only conclusion I follows

   B) Only conclusion II follows

   C) Either conclusion I or II follows

   D) Neither conclusion I nor II follows

Solution:

First go for conclusion I.  we have to check relation between Q and O

So check for all symbols between Q and O .  We can write relation between Q and O as

O > = Q.  We can see O is  Greater than Q . so Conclusion I follows

Next go for conclusion II. We have to check relation between P and N

So check for all symbols between   P and N . wec can write relation between P and N as

  N < > P . We can see there is one less than symbol and one greater than symbol . so we cannot determine relation between N and P.

Correct Answer: A

Question 3

Statement:   J > K ≤ L = M < N

Conclusion:  I. K < N   II.  K=M

  A) Only conclusion I follows

   B) Only conclusion II follows

   C) Either conclusion I or II follows

   D) Neither conclusion I nor II follows

Solution:

  Conclusion I → between K and N . So check relation between them  i. e K ≤ = < N

So , K is less than N . and Conclusion I follows

Conclusion 2 → between K and M. So check relation between them I .e K ≤ = M

So K ≤ M only . So conclusion II does not follow

Correct answer: A

Question 4

Statement:  M ≤ N = O, Q >O =P

Conclusion: I. M = P    II. M < P

  A) Only conclusion I follows

   B) Only conclusion II follows

   C) Either conclusion I or II follows

   D) Neither conclusion I nor II follows

Solution :

 Conclusion I → Relation  between M and P . so check for relation between them . i. e M ≤ = P ( because  O = P, replace O position with P in the statement) .  So M is only less than or equal to P , not equal to P. Conclusion I does not follow

Conclusion  II → Relation between M and P again . as we already know M can be either greater than or equal to P . So if Conclusion I is true then conclusion II will be false and vice versa. So correct answer is Either I or II follows

Correct Answer : C

Question 5

Statement:  M ≤ N = O, Q >O =P

Conclusion: I. N = Q    II. M <P

   A) Only conclusion I follows

   B) Only conclusion II follows

   C) Either conclusion I or II follows

   D) Neither conclusion I nor II follows

Solution:

 Conclusion I → relation between N and Q . So check symbols between them I .e  N =  < Q ( here statement is divided in to two parts to confuse students . don’t worry  before proceeding write down the statement combining both parts as follows M ≤ N = P = O < Q . ) So relation between N and Q is N = = < Q . which means N is less than Q . So conclusion I does not follow

Conclusion II →  M and P . check symbols between M and P i.e M ≤ =  P . so M is less than or equal to P .So  conclusion II does not follows

Correct answer : D

Question 6

Statement:  A ≥ B > C ≤ D , P <C

Conclusion: I.P>D   II. B < P  III.  A = C

   A) Only I follows

   B) Only II follows

   C) Only III follows

   D) None follows

Correct Answer:   A ≥ B ≥   C > P  ≤ D

Correct answer: D

Question 7

Statement:  P ≤ Q < R ≥ S, Q ≥ G

Conclusion: I. G < S   II. R > S  III. R = S

   A) Only I & III follow

   B) Only I & II follow

   C) All follow

   D) Either II or III follows

Answer:  D

Question 8

Statement:  R = O ≥ L ,  B ≤ A , A < L

Conclusion: I. L=R  II.O > B  III. A < R

   A) All follow

    B) Only I & II follow

   C) Only I & III follow

   D) Only II & III follows

Correct answer: R = O ≥ L > A ≥B

Correct answer: D

Question 9 

Statement :  A ≥ B > C ≥  D < E , A < G

Conclusion : I. G > B   II. G >D  III. C > A

   A) Only I & III follow

   B) Only I & II follow

   C) All follow

  D) Only II & III follow

Solution : G >A >D

Correct answer : B  

Question 10: 

Statement:  E > K ≥ T < M , K ≤ N > T

Conclusion: I. N > E II. T < E  III. N > M

   A) Only I & II follow

   B) All follow

  C) Only II & III follow

   D) None of these

Solution:  E >  N > T  ≥ K  ≥ T < M

 

Correct answer:  D   

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