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<CA≤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
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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