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Inequality Questions and Answers For Competitive Exams


Government exams are seeing increasing level of competition as the level of questions is on steep rise year by year. Inequality is important section of Reasoning Section asked in all kinds of exams. Be it banking, SSC, or any other competitive exams, there are always 2- 4 questions based on this section. Questions where relationship is denoted by <, >, = ≤ or ≥; are considered as Inequality questions. Student have to determine relationship between different variables and come at a conclusion. There is always a possibility of there being more than one solution to a given inequality question. Students are advised to get their basics related to signs clear and attempt question after going through few of our classes on this section. Basic signs and their meaning:



Important Inequality Questions For Government Job Exams



Symbol Inference
X > Y X is greater than Y
X < Y  X is less than Y
X = Y X is neither greater than no equal to Y
X ≤ Y X is smaller than or equal to Y
X ≥ Y X is greater than or equal to Y

Direction (1-20): In the given question, assuming the given statements to be true, find which of the conclusions I and II given below the statements is/are definitely true.



Q-1) Statements: D < J, D = B, J ≤ K, A ≤ B
Conclusions:
J = B
K > A

If only conclusion I follows
If only conclusion II follows
If either conclusion I or conclusion II follows
If neither conclusion I nor conclusion II follows
If both conclusions follow

Q-2) Statements: P≤ Q > M; N ≥ Q > T; M < T
Conclusions:
T > Q
N ≥ P

Only I is true
Only II is true
Either I or II is true
Both I and II are true
Neither I nor II is true

Q-3) Statements: A = B < C; B > D; D > E Conclusions:
I. D < C II. A > E

Only conclusions I is true.
Only conclusions II is true.
Either conclusions I or II is true.
Neither conclusions I nor II is true.
Both conclusions I and II are true.

Q-4) Statements: Q < W > R, W = T, T < S
Conclusions: I. R = T II. S > Q

Only conclusions I is true.
Only conclusions II is true.
Either conclusions I or II is true.
Neither conclusions I nor II is true.
Both conclusions I and II are true.

Q-5) Statements: A > B ≤ C; B > D > E; A < F ≤ G Conclusions:
I. A > E II. F > D

Only II is true
Only I is true
Both I and II are true
None is true
Either I or II is true

Q-6) Statements: P < Q ≥ R; R < S ≤ T; Q > U ≤ T Conclusions:

P > T
Q ≥ S

Only II is true
Only I is true
Both I and II are true
None is true
Either I or II is true

Q-7) Statements: 1 < 2 < 3; 3 ≤ 4 > 5; 6 > 7 ≥ 1 Conclusions:
I. 7 ≥ 3
7 < 3

Only II is true
Only I is true
Both I and II are true
None is true
Either I or II is true

Q-8) Statements: 10 > 9 = 8; 10 < 11 ≤ 12; 11 > 13 = 14 Conclusions:
12 ≥ 14
13 > 9

Only II is true
Only I is true
Both I and II are true
None is true
Either I or II is true

Q-9) Statements: P ≤ Q = R; R ≤ S > T; T = U > V Conclusions:
S > P
S = P

Only II is true
Only I is true
Both I and II are true
None is true
Either I or II is true
Q-10) Statements: P ≤ Q > R ≥ S; T > R < X Conclusions:
X > S
Q > S

Only conclusion I follows.
Both conclusions I & II follow.
Only conclusion II follow.
Either I or II follows.
Neither conclusion I nor conclusion II follows.

Q-11) Statements: A > E > C ; C = D ; E < F Conclusions:
D < E
C < A
A > F

Either II or III is correct.
Only conclusion III is incorrect.
Neither II nor III are correct.
All conclusions are correct.
Only conclusion I is correct.

Q-12) Statements: A > B = C; D < E = B; F > E Conclusions:
F > C
A < F III. D > A

No conclusion is correct.
Only conclusion II is incorrect.
Neither I nor III are correct.
All conclusions are correct.
Only conclusion I is correct.

Q-13) Statements: > D > E; A > D; F < E < B Conclusions:
B > F
A > C III. D < B

Conclusions I and III are correct.
Only conclusion II is incorrect.
Conclusion II is correct.
All conclusions are correct.
Only conclusion I is correct.

Q-14) Statements: C ≥ D, D ≤ F, F > G, G < H Conclusions:
C > F
H > F
G < D

Only I follows
Only II follows
Only III follows
Both I and II follow
None follows

Q-15) Statements: G < I, I ≥ K, K = M, M < O Conclusions:
I ≥ M
K G>K

Only I follows
Both II and III follow
Both I and II follow
All follow
Both I and III follow

Q-16) Statements: ≥ E > F = A ≤ U < L ≥ T = R Conclusions:
F < L
D > A

None is true
I are True
Only II is True
Only I is True
Either I and II is True

Q-17) Statements: J ≥ N ≤ T; T = S > R; K > V ≥ J Conclusions:
I. V ≥ N II. K > J

Only II is true
Only I is true
Either I or II is true
Both I and II are true
None of these

Q-18) Statements: Q ≤ R; S < T; P > Q; R > S Conclusions:
I. S = Q II. T ≥ P

Only I is true
Only II is true
Either I or II true
Neither I nor II is true
Both I and II is true

Q-19) Statement: X < C, W > D, G ≥ W, C = D Conclusion:
I. C ≤ G II. W > X

None is true
Only II is true
Both I and II are true
Only I is true
Either I or II is true

Q-20) Statements: D = F; B > C; D < C; A > B Conclusions:
I. C ≥ F II. B > F

Only I is true
Only II is true
Either I or II is true
Neither I nor II is true
Both I and II is true

Explanation:

Solution 1

Given: D < J, D = B, J ≤ K, A ≤ B
On combining: A ≤ B = D < J ≤ K Conclusions:
J = B → False
K > A → True
Hence, option b is correct.

Solution 2
Given statements: P ≤ Q> M; N ≥ Q > T; M < T On combining: P ≤ Q> M < T; N ≥ Q > T
Conclusions:
T > Q →False (as Q> M < T, the relation between T and Q is not clear)
N ≥ P →True (as P ≤ Q ≤ N → N ≥ P) Hence, only II is true.

Solution 3
On combining: D < B < C; A = B > D > E D < C is true as D < B < C.
A > E is true as A > D > E. Hence both the conclusions are true.

Solution 4
On combining: Q < W = T < S; R < W = T < S
= T → False as R > T
> Q → True as Q < W = T < S.Hence only conclusion II is true.

Solution 5
Given statement: A > B ≤ C; B > D > E; A < F ≤ GOn combining: G ≥ F > A > B > D > E Conclusion:
I. A > E → True (as A > B > D > E → A > E)
F > D → True (as F > A > B > D → F > D) Hence, both conclusion I and II are true.

Solution 6
Given statement: P < Q ≥ R; R < S ≤ T; V > U ≤ TOn combining: P < Q ≥ R < S ≤ T ≥ U < V Conclusion:
P > T → False (as P < Q ≥ R < S ≤ T) thus clear relation between P and T cannot be determined as the symbols are in reverse order.
Q ≥ S → False (as Q ≥ R < S) thus clear relation between Q and S cannot be determined as the symbols are in reverse order.
Hence, none is true.

Solution 7
Given statement: 1 < 2 < 3; 3 ≤ 4 > 5; 6 > 7 ≥ 1
On combining: 6 > 7 ≥ 1 < 2 < 3 ≤ 4 > 5
Conclusion:
7 ≥ 3 → False (as 7 ≥ 1 < 2 < 3) thus clear relation between 7 and 3 cannot be determined
7 < 3 → False (as 7 ≥ 1 < 2 < 3) thus clear relation between 7 and 3 cannot be determined
Therefore, conclusions I and II forms complementarypairs. All the three relations are given.
Hence, either I or II follows

Solution 8
Given statement: 10 > 9 = 8; 10 < 11 ≤ 12; 11 > 13 = 14
On combining: 12 ≥ 11 > 10 > 9 = 8; 11 > 13 = 14 Conclusion: I. 12 ≥ 14 → False (as 12 ≥ 11→ 11 > 13→ 13 = 14) „>‟
symbol is there between 12 and 14. Thus, the relation between 12 and 14 is ‟12 > 14‟.
II. 13 > 9 → False (as 13 < 11 > 10 > 9) thus clear relation between 13 and 9 cannot be determined as the symbols are in reverse order.
Hence, none is true is true.

Solution 9
Given statement: P ≤ Q = R; R ≤ S > T; T = U > VOn combining: P ≤ Q = R ≤ S > T = U > V
Conclusion:
S > P → False (as P ≤ Q = R ≤ S → P ≤ S)
S = P → False (as P ≤ Q = R ≤ S → P ≤ S)So either S > P or S = P is true Hence, either I or II follows.

Solution 10
Given: P ≤ Q > R ≥ S; T > R < X
On combining: P ≤ Q > R < X; R ≥ S, R < T
X > S - True (R < X; R ≥ S)
Q > S - True (Q > R ≥ S)
Hence, the conclusions I & II follows.

Solution 11
Given statements: A > E > C ; C = D ; E < F Conclusions:
D < E → True ( as D = C < E < A → thus D < E )
C < A → True (as D = C < E < A → thus C < A )
A > F → False (as D = C < E < A ; E < F → thus theclear relation between A and F cannot be determined) Hence, conclusion I and II are correct and conclusion IIIis incorrect.

Solution 12
Given statements: A > B = C; D < E = B; F > E
Conclusions:
F > C → True (as F > E = B = C → thus we can conclude that F > C)
A < F → False (as A > B = C = E > D; F > E = B = C
→ F > B = C = E > D; A > B but the clear relation between A and F cannot be determined)
D > A → False (as A > B = C = E > D → D < A;thus, it is clear that the given conclusion is incorrect.) Hence conclusion I is correct.

Solution 13
Given statements: C > D > E; A > D; F < E < B Conclusions:
B > F → True (as A > D > E > F & B > E → B > E >F → B > F . So, this conclusion is correct.)
A > C → False (as A > D > E > F & C > D; thus no clear relation between A and C could be inferred from the given data.)
D < B → False (as A > D > E > F; C > D; B > E; thus clear relation between D and B cannot be determined.)
Hence, conclusion I is correct.

Solution 14
Given statements: C ≥ D, D ≤ F, F > G, G < HOn combining: C ≥ D ≤ F > G < H
Conclusions:
C > F → False (as C ≥ D ≤ F → thus the clear relation between C and F cannot be determined)
H > F → False (as F > G < H → thus the clearrelation between H and F cannot be determined)
G < D → False (as D ≤ F > G → thus the clear relation between G and D cannot be determined)
Hence, no conclusions follow.

Solution 15
Given statements: G < I, I ≥ K, K = M, M < OOn combining: G < I ≥ K = M < O
Conclusions:
I ≥ M → True (as I ≥ K = M → I ≥ M)
K < O → True (as K = M < O → K < O)
G > K → False (as G < I ≥ K → thus the clear relation between G and K cannot be determined)
Hence, both conclusions I and II follow.

Solution 16
Given statements: D ≥ E > F = A ≤ U < L ≥ T = R Conclusions:
I. F < L → True (as D ≥ E > F = A ≤ U < L ≥ T = R)
D > A → True (as D ≥ E > F = A ≤ U < L ≥ T = R) Therefore, both conclusions follow.

Solution 17
Statements: J ≥ N ≤ T; T = S > R; K > V ≥ J On combining: K > V ≥ J ≥ N ≤ T = S > R
Conclusions:
V ≥ N → True (As V ≥ J ≥ N)
K > J → True (As K > V ≥ J) Thus,
Both I and II are true. Solution 18 Given statements: Q ≤ R; S < T; P > Q; R > S On combining: P > Q ≤ R > S < T Conclusions:
I. S = Q → False (as Q ≤ R > S, so a definite relation between S and Q cannot be determined) II. T ≥ P → False (P > Q ≤ R > S < T, so a definite relation between T and P cannot be determined) Hence, neither I nor II is true.

Solution 19
Given Statements: X < C, W > D, G ≥ W, C = D
On combining: X < C = D < W ≤ G
Conclusions:
I. C ≤ G → False (as C = D < W ≤ G → C < G) II. W > X → True (as X < C = D < W → X < W) Hence, only II is true.

Solution 20
Given statements: D = F; B > C; D < C; A > BOn combining: A > B > C > D = F
I. Conclusions: C ≥ F → False (as C > D = F, so C > F) II. B > F → True (as B > D = F, so B > F)Hence, only II is true.

We hope these inequality questions and answers for competitive exams were helpful and students have a fair idea on Inequality questions by now. Like any reasoning section this needs lots of practice. Considering high competition you are advised not to leave any loose ends.

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