Inequalities Questions and Answers updated daily – Logical Reasoning


Inequalities Questions and Answers updated daily – Logical Reasoning



222 Inequalities Questions and answers section with explanation for various online exam preparation, various interviews, Logical Reasoning Inequalities online test. Inequalities Questions with detailed description, explanation will help you to master the topic.

Inequalities Questions

P © Q means P is neither greater than nor smaller than Q
P # Q means P is either smaller than or equal to Q
P @ Q means P is either greater than or equal to Q
P % Q means P is greater than Q
P $ Q means P is smaller than Q

Refer the above for the Questions 1 to 5
1. Statements
F % B , B @ D , D # K 

Conclusions

I) K @ B
II) D # F



SHOW ANSWER
Correct Ans:If Neither Conclusion I nor II is true
Explanation:
Given

© means =
# means ≤
@ means ≥
% means >
$ means <

Statements
F % B , B @ D , D # K
Denoted as F > B ≥ D ≤ K

Conclusions

I) K @ B--> K ≥ B --> False
II) D # F--> D ≤ F --> False (According to given statements, D < F)

Therefore, Neither conclusion I nor II follows.


2. Statements:
D © J , J # M , M @ Y 

Conclusions
I) D © M
II) M % D



SHOW ANSWER
Correct Ans:If Either Conclusion I or II is true
Explanation:
Given

© means =
# means ≤
@ means ≥
% means >
$ means <

Statements: D © J , J # M , M @ Y
Denoted as D = J ≤ M ≥ Y

Conclusions
I) D © M --> D = M ---> False (According to given statements, D ≤ M)
II) M % D --> M > D ---> False (According to given statements, M ≥ D )

Rules for Either .... or ... case:

1) Both conclusions are False. Here Conclusion I and II are False.
2) Both conclusions have same variable.(i.e., D and M are present in both Conclusion I and II)
3) Symbols "=" and ">" are together in those conclusions.

Hence, either conclusion I or II follows.


3. Statements:
B © K , K @ T , T $ F

Conclusions:
I) T # B
II) F % B



SHOW ANSWER
Correct Ans:If only Conclusion I is true
Explanation:
Given

© means =
# means ≤
@ means ≥
% means >
$ means <

Statements:
B © K , K @ T , T $ F
Denoted as B = K ≥ T < F

Conclusions:
I) T # B --> T ≤ B --> True
II) F % B --> F > B --> False

Here Only Conclusion I Follows.


4. Statements
D # J , J $ N ,N @ W 

Conclusions
I) W # J
II) D $ N



SHOW ANSWER
Correct Ans:If only Conclusion II is true
Explanation:
Given

© means =
# means ≤
@ means ≥
% means >
$ means <

Statements
D # J , J $ N ,N @ W
Denoted as D ≤ J < N ≥ W

Conclusions
I) W # J --> W ≤ J --> False
II) D $ N --> D < N --> True.

Only conclusion II follows.


5. Statement : M % T ,R @ T, R © K

Conclusions
I) K $ M
II) T @ K



SHOW ANSWER
Correct Ans:If Neither Conclusion I nor II is true
Explanation:
Given

© means =
# means ≤
@ means ≥
% means >
$ means <

Statement : M % T ,R @ T, R © K
Denoted as M > T ≤ R = K

Conclusions:
I) K $ M --> K < M --> False
II) T @ K --> T ≥ K --> False (According to given statement, T ≤ K)

Hence, Neither Conclusion I nor Conclusion II follows.


A @ B means A is not smaller than B
A # B means A is not greater than B
A % B means A is neither greater than nor smalller than B
A + B means A is neither smaller than nor equal to B
A $ B means A is neither greater than nor equal to B

Refer the above for the Questions 6 to 10
6. Statement : J # W, W + A, A @ F

Conclusion:
I) F $ W
II) F % W
III) J + F 



SHOW ANSWER
Correct Ans:Only I follows
Explanation:
Given
@ means ≥
# means ≤
% means =
+ means >
$ means <

Statement : J # W, W + A, A @ F
Denoted as: J ≤ W > A ≥ F

Conclusions:
I) F $ W ----- F < W (True)
II) F % W ---- F = W (False)
III) J + F ----- J > F (False)

Therefore, only Conclusion I follows.


7. Statement : L @ U, U + A, A $ G

Conclusion:
I) G $ L
II) L # G
III) L + A



SHOW ANSWER
Correct Ans:Either I or II follows and III follows.
Explanation:
Given
@ means ≥
# means ≤
% means =
+ means >
$ means <

Statement : L @ U, U + A, A $ G
Denoted as: L ≥ U > A < G

Conclusions:
I) G $ L ----- G < L (Not definite)

II) L # G ----- L ≤ G (Not definite)

III) L + A ---- L > A (True)

Rules for Either .... or ... case:
1) Both conclusions are False. Here Conclusion I and II are False
2) Both conclusions have same variable.(i.e., "G and L" are present in both Conclusion I and II)
3) Symbols "<" and ">=" are together in those conclusions.

Thus, either Conclusion I or II and III follows the given statements.


8. Statement : N @ S ,S % M , M+ H

Conclusion:
I) M # N
II) N + H
III) M + N 



SHOW ANSWER
Correct Ans:Only I and II follows
Explanation:
Given
@ means ≥
# means ≤
% means =
+ means >
$ means <

Statement : N @ S ,S % M , M + H
Denoted as: N ≥ S = M > H

Conclusions:
I) M # N => M ≤ N --> True

II) N + H => N > H ---> True

III) M + N => M > N ---> False (According to given statements, M ≤ N)

Thus Only I and II follows.


9. Statement : B + M, M @ Z, Z $ C

Conclusions:
I) C + M ,
II) B + Z ,
III) C + B



SHOW ANSWER
Correct Ans:Only II follows
Explanation:
Given
@ means ≥
# means ≤
% means =
+ means >
$ means <

Statement : B + M, M @ Z, Z $ C
Denoted as: B > M ≥ Z < C

Conclusions:
I. C + M => C > M ---> False
II. B + Z => B > Z ---> True
III. C + B => C > B ---> False

Thus only Conclusion II follows.


10. Statement :
Y $ W, W @ O, O # H

Conclusions :
I) Y + O
II) H % W
III) H + Y



SHOW ANSWER
Correct Ans:None follows
Explanation:
Given
@ means ≥
# means ≤
% means =
+ means >
$ means <

Statement :
Y $ W, W @ O, O # H
Denoted as: Y < W ≥ O ≤ H

Conclusions :
I) Y + O ----> Y > O --- False

II) H % W ----> H = W --- False

III) H + Y -----> H > Y --- False

Thus None of the given conclusion follows the given statement.


Directions:
A @ B means "A is smaller than B "
A # B means "A is not smaller than B "
A $ B means "A is neither smaller than nor greater than B"
A % B means "A is greater than B"
A © B means "A is not greater than B"

Refer the above for the Questions 11 to 15
11. Statements : R @ Q ,Q % P ,P © V , V # M

Conclusions:
I ) R @ P
II) R # P



SHOW ANSWER
Correct Ans:If either conclusion I or II follows
Explanation:
Given
@ --- <
# ---- ≥
$ ---- =
% ---- >
© ---- ≤

Statements : R @ Q ,Q % P ,P © V , V # M
Denoted as R < Q > P ≤ V ≥ M

Conclusions
I ) R @ P ---> R < P = false
II) R # P ---> R ≥ P= false

Rules for Either .... or ... case:

1) Both conclusions are False. Here Conclusion I and II are False.
2) Both conclusions have same variable.(i.e., R and P are present in both Conclusion I and II
3) Symbols "<" and "≥" are together in those conclusions.

Here either conclusion I or II follows.


12. Statements: J © T, T @ H , H % I , I $ L
Conclusions:
I) L © H
II) J © I



SHOW ANSWER
Correct Ans:if neither conclusion I nor II follows
Explanation:
Given
@ --- <
# ---- ≥
$ ---- =
% ---- >
© ---- ≤
Statement : J © T, T @ H , H % I , I $ L
Denoted as J ≤ T < H > I = L

Conclusions:
I) L © H ---> L ≤ H = false (According to given statement, L < H)
II) J © I ---> J ≤ I = false

Therefore, neither conclusion I nor II follows.


13. Statement : E % W , W © Q , Q $ T , T @ H
Conclusions
I) H # W
II) H # E



SHOW ANSWER
Correct Ans:if neither conclusion I nor II follows
Explanation:
Given
@ --- <
# ---- ≥
$ ---- =
% ---- >
© ---- ≤
Statement : E % W ,W © Q, Q $ T ,T @ H
Denoted as => E > W ≤ Q =T < H
Conclusions:
I) H # W ---> H ≥ W = false (According to given statement, H > W)
II) H # E ---> H ≥ E = false.

Here ,neither conclusion I nor II follows.


14. Statement : L @ D ,D © P , P # V , V % G
Conclusions
I) P % L
II) G @ P



SHOW ANSWER
Correct Ans:If both the conclusion follows
Explanation:
Given
@ --- <
# ---- ≥
$ ---- =
% ---- >
© ---- ≤
Statement : L @ D , D © P , P # V , V % G

Denoted as: L < D ≤ P ≥ V > G

Conclusions
I) P % L ---> P > L= True
II) G @ P --> G < P = True

Here Both Conclusion I and II follows.


15. Statement : F # H , H % K , K $ R , R © M
Conclusions
I) F % R
II) F # M



SHOW ANSWER
Correct Ans:If only conclusion I follows
Explanation:
Given
@ --- <
# ---- ≥
$ ---- =
% ---- >
© ---- ≤
Statement : F # H , H % K , K $ R , R © M

denoted as: F ≥ H > K = R ≤ M

Conclusions
I) F % R --> F > R = true
II) F # M --> F ≥ M = false

Here only Conclusion I follows


Directions:
A $ B means A is not smaller than B
A # B means A is neither greater than nor equal to B
A @ B means A neither smaller than nor equal to B
A % B means A is not greater than B
A ★ B means A is neither greater than nor smaller than B

Refer the above for the Questions 16 to 20
16. Statements:
K @ T, T # D , D ★ F , F % G

Conclusions:
I) G @ K
II) G ★ T
III) G @ T



SHOW ANSWER
Correct Ans:III follows
Explanation:
Given
$ means ≥
# means <
@ means >
% means ≤
★ means =

Statements:
K @ T, T # D , D ★ F , F % G
Denoted as K > T < D = F ≤ G

Conclusions:
I) G @ K ---> G > K ---> False
II) G ★ T ---> G = T ---> False (According to given statements, G > T)
III) G @ T---> G > T ---> True

Hence, Only Conclusion III follows.


17. Statements:
F @ H , M % H , M $ R , G ★ M

Conclusions:
I) F $ R
II) F @ R
III) H $ G



SHOW ANSWER
Correct Ans:II and III only follows
Explanation:
Given
$ means ≥
# means <
@ means >
% means ≤
★ means =

Statements:
F @ H , M % H , M $ R , G ★ M
Denoted as F > H, M ≤ H, M ≥ R, G = M
which can be written as F > H ≥ M = G ≥ R

Conclusions:
I) F $ R ---> F ≥ R ---> False (According to the given statements, F > R)
II) F @ R ---> F > R ---> True
III) H $ G ---> H ≥ G ---> True

Hence, only Conclusions II and III are true.


18. Statements:
P # M , M % R , R ★ T , T # L

Conclusions:
I) P # R
II) P ★ R
III) M % L



SHOW ANSWER
Correct Ans:I only follows
Explanation:
Given
$ means ≥
# means <
@ means >
% means ≤
★ means =

Statement:
P # M , M % R , R ★ T , T # L
Denoted as P < M ≤ R = T < L

Conclusions:
I) P # R ---> P < R ---> True
II) P ★ R ---> P = R ----> False (According to given statements, P < R)
III) M % L ---> M ≤ L ----> False (According to given statements, M < L)

Hence Only Conclusion I follows


19. Statement:
Z @ Y , Y # K , K % M , M @ T

Conclusions:
I) Z @ M
II) Y @ T
III) Z # K



SHOW ANSWER
Correct Ans:None is true
Explanation:
Given
$ means ≥
# means <
@ means >
% means ≤
★ means =

Statement
Z @ Y , Y # K , K % M , M @ T
Denoted as Z > Y < K ≤ M > T

Conclusions
I) Z @ M ---> Z > M ---> False
II) Y @ T ---> Y > T ----> False
III) Z # K ----> Z < K ----> False

Hence None of the Conclusion is true from the above statements.


20. Statement:
D ★ Q , Q @ L , L $ B , B # G

Conclusions:
I) D @ B
II) B ★ D
III) G @ L



SHOW ANSWER
Correct Ans:I only follows
Explanation:
Given
$ means ≥
# means <
@ means >
% means ≤
★ means =

Statement :
D ★ Q , Q @ L , L $ B , B # G
Denoted as D = Q > L ≥ B < G

Conclusions:
I) D @ B --- > D > B ---> True
II) B ★ D ---> B = D ---> False (According to given statements, B < D)
III) G @ L---> G > L ---> False (According to given statements, G > B ≤ L)

Hence only Conclusion I follows.



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