# Inequalities Questions and Answers updated daily – Logical Reasoning

247 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

Study the following information to answer the given questions:
P \$ Q means P is not smaller than Q
P @ Q means P is neither smaller than nor equal to Q
P # Q means P is neither greater than nor equal to Q
P & Q means P is neither greater than nor smaller than Q
P * Q means P is not greater than Q

Refer the above for the Questions 1 to 5
1. Statements: C # P, P * L, L @ E, E \$ M

Conclusions:
I. M # P
II. M @ L
III. P # E
IV. L # C

Correct Ans:None is true
Explanation:
Given,
\$ means ≥
@ means >
# means <
& means =
* means ≤

Given Statements: C # P, P * L, L @ E, E \$ M
Which can be written as: C < P ≤ L > E ≥ M

Given Conclusions:
I. M # P ---- M < P (False)
II. M @ L ---- M > L (False) --- According to given statements, the correct relation between M and L is "M < L"
III. P # E ----P < E (False)
IV. L # C ---- L < C (False) --- According to given statements, the correct relation between L and C is "L > C"

Thus, None of the given conclusion follows the given statements.

2. Statements: S @ L, L # M, M & B, B * Q

Conclusions:
I. Q \$ M
II. B @ L
III. S @ Q
IV. L @ Q

Correct Ans:I, II are true
Explanation:
Given,
\$ means ≥
@ means >
# means <
& means =
* means ≤

Given Statements: S @ L, L # M, M & B, B * Q
Which can be written as: S > L, L < M, M = B, B ≤ Q
i.e., S > L < M = B ≤ Q

Given Conclusions:
I. Q \$ M ---- Q ≥ M (True)
II. B @ L ---- B > L (True)
III. S @ Q ---- S > Q (False)
IV. L @ Q ---- L > Q (False)

ThusConclusionsI and II are true according to given statements.

3. Statements: T * Y, S # M, Y \$ S, M @ K

Conclusions:
I. K # S
II. Y @ M
III.T # M
IV.Y @ K

Correct Ans:None is true
Explanation:
Given,
\$ means ≥
@ means >
# means <
& means =
* means ≤

Given Statements: T * Y, S # M, Y \$ S, M @ K
Which can be written as: T ≤ Y, S < M, Y ≥ S, M > K
i.e., T ≤ Y ≥ S < M > K

Given Conclusions:
I. K # S ----- K < S (False)
II. Y @ M ---- Y > M (False)
III.T # M ---- T < M (False)
IV.Y @ K ---- Y > K (False)

Thus, None of the given conclusion follows the given statements.

4. Statements: W * N, K * V, Y @ V, W @ K

Conclusions:
I. Y @ K
II. W \$ N
III. W @ Y
IV. W @ V

Correct Ans:Only I is true
Explanation:
Given,
\$ means ≥
@ means >
# means <
& means =
* means ≤

Given Statements: W * N, K * V, Y @ V, W @ K
which can be written as: W ≤ N, K ≤ V, Y > V, W > K
i.e., N ≥ W > K ≤ V < Y

Given Conclusions:
I. Y @ K ---- Y > K (True)
II. W \$ N ---- W ≥ N (False)
III. W @ Y ---- W > Y (False)
IV. W @ V ---- W > V (False)

Thus, Only Conclusion I is true according to the given Statements.

5. Statements: A \$ M, P @ L, K # P, A \$ L

Conclusions:
I. K # L
II. A @ P
III. L * A
IV. M # P

Correct Ans:Only III is true
Explanation:
Given,
\$ means ≥
@ means >
# means <
& means =
* means ≤

Given Statements: A \$ M, P @ L, K # P, A \$ L
Which can be written as: A ≥ M, P > L, K < P, A ≥ L
i.e., M ≤ A ≥ L < P > K

Given Conclusions:
I. K # L ----- K < L (False)
II. A @ P ---- A > P (False)
III. L * A ---- L ≤ A (True)
IV. M # P ----- M < P (False)

Thus, Only Conclusion III is true according to the given Statements.

6. Statement:
L > G = M ≤ T ; U < S < M

Conclusions:
I) T ≥ L
II) S < L
III) T > U
IV) G ≤ U

Correct Ans:Only II,III are true
Explanation:
Given
Statement:
L > G = M ≤ T ; U < S < M

Conclusion I) T ≥ L ---> False (According to the given statements, L > G ≤ T)

Conclusion II) S < L ---> True (According to the given statements, S < M < L, which means S < L)

Conclusion III) T > U ---> True (According to the given statements, T ≥ M > S > U, which means T > U)

Conclusion IV) G ≤ U --> False (According to the given statements, G = M > S > U, which means G > U)

Thus, Only Conclusions II, III are true

7. Statement:
D > M > U ≥ E ; N < U ≥ J

Conclusions:
I ) D > E
II) E ≤ J
III) M > N
IV) D > J

Correct Ans:Only I,III ,IV are true
Explanation:
Given
Statements: D> M > U ≥ E ; N < U ≥ J

Conclusion I ) D > E ---> True (According to given statements, D> M > U ≥ E)

Conclusion II) E ≤ J ---> False (According to given statements, E ≤ U ≥ J)

Conclusion III) M > N ----> True (According to given statements, M > U > N)

Conclusion IV) D > J ----> True (According to given statements, D > M > U ≥ J)

Thus , Only Conclusions I, III and IV are true

8. Statement:
K > H < Y ≤ Z < A > R ≥ L

Conclusions:
I) A > Y
II) L < A
III) H < A
IV) K > R

Correct Ans:Only I,II,III are true
Explanation:
Given Statement:
K > H < Y ≤ Z < A > R ≥ L

Conclusion I) A > Y ----- True (According to given statements, Y ≤ Z < A, which means, Y < A, i.e., A > Y)

Conclusion II) L < A ----- True (According to given statements, A > R ≥ L, which means, A > L, i.e., L < A)

Conclusion III) H < A ----- True (According to given statements, H < Y ≤ Z < A, which means, H < A)

Conclusion IV) K > R ----- False (According to given statements, K > H < Y ≤ Z < A > R, so exact relation between K and R cannot be determined from this data)

Thus, Only Conclusions I, II and III are true.

9. Statement:
S > H ≥ P ≤ C ; Y > P ≥ N

Conclusions:
I) H > Y
II) S > C
III) C = Y
IV) C ≥ N

Correct Ans:Only IV is true
Explanation:
Given
Statement:
S > H ≥ P ≤ C ; Y > P ≥ N

Conclusion I) H > Y ---- False (According to given statements, H ≥ P < Y)

Conclusion II) S > C ----- False (According to given statements, S > H ≥ P ≤ C)

Conclusion III) C = Y ----- False (According to given statements, C ≥ P < Y)

Conclusion IV) C ≥ N ----- True (According to given statements, C ≥ P ≥ N, which means C ≥ N)

Thus, Only conclusion IV is true.

10. Statement:
P > R ≥ S = T < M ≤ N < K

Conclusions:
I) T< P
II) N > S
III) K < S
IV) S ≥ P

Correct Ans:Only I and II are true
Explanation:
Given
Statement: P > R ≥ S = T < M ≤ N < K ,

Conclusions:
I) T< P ---> True
II) N > S ---> True
III) K < S ---> False (According to given statements, correct relation between K and S is "K > S")
IV) S ≥ P ---> False (According to given statements, correct relation between S and P is "S < P")

Thus Conclusions I and II are true

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

Refer the above for the Questions 11 to 15
11. Statement:
R # D , D \$ M , M © N

Conclusions:
I) R # M
II) N # D
III) N \$ R

Correct Ans:Only II is true
Explanation:
Given
\$ means ≥
# means ≤
@ means >
% means <

Statement :
R # D , D \$ M , M © N
Denoted as R ≤ D ≥ M = N

Conclusions
I) R # M --> R ≤ M ---> False
II) N # D --> N ≤ D ---> True
III) N \$ R ---> N ≥ R --> False

Hence, Only Conclusion II is true.

12. Statement:
M @ D , D © V, V \$ W

Conclusions:
I) W @ M
II) M % V
III) D \$ W

Correct Ans:Only III is true
Explanation:
Given

\$ means ≥
# means ≤
@ means >
% means <

Statement:
M@ D , D © V, V \$ W
Denoted as M > D = V ≥ W

Conclusions:
I) W @ M---> W > M---> False
II) M % V ---> M < V ---> False
III) D \$ W ---> D ≥ W ---> True

Only Conclusion III is true.

13. Statement:
K # N ,N \$ T, T% J

Conclusions
I) J @ N
II) K @ T
III) T @ K

Correct Ans:None is true
Explanation:
Given

\$ means ≥
# means ≤
@ means >
% means <

Statement:
K # N ,N \$ T, T% J
Denoted as K ≤ N ≥ T < J

Conclusions:
I) J @ N ---> J > N ---> False
II) K @ T ---> K > T---> False
III) T @ K ---> T > K ---> False

Here None is true.

14. Statement :
M @ J, J \$ T, T © N

Conclusion:
I) N # J
II) T % M
III) M @ N

Correct Ans:All are true
Explanation:
Given

\$ means ≥
# means ≤
@ means >
% means <

Statement :
M @ J, J \$ T, T © N
Denoted as M > J ≥ T = N

Conclusion
I) N # J --> N ≤ T ---> True
II) T % M --> T < M ---> True
III) M @ N ---> M > N ---> True

All the conclusions are true

15. Statement:
H % J , J © N,N @ R

Conclusion:
I) R % J
II) H @ J
III) N @ H

Correct Ans:Only I and III are true
Explanation:
Given

\$ means ≥
# means ≤
@ means >
% means <

Statement:
H % J , J © N,N @ R
Denoted as H < J = N > R

Conclusion:
I) R % J --> R < J --->True
II) H @ J --> H > J ---> False
III) N@ H --> N > H --->True

Thus Only Conclusions I and III are true.

Directions: The symbols #, %, @, \$ and â¦¾ are used with the following meanings as illustrated below:
‘P # Q’ means ‘P is not smaller than Q’
‘P % Q’ means ‘P is not greater than Q'
‘P @ Q’ means ‘P is neither smaller than nor equal to Q’
‘P \$ Q’ means ‘P is neither greater than nor equal to Q’
‘P â¦¾ Q’ means ‘P is neither smaller than nor greater than Q’

Refer the above for the Questions 16 to 20
16. Statements:
R # T, T â¦¾ M, M @ D

Conclusions:
I) D \$ T
II) R # M

Correct Ans:Both conclusion I and II are true
Explanation:
Given,
# means ≥
% means ≤
@ means >
\$ means <
â¦¾ means =

Statements:
R # T, Tâ¦¾ M, M @ D
Denoted as R ≥ T = M > D

Conclusions:
I) D \$ T --- D < T (True)
II) R # M --- R ≥ M (True)

Hence, Both the conclusions I and II are true.

17. Statements:
H @ W, W \$ M, M # K

Conclusions:
I) K \$ W
II) H @ M

Correct Ans:Neither conclusion I nor II is true
Explanation:
Given,
# means ≥
% means ≤
@ means >
\$ means <
â¦¾ means =

Statements:
H @ W, W \$ M, M # K
----- H > W < M ≥ K

Conclusions:
I) K \$ W --- K < W (False)
II) H @ M --- H > M (False)

Hence, Neither conclusion I nor II is true

18. Statements:
R % N, N # F, F @ B

Conclusions:
I) F â¦¾ R
II) B \$ N

Correct Ans:Only conclusion II is true
Explanation:
Given,
# means ≥
% means ≤
@ means >
\$ means <
â¦¾ means =

Statements:
R % N, N # F, F @ B
----- R ≤ N ≥ F > B

Conclusions:
I) Fâ¦¾ R ---- F = R (False), According to given statements, F is either≤ or≥ R.
II) B \$ N ---- B < N (True)

Hence, Only Conclusion II is true.

19. Statements:
M \$ T, T @ K, K â¦¾ D

Conclusions:
I) D \$ T
II) K \$ M

Correct Ans:Only conclusion I is true
Explanation:
Given,
# means ≥
% means ≤
@ means >
\$ means <
â¦¾ means =

Statements:
M \$ T, T @ K, K â¦¾ D
----- M < T > K = D

Conclusions:
I) D \$ T ---- D < T (True)
II) K \$ M ---- K < M (False)

Hence, Only conclusion I is true.

20. Statements :
H â¦¾ W, W % R, R @ F

Conclusions:
I) R â¦¾ H
II) R @ H

Correct Ans:Either conclusion I or II is true
Explanation:
Given,
# means ≥
% means ≤
@ means >
\$ means <
â¦¾ means =

Statements :
H â¦¾ W, W % R, R @ F
----- H = W ≤ R > F

Conclusions:
I) R â¦¾ H ---- R = H (Not definite - False)
II) R @ H ---- R > H (Not definite - 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 H are present in both Conclusion I and II)
3) Symbols "=" and ">" are together in those conclusions.

Thus, either Conclusion I or II follows.

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