Inequalities Questions and Answers updated daily – Logical Reasoning

Inequalities Questions: Solved 468 Inequalities Questions and answers section with explanation for various online exam preparation, various interviews, Logical Reasoning Category online test. Category Questions section with detailed description, explanation will help you to master the topic.

Inequalities Questions

Direction:In the following questions, assuming the given statements to be true, find which of the two conclusions I and II given them is/are definitely true.

Refer the above for the Questions 1 to 0
1. Statements: A > B, B ≥ C, C < D
Conclusions:
I. A > C
II. A = C




SHOW ANSWER
Correct Ans:Only I is true
Explanation:

Statements: A > B, B ≥ C, C < D

Conclusions:
I. A > C(true)
II. A = C(false)

Only I is true
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Direction:In the following questions, assuming the given statements to be true, find which of the two conclusions I and II given them is/are definitely true.

Refer the above for the Questions 2 to 1
2. Statements: P = E, Q ≥ P, V < Q
Conclusions:
I. Q ≤ E
II. E > V




SHOW ANSWER
Correct Ans:Neither I nor II is true
Explanation:
Solution:

Statements: P = E, Q ≥ P, V < Q
Conclusions:
I. Q ≤ E (False)
II. E > V (False)

Neither I nor II is true
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Direction: In the question symbols $, #, % are used for different meaning as follows.

$ means ‘neither greater nor equal to’. 
# means ‘neither greater nor smaller than’. 
% means ‘neither smaller nor equal to’. 

In each of the following questions assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true.

Refer the above for the Questions 3 to 2
3. Statements: T % I, I # L, L % U
Conclusions:
I. T $ L
II. U $ T




SHOW ANSWER
Correct Ans:Only II is true
Explanation:
$ → <
# → =
% → >

Statements: T%I, I#L, L%U
T> I=L>U

Conclusions:
I. T$L → T < L(False)
II. U$T → U < T(True)

Hence, only conclusion II is definitely true.
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Direction: In the question symbols $, #, % are used for different meaning as follows.

$ means ‘neither greater nor equal to’. 
# means ‘neither greater nor smaller than’. 
% means ‘neither smaller nor equal to’. 

In each of the following questions assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true.

Refer the above for the Questions 4 to 3
4. Statements: M # K, K % P, P $ R
Conclusions:
I. R $ M
II. P % M     




SHOW ANSWER
Correct Ans:Neither I nor II is true
Explanation:
$ → <
# → =
% → >

Statements: M#K, K%P, P$R
M = K > P < R
Conclusions:
I. R$M→R
II. P%M→P>M (False)

Hence, neither conclusion I nor II is definitely true.
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Direction: In the question symbols $, #, % are used for different meaning as follows.

$ means ‘neither greater nor equal to’. 
# means ‘neither greater nor smaller than’. 
% means ‘neither smaller nor equal to’. 

In each of the following questions assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true.

Refer the above for the Questions 5 to 4
5. Statements: N $ B, B # D, D % C
Conclusions:
I. D $ N
II. B % C       




SHOW ANSWER
Correct Ans:Only II is true
Explanation:
$ → <
# → =
% → >

Statements: N$B, B#D, D%C
N<B=D>C
Conclusions:
I. D$N→D<N(False)
II. B%C→B>C(True)
Hence, only conclusion II is definitely true.
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Direction: In the question symbols $, #, % are used for different meaning as follows.

$ means ‘neither greater nor equal to’. 
# means ‘neither greater nor smaller than’. 
% means ‘neither smaller nor equal to’. 

In each of the following questions assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true.

Refer the above for the Questions 6 to 5
6. Statements: L $ P, P % Q, Q # R
Conclusions:
I. R $ L
II. R % L       




SHOW ANSWER
Correct Ans:Neither I nor II is true
Explanation:
$ → <
# → =
% → >

Statements: L$P, P%Q, Q#R
L<P, P>Q
Q = R


Conclusion
I. R$L→R<L(False)
II. R%L→R>L(False)

Hence, neither conclusion I nor II is definitely true
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Directions: In the following questions, the symbols @, ©, %, $ and Ù­are used with the following meaning as illustrated below:

‘P © Q’ means ‘P is either equal to or greater than Q’.
‘P % Q’ means ‘P is smaller than Q’.
‘P * Q’ means ‘P is either equal to or smaller than Q’.
‘P @ Q’ means ‘P is greater than Q’.
‘P $Q’ means ‘P is equal to Q’.

Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.

Refer the above for the Questions 7 to 6
7. Statements:
W * X, X @ Y, Y % Z

Conclusions:
I. W % Y
II. Z @ W




SHOW ANSWER
Correct Ans:Neither Conclusion I nor II is true.
Explanation:
W ≤ X …... (i)
X > Y ….... (ii)
Y < Z ….....(iii)
Combining these,
we get W ≤ X > Y < Z

Conclusions:
I. W < Y = W and Y can't be compared and it does not follow.
II. Z > W = W and Z can't be compared and it does not follow.
Hence, neither Conclusion I nor II is true.
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Directions: In the following questions, the symbols @, ©, %, $ and Ù­are used with the following meaning as illustrated below:

‘P © Q’ means ‘P is either equal to or greater than Q’.
‘P % Q’ means ‘P is smaller than Q’.
‘P * Q’ means ‘P is either equal to or smaller than Q’.
‘P @ Q’ means ‘P is greater than Q’.
‘P $Q’ means ‘P is equal to Q’.

Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.

Refer the above for the Questions 8 to 7
8. Statements:
R @ S, S © T, T $ V

Conclusions:
I. R @ T
II.V * S




SHOW ANSWER
Correct Ans:Both Conclusion I and II are true.
Explanation:
R > S ….... (i)
S ≥ T …..... (ii)
T = V …...... (iii)
Combining these,
we get R > S ≥ T = V

Conclusions:
I. R > T = It follows.
II. V ≤ S = It follows.
Hence, both Conclusion I and II are true.
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Directions: In the following questions, the symbols @, ©, %, $ and Ù­are used with the following meaning as illustrated below:

‘P © Q’ means ‘P is either equal to or greater than Q’.
‘P % Q’ means ‘P is smaller than Q’.
‘P * Q’ means ‘P is either equal to or smaller than Q’.
‘P @ Q’ means ‘P is greater than Q’.
‘P $Q’ means ‘P is equal to Q’.

Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.

Refer the above for the Questions 9 to 8
9. Statements:
H % G, G © F, F ٭ E

Conclusions:
I. F % H
II. G © E




SHOW ANSWER
Correct Ans:Neither Conclusion I nor II is true.
Explanation:
H < G …..... (i)
G ≥ F …..... (ii)
F ≤ E …... (iii)
Combining these,
we get H < G ≥ F ≤ E

Conclusions:
I. F < H = F and H can't be compared and it does not follow.
II. G ≥ E = G and E can't be compared and it does not follow.
Hence, neither Conclusion I nor II is true.
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Directions: In the following questions, the symbols @, ©, %, $ and Ù­are used with the following meaning as illustrated below:

‘P © Q’ means ‘P is either equal to or greater than Q’.
‘P % Q’ means ‘P is smaller than Q’.
‘P * Q’ means ‘P is either equal to or smaller than Q’.
‘P @ Q’ means ‘P is greater than Q’.
‘P $Q’ means ‘P is equal to Q’.

Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.

Refer the above for the Questions 10 to 9
10. Statements:
A © B, B @ C, C * D

Conclusions:
I.D © B
II.C % A




SHOW ANSWER
Correct Ans:Only Conclusion II is true.
Explanation:
A ≥ B ….... (i)
B > C ….... (ii)
C ≤ D …..... (iii)
Combining these,
we get A ≥ B > C ≤ D

Conclusions:
I. D ≥ B = D and B can't be compared and it does not follow.
II. C > A = It follows
Hence, only Conclusion II is true.
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Directions: In the following questions, the symbols @, ©, %, $ and Ù­are used with the following meaning as illustrated below:

‘P © Q’ means ‘P is either equal to or greater than Q’.
‘P % Q’ means ‘P is smaller than Q’.
‘P * Q’ means ‘P is either equal to or smaller than Q’.
‘P @ Q’ means ‘P is greater than Q’.
‘P $Q’ means ‘P is equal to Q’.

Now in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.

Refer the above for the Questions 11 to 10
11. Statements:
L* M, M $ N, N % K

Conclusions:
I. K @ L
II. L * N




SHOW ANSWER
Correct Ans:Both Conclusion I and II are true.
Explanation:
L ≤ M ….. (i)
M = N ..... (ii)
N < K … (iii)
Combining these,
we get L ≤ M = N < K

Conclusions:
I. K > L = It follows
II. L ≤ N = It follows
Hence, both Conclusion I and II are true.
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12. In the following question assuming the given statements to be true, find which of the conclusion among given conclusions is /are definitely true and then give your answers accordingly.

Statement:
A ≥ D ≤ Z; P ≤ D; R > Q = D

Conclusion:
I. R > A
II. P ≤ Z




SHOW ANSWER
Correct Ans:Only Conclusion II is true.
Explanation:
Given:
A ≥ D ≤ Z; P ≤ D; R > Q = D

Conclusion:
I. R > Q = D ≤ A; R > A - False
II. P ≤ D ≤ Z; P ≤ Z - True
Hence, only Conclusion II is true.
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13. In the following question assuming the given statements to be true, find which of the conclusion among given conclusions is /are definitely true and then give your answers accordingly.

Statement:
S > A = N > D; A > L > E; M < L < O

Conclusion:
I. S > E
II. A < O




SHOW ANSWER
Correct Ans:Only Conclusion I is true.
Explanation:
Given:
S > A = N > D; A > L > E; M < L < O

Conclusion:
I. S > A > L > E; S > E - True
II. A > L < O; A < O - False
Hence, only conclusion I is true.
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14. In the following question assuming the given statements to be true, find which of the conclusion among given conclusions is /are definitely true and then give your answers accordingly.

Statement:
D ≤ R > E ≤ B; S ≤ M = E > D; G > B

Conclusion:
I. D > G
II. B < R




SHOW ANSWER
Correct Ans:Neither Conclusion I nor II is true.
Explanation:
Given:
D ≤ R > E ≤ B; S ≤ M = E > D; G > B

Conclusion:
I. D ≤ R > E ≤ B < G; D > G - False
II. R > E ≤ B; B < R - False
Hence, neither I nor II follows.
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15. In the following question assuming the given statements to be true, find which of the conclusion among given conclusions is /are definitely true and then give your answers accordingly.

Statement:
A ≥ B > F; B > M > O; F > S; R < S

Conclusion:
I. S < A
II. F < O




SHOW ANSWER
Correct Ans:Only Conclusion I is true.
Explanation:
Given:
A ≥ B > F; B > M > O; F > S; R < S

Conclusion:
I. A ≥ B > F > S; S < A - True
II. O < M < B > F; F < O - False (as we can’t find exact relationship between them)
Hence, only conclusion I follows.
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16. In the following question assuming the given statements to be true, find which of the conclusion among given conclusions is /are definitely true and then give your answers accordingly.

Statement:
E ≤ S > F ≤ C; T ≤ N = F > E; H > C

Conclusion:
I. T < C
II. C = T




SHOW ANSWER
Correct Ans:Either Conclusion I or II is true.
Explanation:
Given:
E ≤ S > F ≤ C; T ≤ N = F > E; H > C

Conclusion:
1) T ≤ N = F ≤ C; T < C - False (T ≤ C)
2) T ≤ N = F ≤ C; C = T - False (T ≤ C)
As T ≤ C therefore either T < C or T = C.
Hence, either I or II follows.
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Directions: In each of the following questions, a relationship between different elements is shown in the statements. The statements are followed by two conclusions I and II. Assuming the given statements to be true, find out which of the two conclusions I and II given below is/are definitely true.

'M$N' means 'M is not smaller than N'.
'[email protected]' means 'M is not greater than N'.
'M©N' means 'M is neither smaller than nor equal to N'.
'M%N' means 'M is neither greater than nor equal to N'.
'M#N' means 'M is neither smaller than nor greater than N'.

Refer the above for the Questions 17 to 16
17. Statements:
G#H, I%J, J ©G

Conclusions:
I. H%J
II. G%I




SHOW ANSWER
Correct Ans:Only conclusion I is true.
Explanation:
% = <, @ = ≤, # = (=), © = >, $ = ≥
Given;
G # H – G = H ........... (i)
I % J – I < J........ (ii)
J © G – J > G ....... (iii)
Combining (i), (ii) and (iii), we get
I < J > G = H
I) H % J – H < J is true. So, conclusion I is true.
II) G % I – G < I, we can’t compare G and I.
So, Conclusion II is not true.
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Directions: In each of the following questions, a relationship between different elements is shown in the statements. The statements are followed by two conclusions I and II. Assuming the given statements to be true, find out which of the two conclusions I and II given below is/are definitely true.

'M$N' means 'M is not smaller than N'.
'[email protected]' means 'M is not greater than N'.
'M©N' means 'M is neither smaller than nor equal to N'.
'M%N' means 'M is neither greater than nor equal to N'.
'M#N' means 'M is neither smaller than nor greater than N'.

Refer the above for the Questions 18 to 17
18. Statements:
[email protected], T#R, S ©U

Conclusions:
I. S#T
II. S ©T




SHOW ANSWER
Correct Ans:Either conclusion I or II is true.
Explanation:
% = <, @ = ≤, # = (=), © = >, $ = ≥
Given;
R @ S – R ≤ S ............. (i)
T # R – T = R .............. (ii)
S © U – S > U ............ (iii)
Combining (i), (ii) and (iii), we get
T = R ≤ S > U
I) S# T – S = T is not true.
II) S © T – S > T is not true.
Both are complementary pairs.
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Directions: In each of the following questions, a relationship between different elements is shown in the statements. The statements are followed by two conclusions I and II. Assuming the given statements to be true, find out which of the two conclusions I and II given below is/are definitely true.

'M$N' means 'M is not smaller than N'.
'[email protected]' means 'M is not greater than N'.
'M©N' means 'M is neither smaller than nor equal to N'.
'M%N' means 'M is neither greater than nor equal to N'.
'M#N' means 'M is neither smaller than nor greater than N'.

Refer the above for the Questions 19 to 18
19. Statements:
A$B, C ©D, D%A

Conclusions:
I. C%B
II. C ©A




SHOW ANSWER
Correct Ans:Neither conclusion I nor II is true.
Explanation:
% = <, @ = ≤, # = (=), © = >, $ = ≥
Given;
A $ B – A ≥ B ............... (i)
C © D – C > D ............... (ii)
D % A – D < A .............. (iii)
Combining (i), (ii) and (iii), we get
C > D < A ≥ B
I) C % B – C < B, we can’t compare C and B.
So, conclusion I is not true.
II) C © A – C > A , we can’t compare C and A.
So, Conlcusion II is also not true.
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Directions: In each of the following questions, a relationship between different elements is shown in the statements. The statements are followed by two conclusions I and II. Assuming the given statements to be true, find out which of the two conclusions I and II given below is/are definitely true.

'M$N' means 'M is not smaller than N'.
'[email protected]' means 'M is not greater than N'.
'M©N' means 'M is neither smaller than nor equal to N'.
'M%N' means 'M is neither greater than nor equal to N'.
'M#N' means 'M is neither smaller than nor greater than N'.

Refer the above for the Questions 20 to 19
20. Statements:
L$M, [email protected], M ©O

Conclusions:
I. M#N
II. O%L




SHOW ANSWER
Correct Ans:Only conclusion II is true.
Explanation:
% = <, @ = ≤, # = (=), © = >, $ = ≥
Given;
L $ M – L ≥ M ............... (i)
N @ L – N ≤ L ............. (ii)
M © O – M > O ............ (iii)
Combining (i), (ii) and (iii), we get
N ≤ L ≥ M > O
I. M # N – M = N is not true because we can’t compare M and N.
So, conclusion I is not true.
II. O % L – O < L is true.
So, conclusion II is true.
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