# 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

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

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)

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

Conclusions:

I. T $ L

II. U $ T

SHOW ANSWER

Correct Ans:Only II is true

Explanation:

$ â†’ <

# â†’ =

% â†’ >

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

T> I=L>U

Conclusions:

I. T$L â†’ T < L(False)

II. U$T â†’ U < T(True)

# â†’ =

% â†’ >

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

T> I=L>U

Conclusions:

I. T$L â†’ T < L(False)

II. U$T â†’ 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

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)

# → =

% → >

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

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)

# → =

% → >

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

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)

# → =

% → >

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.

W * X, X @ Y, Y % Z

I. W % Y

II. Z @ W

**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 â€¦... (i)

X > Y â€¦.... (ii)

Y < Z â€¦.....(iii)

Combining these,

we get W ≤ X > Y < Z

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.

X > Y â€¦.... (ii)

Y < Z â€¦.....(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.

R @ S, S Â© T, T $ V

I. R @ T

II.V * S

**Statements:**R @ S, S Â© T, T $ V

**Conclusions:**I. R @ T

II.V * S

SHOW ANSWER

Correct Ans:Both Conclusion I and II are true.

Explanation:

R > S â€¦.... (i)

S ≥ T â€¦..... (ii)

T = V â€¦...... (iii)

Combining these,

we get R > S ≥ T = V

I. R > T = It follows.

II. V ≤ S = It follows.

Hence, both Conclusion I and II are true.

S ≥ T â€¦..... (ii)

T = V â€¦...... (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.

H % G, G Â© F, F Ù E

I. F % H

II. G Â© E

**Statements:**H % G, G Â© F, F Ù E

**Conclusions:**I. F % H

II. G Â© E

SHOW ANSWER

Correct Ans:Neither Conclusion I nor II is true.

Explanation:

H < G â€¦..... (i)

G ≥ F â€¦..... (ii)

F ≤ E â€¦... (iii)

Combining these,

we get H < G ≥ F ≤ E

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.

G ≥ F â€¦..... (ii)

F ≤ E â€¦... (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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‘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.

A Â© B, B @ C, C * D

I.D Â© B

II.C % A

**Statements:**A Â© B, B @ C, C * D

**Conclusions:**I.D Â© B

II.C % A

SHOW ANSWER

Correct Ans:Only Conclusion II is true.

Explanation:

A ≥ B â€¦.... (i)

B > C â€¦.... (ii)

C ≤ D â€¦..... (iii)

Combining these,

we get A ≥ B > C ≤ D

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.

B > C â€¦.... (ii)

C ≤ D â€¦..... (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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‘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.

L* M, M $ N, N % K

I. K @ L

II. L * N

**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 â€¦.. (i)

M = N ..... (ii)

N < K â€¦ (iii)

Combining these,

we get L ≤ M = N < K

I. K > L = It follows

II. L ≤ N = It follows

Hence, both Conclusion I and II are true.

M = N ..... (ii)

N < K â€¦ (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.

A â‰¥ D â‰¤ Z; P â‰¤ D; R > Q = D

I. R > A

II. P â‰¤ Z

**Statement:**A â‰¥ D â‰¤ Z; P â‰¤ D; R > Q = D

**Conclusion:**I. R > A

II. P â‰¤ Z

SHOW ANSWER

Correct Ans:Only Conclusion II is true.

Explanation:

Given:

A â‰¥ D â‰¤ Z; P â‰¤ D; R > Q = D

Conclusion:

I. R > Q = D â‰¤ A; R > A - False

II. P â‰¤ D â‰¤ Z; P â‰¤ Z - True

Hence, only Conclusion II is true.

A â‰¥ D â‰¤ Z; P â‰¤ D; R > Q = D

Conclusion:

I. R > Q = D â‰¤ A; R > A - False

II. P â‰¤ D â‰¤ Z; P â‰¤ 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.

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

I. S > E

II. A < O

**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.

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.

D â‰¤ R > E â‰¤ B; S â‰¤ M = E > D; G > B

I. D > G

II. B < R

**Statement:**D â‰¤ R > E â‰¤ B; S â‰¤ 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 â‰¤ R > E â‰¤ B; S â‰¤ M = E > D; G > B

Conclusion:

I. D â‰¤ R > E â‰¤ B < G; D > G - False

II. R > E â‰¤ B; B < R - False

Hence, neither I nor II follows.

D â‰¤ R > E â‰¤ B; S â‰¤ M = E > D; G > B

Conclusion:

I. D â‰¤ R > E â‰¤ B < G; D > G - False

II. R > E â‰¤ 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.

A â‰¥ B > F; B > M > O; F > S; R < S

I. S < A

II. F < O

**Statement:**A â‰¥ 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 â‰¥ B > F; B > M > O; F > S; R < S

Conclusion:

I. A â‰¥ B > F > S; S < A - True

II. O < M < B > F; F < O - False (as we canâ€™t find exact relationship between them)

Hence, only conclusion I follows.

A â‰¥ B > F; B > M > O; F > S; R < S

Conclusion:

I. A â‰¥ B > F > S; S < A - True

II. O < M < B > F; F < O - False (as we canâ€™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.

E â‰¤ S > F â‰¤ C; T â‰¤ N = F > E; H > C

I. T < C

II. C = T

**Statement:**E â‰¤ S > F â‰¤ C; T â‰¤ 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 â‰¤ S > F â‰¤ C; T â‰¤ N = F > E; H > C

Conclusion:

1) T â‰¤ N = F â‰¤ C; T < C - False (T â‰¤ C)

2) T â‰¤ N = F â‰¤ C; C = T - False (T â‰¤ C)

As T â‰¤ C therefore either T < C or T = C.

Hence, either I or II follows.

E â‰¤ S > F â‰¤ C; T â‰¤ N = F > E; H > C

Conclusion:

1) T â‰¤ N = F â‰¤ C; T < C - False (T â‰¤ C)

2) T â‰¤ N = F â‰¤ C; C = T - False (T â‰¤ C)

As T â‰¤ 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.

G#H, I%J, J Â©G

I. H%J

II. G%I

**Statements:**G#H, I%J, J Â©G

**Conclusions:**I. H%J

II. G%I

SHOW ANSWER

Correct Ans:Only conclusion I is true.

Explanation:

% = <, @ = ≤, # = (=), Â© = >, $ = ≥

Given;

G # H â€“ G = H ........... (i)

I % J â€“ I < J........ (ii)

J Â© G â€“ J > G ....... (iii)

Combining (i), (ii) and (iii), we get

I < J > G = H

I) H % J â€“ H < J is true. So, conclusion I is true.

II) G % I â€“ G < I, we canâ€™t compare G and I.

So, Conclusion II is not true.

Given;

G # H â€“ G = H ........... (i)

I % J â€“ I < J........ (ii)

J Â© G â€“ J > G ....... (iii)

Combining (i), (ii) and (iii), we get

I < J > G = H

I) H % J â€“ H < J is true. So, conclusion I is true.

II) G % I â€“ G < I, we canâ€™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

SHOW ANSWER

Correct Ans:Either conclusion I or II is true.

Explanation:

% = <, @ = ≤, # = (=), Â© = >, $ = ≥

Given;

R @ S â€“ R ≤ S ............. (i)

T # R â€“ T = R .............. (ii)

S Â© U â€“ S > U ............ (iii)

Combining (i), (ii) and (iii), we get

T = R ≤ S > U

I) S# T â€“ S = T is not true.

II) S Â© T â€“ S > T is not true.

Both are complementary pairs.

Given;

R @ S â€“ R ≤ S ............. (i)

T # R â€“ T = R .............. (ii)

S Â© U â€“ S > U ............ (iii)

Combining (i), (ii) and (iii), we get

T = R ≤ S > U

I) S# T â€“ S = T is not true.

II) S Â© T â€“ 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.

A$B, C Â©D, D%A

I. C%B

II. C Â©A

**Statements:**A$B, C Â©D, D%A

**Conclusions:**I. C%B

II. C Â©A

SHOW ANSWER

Correct Ans:Neither conclusion I nor II is true.

Explanation:

% = <, @ = ≤, # = (=), Â© = >, $ = ≥

Given;

A $ B â€“ A ≥ B ............... (i)

C Â© D â€“ C > D ............... (ii)

D % A â€“ D < A .............. (iii)

Combining (i), (ii) and (iii), we get

C > D < A ≥ B

I) C % B â€“ C < B, we canâ€™t compare C and B.

So, conclusion I is not true.

II) C Â© A â€“ C > A , we canâ€™t compare C and A.

So, Conlcusion II is also not true.

Given;

A $ B â€“ A ≥ B ............... (i)

C Â© D â€“ C > D ............... (ii)

D % A â€“ D < A .............. (iii)

Combining (i), (ii) and (iii), we get

C > D < A ≥ B

I) C % B â€“ C < B, we canâ€™t compare C and B.

So, conclusion I is not true.

II) C Â© A â€“ C > A , we canâ€™t compare C and A.

So, Conlcusion II is also not true.

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'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

SHOW ANSWER

Correct Ans:Only conclusion II is true.

Explanation:

% = <, @ = ≤, # = (=), Â© = >, $ = ≥

Given;

L $ M â€“ L ≥ M ............... (i)

N @ L â€“ N ≤ L ............. (ii)

M Â© O â€“ M > O ............ (iii)

Combining (i), (ii) and (iii), we get

N ≤ L ≥ M > O

I. M # N â€“ M = N is not true because we canâ€™t compare M and N.

So, conclusion I is not true.

II. O % L â€“ O < L is true.

So, conclusion II is true.

Given;

L $ M â€“ L ≥ M ............... (i)

N @ L â€“ N ≤ L ............. (ii)

M Â© O â€“ M > O ............ (iii)

Combining (i), (ii) and (iii), we get

N ≤ L ≥ M > O

I. M # N â€“ M = N is not true because we canâ€™t compare M and N.

So, conclusion I is not true.

II. O % L â€“ O < L is true.

So, conclusion II is true.

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