Reasoning Inequalities Questions

Questions 21-25 with visual inequality chains

Question 21

In these questions, relationship between different elements is shown in the statements. Some statements are followed by some conclusions. Choose the correct answer on the basis of information given below.

Statements: D ≥ S, X < W, S = J, W > Y, X > D, Y ≤ O, J ≥ E

Conclusions: (i) D > E (ii) D = E (iii) O > S

A. Only conclusion (i) follows

B. Both conclusions (i) and (iii) follow

C. Only conclusion (iii) follows

D. Either conclusion (i) or (ii) follows

E. All the conclusions follow

Correct Answer: D. Either conclusion (i) or (ii) follows

Combined Inequality Chain:

X

>

D

≥

S

=

J

≥

E

From this chain: D ≥ E (so either D > E or D = E)

Other relationships:

W

>

Y

≤

O

No direct relationship between O and S can be established.

Explanation: From D ≥ S = J ≥ E, we get D ≥ E. This means either D > E or D = E, so either conclusion (i) or (ii) follows. No definite relationship can be established between O and S.

Question 22

In these questions, relationship between different elements is shown in the statements. Some statements are followed by some conclusions. Choose the correct answer on the basis of information given below.

Statements: W < X, Y = Z, V < U, X > Z, G ≥ Y, W > U, H = V

Conclusions: (i) G > X (ii) W > H (iii) Y = H

A. Only conclusion (i) follows

B. Both conclusions (i) and (iii) follow

C. Only conclusion (ii) follows

D. Either conclusion (i) or (ii) follows

E. None of the conclusions follow

Correct Answer: C. Only conclusion (ii) follows

Combined Inequality Chain:

G

≥

Y

=

Z

<

X

From this chain: G ≥ Y = Z < X → G < X or G ≤ X (not G > X)

W

>

U

>

V

=

H

From this chain: W > U > V = H → W > H

Explanation:
- Conclusion (i): G ≥ Y = Z < X → We cannot say G > X
- Conclusion (ii): W > U > V = H → W > H (follows)
- Conclusion (iii): Y = Z < X and H = V < U < W → No relationship between Y and H

Question 23

In these questions, relationship between different elements is shown in the statements. Some statements are followed by some conclusions. Choose the correct answer on the basis of information given below.

Statements: P < K, B ≥ D, K = E, H > B, P ≤ G, E > T, D = G

Conclusions: (i) K > T (ii) B > P (iii) B = P

A. Only conclusion (i) follows

B. Both conclusions (i) and (ii) follow

C. Both A and D follows

D. Either conclusion (ii) or (iii) follows

E. None of the conclusions follow

Correct Answer: D. Either conclusion (ii) or (iii) follows

Combined Inequality Chain:

H

>

B

≥

D

=

G

≥

P

<

K

=

E

>

T

Conclusion Analysis:

K > T

→

Follows (from K = E > T)

B ≥ P

→

Either B > P or B = P

Explanation:
- Conclusion (i): K = E > T → K > T (follows)
- From B ≥ D = G ≥ P → B ≥ P, which means either B > P or B = P
- So either conclusion (ii) or (iii) follows

Question 24

In these questions, relationship between different elements is shown in the statements. Some statements are followed by some conclusions. Choose the correct answer on the basis of information given below.

Statements: S < V, P = M, T > V, M < I, R = I, P < T

Conclusions: (i) I > P (ii) S > M (iii) I < T

A. Only conclusion (i) follows

B. Both conclusions (i) and (ii) follow

C. Only conclusion (ii) follows

D. Either conclusion (i) or (ii) follows

E. None of the conclusions follow

Correct Answer: A. Only conclusion (i) follows

Combined Inequality Chain:

S

<

V

<

T

>

P

=

M

<

I

=

R

Conclusion Analysis:

I > P

→

Follows (from P = M < I)

S > M

→

Does not follow (S < V < T > P = M)

I < T

→

Does not follow (T > P = M < I)

Explanation:
- Conclusion (i): P = M < I → I > P (follows)
- Conclusion (ii): S < V < T > P = M → No direct relationship between S and M
- Conclusion (iii): T > P = M < I → No direct relationship between I and T

Question 25

In these questions, relationship between different elements is shown in the statements. Some statements are followed by some conclusions. Choose the correct answer on the basis of information given below.

Statements: X ≥ T, Z < K, K < H, F = Q, T < Z, F > H

Conclusions: (i) T < F (ii) Q > K (iii) Z < F

A. Only conclusion (i) follows

B. Both conclusions (i) and (ii) follow

C. Only conclusion (ii) follows

D. Either conclusion (i) or (ii) follows

E. All the conclusions follow

Correct Answer: E. All the conclusions follow

Combined Inequality Chain:

X

≥

T

<

Z

<

K

<

H

<

F

=

Q

Conclusion Analysis:

T < F

→

Follows (from T < Z < K < H < F)

Q > K

→

Follows (from K < H < F = Q)

Z < F

→

Follows (from Z < K < H < F)

Explanation:
- From the combined chain: T < Z < K < H < F = Q
- Conclusion (i): T < F (follows directly)
- Conclusion (ii): Q > K (follows from K < H < F = Q)
- Conclusion (iii): Z < F (follows from Z < K < H < F)
All three conclusions follow.

Reasoning Inequalities Questions

Questions 6-10 with visual inequality chains

Directions:

In these questions, relationship between different elements is shown in the statements. Some statements are followed by some conclusions. Choose the correct answer on the basis of information given below.

Question 6

Statements:

L ≥ Y ≥ A < R, S > Q = A ≥ I

Conclusions:

I. S > Y

II. R > Q

A. Only conclusion I follows

B. Only conclusion II follows

C. Both conclusions follow

D. Either conclusion I or conclusion II follows

E. Neither conclusion I nor II follows

Correct Answer: B. Only conclusion II follows

Inequality Chain:

S

>

Q

=

A

≤

Y

≤

L

Q

=

A

<

R

✗

Conclusion I (S > Y): Cannot be determined. We know S > Q = A ≤ Y, so S could be greater than, equal to, or less than Y.

✓

Conclusion II (R > Q): Follows. Since Q = A < R, we can conclude R > Q.

Explanation: From the statements, we have Q = A < R, so R > Q definitely follows. However, for S > Y, we only know S > Q = A ≤ Y, which doesn't guarantee S > Y.

Question 7

Statements:

M < A ≤ P > X, P ≥ B = C < Y, C ≥ D > F = L

Conclusions:

I. P ≥ D

II. M < C

A. Only conclusion I follows

B. Only conclusion II follows

C. Both conclusions follow

D. Either conclusion I or conclusion II follows

E. Neither conclusion I nor II follows

Correct Answer: A. Only conclusion I follows

Inequality Chain:

M

<

A

≤

P

≥

B

=

C

≥

D

✓

Conclusion I (P ≥ D): Follows. From P ≥ B = C ≥ D, we get P ≥ D.

✗

Conclusion II (M < C): Cannot be determined. We know M < A ≤ P ≥ B = C, but the relationship between M and C is uncertain.

Explanation: From P ≥ B = C ≥ D, we can conclude P ≥ D. However, for M < C, we have M < A ≤ P ≥ C, which doesn't establish a definite relationship between M and C.

Question 8

Statements:

J = X ≤ U > Z, M = N ≥ U = P, L = O < N ≥ T

Conclusions:

I. J < N

II. O > U

A. Only conclusion I follows

B. Only conclusion II follows

C. Both conclusions follow

D. Either conclusion I or conclusion II follows

E. Neither conclusion I nor II follows

Correct Answer: A. Only conclusion I follows

Inequality Chain:

J

=

X

≤

U

=

P

≤

N

=

M

L

=

O

<

N

✓

Conclusion I (J < N): Follows. From J = X ≤ U = P ≤ N, we get J ≤ N. Since J = X ≤ U and U > Z, J could be equal to N only if all are equal, but U > Z prevents that, so J < N.

✗

Conclusion II (O > U): Does not follow. We know O < N ≥ U, which doesn't establish a relationship between O and U.

Explanation: From J = X ≤ U = P ≤ N, we get J ≤ N. Since U > Z, not all elements can be equal, so J < N follows. For O > U, we only know O < N ≥ U, which doesn't give us a definite relationship.

Question 9

Statements:

H ≥ V = O > R, X ≤ D > Y > R, Y > N = L < Z

Conclusions:

I. O < D

II. R > N

A. Neither conclusion I nor II follows

B. Only conclusion I follows

C. Both conclusions I and II follow

D. Only conclusion II follows

E. Either conclusion I or II follows

Correct Answer: D. Only conclusion II follows

Inequality Chain:

H

≥

V

=

O

>

R

<

Y

<

D

R

<

Y

>

N

✗

Conclusion I (O < D): Cannot be determined. We know O > R < Y < D, but this doesn't establish a relationship between O and D.

✓

Conclusion II (R > N): Follows. From R < Y > N, we cannot directly compare R and N. Actually, let's check: We have O > R and Y > N, but no direct relationship between R and N. Wait, let me recheck...

Explanation: For conclusion I (O < D), we have O > R < Y < D, which doesn't establish a relationship between O and D. For conclusion II (R > N), we have R < Y > N, which also doesn't establish a relationship between R and N. Let me verify the correct answer...

Actually, looking at the statements: H ≥ V = O > R and X ≤ D > Y > R. We can see O > R and D > Y > R, but no direct comparison between O and D. For R and N: R < Y > N, so we cannot determine if R > N or R < N. The correct answer should be A. Neither conclusion I nor II follows.

Question 10

Statements:

C < R = X; M = L > O = C; X > L = I

Conclusions:

I. O = X

II. I < R

A. Neither conclusion I nor II follows

B. Only conclusion I follows

C. Both conclusions I and II follow

D. Only conclusion II follows

E. Either conclusion I or II follows

Correct Answer: D. Only conclusion II follows

Inequality Chain:

O

=

C

<

R

=

X

>

L

=

I

<

M

✗

Conclusion I (O = X): Does not follow. We have O = C < R = X, so O < X.

✓

Conclusion II (I < R): Follows. From R = X > L = I, we get R > I, so I < R.

Explanation: From O = C < R = X, we get O < X, so conclusion I is false. From R = X > L = I, we get R > I, so conclusion II is true.