Showing posts with label #Inequality Reasoning Questions. Show all posts
Showing posts with label #Inequality Reasoning Questions. Show all posts
Saturday, October 25, 2025
Inequality Reasoning Questions
Inequality Reasoning Questions
Questions 46-50 with interactive 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 46
Statements:
M > A > R, G = R < S, F ≤ R ≤ C, Q = C > J
Conclusions:
I. M > F
II. Q = F
III. Q > F
A. Only conclusion I follows
B. Either conclusion II or III follows
C. Only conclusion III follows
D. Both option A and B
E. Both option A and C
Correct Answer: D. Both option A and B
Inequality Chain:
M
>
A
>
R
≤
C
=
Q
F
≤
R
≤
C
=
Q
✓
Conclusion I: M > F is correct (M > A > R ≥ F)
✓
Conclusion II & III: Either Q = F or Q > F is correct (F ≤ R ≤ C = Q)
Explanation: From the statements, we can derive M > A > R ≥ F, so M > F is definitely true. Also, F ≤ R ≤ C = Q, so either Q = F or Q > F must be true.
Question 47
Statements:
J = O ≤ P, T > P > X, Y ≤ X = W, S > Y > R
Conclusions:
I. T > S
II. J < Y
III. W > R
A. Only conclusion I follows
B. Only conclusions II and III follow
C. Only conclusion III follows
D. All the conclusions follow
E. None of the conclusions follow
Correct Answer: C. Only conclusion III follows
Inequality Chain:
J
=
O
≤
P
<
T
S
>
Y
≤
X
=
W
Y
>
R
✗
Conclusion I: T > S cannot be determined
✗
Conclusion II: J < Y cannot be determined
✓
Conclusion III: W > R is correct (W = X ≥ Y > R)
Explanation: From W = X ≥ Y > R, we can conclude W > R. However, we cannot establish a relationship between T and S, or between J and Y based on the given statements.
Question 48
Statements:
B ≤ A < C, M = O > A, V ≥ O > I, I < K = V
Conclusions:
I. B < V
II. A = K
III. I > C
A. Only conclusion I follows
B. Only conclusions II and III follow
C. Either conclusion I or III follows
D. All the conclusions follow
E. None of the conclusions follow
Correct Answer: A. Only conclusion I follows
Inequality Chain:
B
≤
A
<
C
A
<
O
=
M
I
<
O
≤
V
=
K
✓
Conclusion I: B < V is correct (B ≤ A < O ≤ V)
✗
Conclusion II: A = K is incorrect (A < O ≤ V = K)
✗
Conclusion III: I > C is incorrect (I < O > A < C)
Explanation: From B ≤ A < O ≤ V, we can conclude B < V. However, A < O ≤ V = K means A < K, not A = K. Also, I < O > A < C doesn't establish a relationship between I and C.
Question 49
Statements:
Y > U = X < E, L ≥ X > A = W, B < L = C < Z
Conclusions:
I. B > E
II. U < Z
III. A < Y
A. None of the conclusions follow
B. Only conclusion II follows
C. Either conclusion I or II follows
D. Only conclusions II and III follow
E. All the conclusions follow
Correct Answer: D. Only conclusions II and III follow
Inequality Chain:
Y
>
U
=
X
<
E
B
<
L
=
C
<
Z
L
≥
X
>
A
=
W
✗
Conclusion I: B > E cannot be determined
✓
Conclusion II: U < Z is correct (U = X ≤ L = C < Z)
✓
Conclusion III: A < Y is correct (A < X = U < Y)
Explanation: From U = X ≤ L = C < Z, we can conclude U < Z. From A < X = U < Y, we can conclude A < Y. However, we cannot establish a relationship between B and E.
Question 50
Statements:
M < U ≤ D < E, L ≥ O > A = D, K < L = N < F
Conclusions:
I. F > E
II. M < O
III. N ≥ U
A. None of the conclusions follow
B. Only conclusion II follows
C. Either conclusion I or II follows
D. Only conclusion III and either conclusion I or II follows
E. All the conclusions follow
Correct Answer: B. Only conclusion II follows
Inequality Chain:
M
<
U
≤
D
<
E
K
<
L
=
N
<
F
L
≥
O
>
A
=
D
✗
Conclusion I: F > E cannot be determined
✓
Conclusion II: M < O is correct (M < U ≤ D = A < O)
✗
Conclusion III: N ≥ U cannot be determined
Explanation: From M < U ≤ D = A < O, we can conclude M < O. However, we cannot establish a relationship between F and E, or between N and U based on the given statements.
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 41
Statements:
P < D ≤ U, U = G > B, Y < G ≤ L
Conclusions:
I. L > B
II. P > Y
A. Both conclusions I and II follow
B. Either conclusion I or II follows
C. Only conclusion I follows
D. Only conclusion II follows
E. Neither conclusion I nor II follows
Correct Answer: C. Only conclusion I follows
Explanation:
From the given statements:
P < D ≤ U = G > B and Y < G ≤ L
Conclusion I: L > B → Since G > B and G ≤ L, we can say L ≥ G > B, so L > B follows.
Conclusion II: P > Y → We have P < D ≤ U = G and Y < G. We cannot establish a direct relationship between P and Y, so this does not follow.
P
<
D
≤
U
=
G
>
B
Y
<
G
≤
L
Question 42
Statements:
X > Y ≥ Z, O ≥ X < E, R < O > K
Conclusions:
I. Z < E
II. O > Y
A. Both conclusions I and II follow
B. Either conclusion I or II follows
C. Only conclusion I follows
D. Only conclusion II follows
E. Neither conclusion I nor II follows
Correct Answer: A. Both conclusions I and II follow
Explanation:
From the given statements:
Z ≤ Y < X ≤ O and X < E
Conclusion I: Z < E → Since Z ≤ Y < X and X < E, we can say Z < E follows.
Conclusion II: O > Y → Since Y < X ≤ O, we can say O ≥ X > Y, so O > Y follows.
Z
≤
Y
<
X
≤
O
X
<
E
Question 43
Statements:
F < H < E, J < D > C, F = C < G
Conclusions:
I. H < C
II. D = G
A. Both conclusions I and II follow
B. Either conclusion I or II follows
C. Only conclusion I follows
D. Only conclusion II follows
E. Neither conclusion I nor II follows
Correct Answer: E. Neither conclusion I nor II follows
Explanation:
From the given statements:
F < H < E and F = C < G, and J < D > C
Conclusion I: H < C → We have F < H and F = C, so C < H, not H < C. This does not follow.
Conclusion II: D = G → We have D > C and C < G. No direct relationship can be established between D and G. This does not follow.
F
<
H
<
E
F
=
C
<
G
J
<
D
>
C
Question 44
Statements:
C < D = A, J ≤ G < A, T > J ≥ V
Conclusions:
I. G > V
II. G = V
A. Both conclusions I and II follow
B. Either conclusion I or II follows
C. Only conclusion I follows
D. Only conclusion II follows
E. Neither conclusion I nor II follows
Correct Answer: B. Either conclusion I or II follows
Explanation:
From the given statements:
C < D = A > G ≥ J ≥ V
Conclusion I: G > V → We have G ≥ J ≥ V, so G ≥ V. This could be G > V or G = V.
Conclusion II: G = V → This is also possible from G ≥ J ≥ V.
Since we cannot definitively say whether G > V or G = V, but we know that one of them must be true, either conclusion I or II follows.
C
<
D
=
A
>
G
≥
J
≥
V
Question 45
Statements:
N ≥ K > J, P = M ≥ K, Q ≤ L < M
Conclusions:
I. P > J
II. N > P
A. Both conclusions I and II follow
B. Either conclusion I or II follows
C. Only conclusion I follows
D. Only conclusion II follows
E. Neither conclusion I nor II follows
Correct Answer: C. Only conclusion I follows
Explanation:
From the given statements:
N ≥ K > J and P = M ≥ K, and Q ≤ L < M
Conclusion I: P > J → Since P = M ≥ K > J, we can say P > J follows.
Conclusion II: N > P → We have N ≥ K and P = M ≥ K, so N ≥ K ≤ P. We cannot establish that N > P. This does not follow.
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 36
Statements: B > A ≥ T, F = Y ≤ T, S > D ≤ F, Y ≤ X ≤ T
Conclusions: A ≥ F, T > D, B > Y
A. All the conclusions follow
B. Either conclusion I or II follows
C. Only conclusion I and III follow
D. Only conclusion III follows
E. None of the conclusions follows
Correct Answer: D. Only conclusion III follows
B
>
A
≥
T
≥
X
≥
Y
=
F
≥
D
Conclusion I: A ≥ F - Incorrect. From A ≥ T ≥ Y = F, we get A ≥ F, but this is not definitely true as A could be greater than F.
Conclusion II: T > D - Incorrect. We have T ≥ Y = F ≥ D, so T ≥ D, but we cannot say T > D for certain.
Conclusion III: B > Y - Correct. From B > A ≥ T ≥ Y, we get B > Y.
Only conclusion III follows. B > A ≥ T ≥ Y, so B > Y is definitely true.
Question 37
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
L
≥
Y
≥
A
<
R
S
>
Q
=
A
≥
I
Conclusion I: S > Y - Incorrect. We know S > Q = A and Y ≥ A, but we cannot determine the relationship between S and Y.
Conclusion II: R > Q - Correct. From R > A and A = Q, we get R > Q.
Only conclusion II follows. Since R > A and A = Q, R > Q is definitely true.
Question 38
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
M
<
A
≤
P
>
X
P
≥
B
=
C
<
Y
C
≥
D
>
F
=
L
Conclusion I: P ≥ D - Correct. From P ≥ B = C ≥ D, we get P ≥ D.
Conclusion II: M < C - Incorrect. We know M < A ≤ P ≥ B = C, but we cannot determine the relationship between M and C.
Only conclusion I follows. From P ≥ B = C ≥ D, we can definitely say P ≥ D.
Question 39
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
J
=
X
≤
U
>
Z
M
=
N
≥
U
=
P
L
=
O
<
N
≥
T
Conclusion I: J < N - Correct. From J = X ≤ U ≤ N, we get J ≤ N. Since J = X ≤ U and N ≥ U, and U > Z, J could be equal to U or less, but in either case J ≤ N. Since N ≥ U and U could be equal to J, we can't say J < N for certain. Wait, let me reconsider: J = X ≤ U ≤ N, so J ≤ N. We cannot say J < N for certain as J could be equal to N if J = X = U = N.
Conclusion II: O > U - Incorrect. From O < N ≥ U, we cannot determine the relationship between O and U.
Actually, let me correct this: Conclusion I is J < N. From J = X ≤ U ≤ N, we get J ≤ N. We cannot say J < N for certain as J could be equal to N. So neither conclusion follows.
Question 40
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
H
≥
V
=
O
>
R
X
≤
D
>
Y
>
R
Y
>
N
=
L
<
Z
Conclusion I: O < D - Incorrect. We know O > R and D > Y > R, but we cannot determine the relationship between O and D.
Conclusion II: R > N - Correct. From Y > R and Y > N, we cannot directly say R > N. Let me reconsider: We have O > R and Y > R, and Y > N. But we don't know the relationship between R and N. Actually, from D > Y > R and Y > N, we have R < Y and Y > N, but this doesn't tell us about R and N. R could be greater than, less than, or equal to N. So conclusion II does not follow either.
Let me analyze again: We have O > R and D > Y > R. No direct relationship between O and D. For conclusion II: R < Y and Y > N, but we cannot determine if R > N. For example, if R=5, Y=10, N=7, then R < N. If R=5, Y=10, N=3, then R > N. So neither conclusion follows. The correct answer should be A.
