Question 1

Given: P ≤ Q, Q < R, R ≥ S, S > T, T ≤ U. Which of the following is INDETERMINATE?

Accepted Answer

From the inequalities: P ≤ Q < R ≥ S > T ≤ U. We can establish: P ≤ Q < R, R ≥ S, S > T, T ≤ U. Now check each option: (a) P < R: Since P ≤ Q and Q < R, we have P < R (definite). (b) S ≤ U: We know S > T and T ≤ U, but this doesn't tell us if S ≤ U or S > U (indeterminate). (c) Q ≥ T: We know Q < R and R ≥ S and S > T, so Q < R and R ≥ S > T, which means Q could be greater than, equal to, or less than T (indeterminate, but let's verify). Actually, we cannot determine Q vs T. (d) P ≤ S: We have P ≤ Q < R ≥ S, so P ≤ Q < R and R ≥ S, but this doesn't guarantee P ≤ S.

Question 2

Given: A > B, B ≥ C, C > D, D = E, E < F. Which of the following conclusions is definitely TRUE?

Accepted Answer

From the given inequalities: A > B ≥ C > D = E < F. We need to determine what must be true. A > B is given. B ≥ C is given. C > D is given. D = E is given. Therefore, A > B ≥ C > D = E. This means A > C is definitely true. However, we cannot determine the relationship between A and F (F could be less than, equal to, or greater than A). We also cannot determine if B > D (though it's likely, the chain A > B ≥ C > D confirms B > D). The only definitive conclusion is A > C.

Question 3

Read the following statements carefully and answer the question.

Statements:
1. A > B ≥ C
2. C > D
3. D ≥ E
4. B < F

Which of the following conclusions is definitely TRUE?

A) E > C
B) F > A
C) A > E
D) E = D

Accepted Answer

From the given statements, we need to establish a chain of inequalities: From Statement 1: A > B ≥ C From Statement 2: C > D From Statement 3: D ≥ E From Statement 4: B < F Combining Statements 1, 2, and 3: A > B ≥ C > D ≥ E This gives us: A > B > C > D ≥ E Therefore: A > E (definitely true) Let's verify each option: A) E > C: FALSE. From the chain, C > D ≥ E, so E ≤ D < C. Thus E is not greater than C. B) F > A: INDETERMINATE. We know B < F and A > B, but we cannot determine if F > A or F ≤ A (F could be between B and A, or greater than A). C) A > E: TRUE. From the complete chain A > B ≥ C > D ≥ E, we definitively have A > E. D) E = D: INDETERMINATE. Statement 3 says D ≥ E, which means D could equal E or D could be greater than E.

Question 4

Given: X ≥ Y, Y > Z, Z ≤ W, W < V, V ≥ U. Which of the following CANNOT be determined?

Accepted Answer

From the inequalities: X ≥ Y > Z ≤ W < V ≥ U. Check each option: (a) X > Z: X ≥ Y and Y > Z, so X > Z (definite). (b) W ≥ Z: Z ≤ W means W ≥ Z (definite). (c) V > Z: V > W and W ≥ Z, so V > Z (definite). (d) X ≥ U: X ≥ Y > Z ≤ W < V ≥ U. We have X ≥ Y and Y > Z, so X > Z. We have Z ≤ W < V ≥ U. But there's no direct chain from X to U. X could be 10, Y could be 9, Z could be 5, W could be 5, V could be 6, U could be 6. Here X > U. But X could be 6, Y could be 6, Z could be 5, W could be 5, V could be 6, U could be 6. Here X = U. Or X could be 5, Y could be 5, Z could be 5, W could be 5, V could be 6, U could be 6. Here X < U. So X ≥ U cannot be determined.

Question 5

Given: M > N > O, O ≥ P, P > Q, Q ≤ R, R < S. Which conclusion is DEFINITELY FALSE?

Accepted Answer

From the inequalities: M > N > O ≥ P > Q ≤ R < S. Now check each option: (a) M > Q: M > N > O ≥ P > Q, so M > Q (true). (b) Q ≥ P: We have P > Q, so Q < P, meaning Q ≥ P is false. (c) R > Q: We have Q ≤ R, which means Q < R or Q = R, so R ≥ Q, making R > Q indeterminate (could be true or false). (d) N > P: We have N > O ≥ P, so N > P (true).

Question 6

Read the following statements carefully and answer the question.

Statements:
1. A > B ≥ C
2. C > D
3. E ≤ B
4. D ≥ F

Which of the following conclusions is DEFINITELY TRUE?

A) E > D
B) F < C
C) A > F
D) E ≥ C

Accepted Answer

This question tests the ability to chain inequalities logically and identify what can be definitively concluded versus what remains indeterminate.

Question 7

Given:
M < N ≤ O
P ≥ O > Q
R = Q < S

Which of the following is DEFINITELY FALSE?

Accepted Answer

This question tests the ability to identify what cannot possibly be true given the constraint chains—requiring both forward and reverse logical reasoning.

Question 8

Given the relationships:
J ≥ K > L
M < L ≤ N
N = O < P

Which of the following is DEFINITELY TRUE?

Accepted Answer

This question tests the ability to correctly chain inequalities with mixed operators (≥, >, <, ≤, =) and identify what must logically follow.

Question 9

Consider:
X ≤ Y < Z
A > Z ≥ B
B = C < D

Which conclusion CANNOT be determined as true or false from the given information?

Accepted Answer

This question assesses the ability to identify indeterminate relationships when constraint chains do not directly connect two variables.

Question 10

Given the following relationships:
A > B ≥ C
D < C ≤ E
E = F > G

Which of the following conclusions is DEFINITELY TRUE?

Accepted Answer

This question tests the ability to chain inequalities correctly and identify what must logically follow from given constraints.

Question 11

Given the following relationships:
A > B ≥ C > D
E < C
F ≤ B
G > A

Which of the following conclusions is DEFINITELY TRUE?

Accepted Answer

This question tests the ability to chain inequalities correctly and identify what must logically follow from multiple constraints.

Question 12

Given:
M < N ≤ O
P > O
Q ≥ N
R < M

Which of the following is DEFINITELY TRUE?

Accepted Answer

This question tests the ability to identify definitive conclusions from overlapping inequality constraints involving six variables.

Question 13

Given the constraints:
D ≤ E < F
G > F
H ≥ E
I < D

Which of the following is INDETERMINATE (cannot be concluded as definitely true or false)?

Accepted Answer

This question tests the ability to distinguish between definitive conclusions and indeterminate relationships—a critical skill in logical reasoning.

Question 14

Consider:
X ≥ Y > Z
A < Z
B ≤ Y
C > X

Which conclusion is DEFINITELY FALSE?

Accepted Answer

This question requires identifying which statement cannot logically follow from the given constraints—testing negation and impossibility recognition.

Question 15

Given the following relationships:
A > B ≥ C > D
E ≤ C
F > A
G < D

Which of the following conclusions is DEFINITELY TRUE?

Accepted Answer

This question tests the ability to chain inequalities correctly and identify what must logically follow from given constraints, while avoiding assumptions about unmeasured relationships.

SBI PO Statement & Assumptions

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Statement & Assumptions — Practice Questions

60-Second Revision — Statement & Assumptions