Question 1

Given: A ≥ B, B > C, C ≥ D, D < E, E ≤ F. Which of the following is DEFINITELY FALSE?

Accepted Answer

From the inequalities: A ≥ B > C ≥ D < E ≤ F. Let's check each option: (1) A > C: A ≥ B and B > C means A > C (true). (2) D < F: D < E and E ≤ F means D < F (true). (3) B > D: B > C and C ≥ D means B > D (true). (4) E > C: E > D and D ≥ C would give E > C, but we have C ≥ D, not D ≥ C. We have D < E, but no direct relationship between E and C. However, C ≥ D and D < E means we cannot conclude E > C. In fact, E could be less than C. Example: C = 10, D = 10, E = 11, but also C = 10, D = 5, E = 6 works with C ≥ D false. Let me reconsider: C ≥ D and D < E. If C = 5, D = 5, E = 6, then E > C. If C = 10, D = 5, E = 6, then E < C. So E > C is indeterminate, not false.

Question 2

Given: P ≤ Q, Q < R, R ≥ S, S > T, T ≤ U. Which conclusion is DEFINITELY FALSE?

Accepted Answer

From the inequalities: P ≤ Q < R ≥ S > T ≤ U. We need to identify what is definitely false. Let's check each option: (1) P < R: P ≤ Q and Q < R means P < R (true). (2) S > T is given (true). (3) R > T: R ≥ S and S > T means R > T (true). (4) P > T: P ≤ Q < R ≥ S > T. We have P ≤ Q and Q < R, so P < R. We have R ≥ S and S > T, so R > T. But we cannot conclude P > T because P could be less than T.

Question 3

Given: M ≥ N, N > O, O ≤ P, P < Q, Q = R. Which of the following is INDETERMINATE (cannot be determined)?

Accepted Answer

From the inequalities: M ≥ N > O ≤ P < Q = R. Let's analyze: (1) M > O: M ≥ N and N > O means M > O (true). (2) P > O: O ≤ P means P ≥ O, so P > O is indeterminate (P could equal O). (3) Q > N: Q = R and P < Q. We have N > O and O ≤ P, so N > O ≤ P < Q. This doesn't establish a definite relationship between Q and N. (4) R ≥ M: R = Q and P < Q, but M ≥ N > O ≤ P. We cannot compare M with R.

Question 4

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

Which of the following conclusions is DEFINITELY TRUE?

Accepted Answer

This question tests the ability to chain inequalities and identify definite relationships while avoiding assumptions about unmeasured comparisons.

Question 5

Study the following statements carefully and answer the question.

Given:
• A > B ≥ C
• C > D
• E ≤ B
• D ≥ F

Which of the following conclusions is definitely TRUE?

I. A > D
II. E ≤ C
III. F < A

Accepted Answer

This is a statement and conclusions question testing the ability to chain inequalities and identify definite logical relationships. Step 1: Map all relationships: - A > B ≥ C (so A > C) - C > D (so A > D via transitivity) - E ≤ B - D ≥ F (so D ≥ F) Step 2: Evaluate Conclusion I (A > D): From A > B ≥ C and C > D, we get A > B > D (since B ≥ C and C > D means B > D). Therefore A > D is DEFINITELY TRUE. ✓ Step 3: Evaluate Conclusion II (E ≤ C): We know E ≤ B and B ≥ C. This means E ≤ B and C ≤ B, but we cannot determine the relationship between E and C. Example: E = 5, B = 10, C = 6 satisfies all conditions but E > C. Therefore E ≤ C is INDETERMINATE. ✗ Step 4: Evaluate Conclusion III (F < A): We know D ≥ F and A > D. So A > D ≥ F means A > F (or A ≥ F at minimum). But the chain A > D ≥ F gives us A > F, so F < A is DEFINITELY TRUE. ✓ Step 5: Identify which conclusions are definitely true: Conclusions I and III are both definitely true. Conclusion II is indeterminate. Therefore, the answer is: Only I and III are definitely true.

Question 6

Given:
A ≤ B < C
D > C
E ≥ B
F < A

Which of the following conclusions is DEFINITELY FALSE?

Accepted Answer

This question requires identifying a statement that contradicts the constraint system, testing negation and inequality reversal logic.

Question 7

Analyze the following:
X ≥ Y > Z
W < Z
V ≤ Y
U > X

Which conclusion is DEFINITELY TRUE?

Accepted Answer

This question tests chaining inequalities across multiple variables and identifying the one relationship that must hold under all valid assignments.

Question 8

Given:
M > N ≥ O
P ≤ N
Q < O
R ≥ M

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

Accepted Answer

This question tests recognition of relationships that cannot be determined from the given constraints, requiring students to avoid over-inference.

Question 9

Study the following statements carefully and answer the question. Given: • A > B ≥ C • C > D • E ≤ B • F < D Which of the following conclusions is DEFINITELY TRUE? I. A > D II. E < C III. F < B IV. A ≥ E

Accepted Answer

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

Question 10

Given the following statements:
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 multiple constraint statements.

Question 11

Given:
M < N ≤ O
O < P = Q
Q ≥ R > S

Which of the following is INDETERMINATE (cannot be proven true or false)?

Accepted Answer

This question tests the ability to distinguish between conclusions that are logically certain, logically impossible, and logically indeterminate based on given constraints.

Question 12

Consider the statements:
X ≥ Y > Z
W ≤ Z < V
V = U > T

Which conclusion is DEFINITELY TRUE?

Accepted Answer

This question tests the ability to identify certain conclusions by chaining inequalities across multiple statements and recognizing transitive relationships.

Question 13

Given:
A ≤ B < C
D > C ≥ E
E > F = G

Which of the following is DEFINITELY FALSE?

Accepted Answer

This question requires students to identify a statement that contradicts the given inequalities, testing logical negation and the ability to recognize impossible relationships.

RRB NTPC Statement & Conclusions

RRB NTPC Statement & Conclusions — Past Exam Questions

Statement & Conclusions— Rules & Concept

Key Points to Remember

Exam-Specific Tips

60-Second Revision — Statement & Conclusions