Three statements are given followed by two conclusions I and II. Assuming the…
2023
Three statements are given followed by two conclusions I and II. Assuming the statements to be true decide which of the conclusions is/are definitely true. Statements: M > Q
P ≥ M
N ≤ M
Conclusions: I. Q = N II. Q < P
- A.
Only conclusion II is true.
- B.
Both conclusions I and II are true.
- C.
Neither conclusion I nor II is true.
- D.
Only conclusion I is true.
Attempted by 152 students.
Show answer & explanation
Correct answer: A
Answer: Only conclusion II is true.
Reasoning:
From M > Q and P ≥ M we get P > Q, so Q < P. Therefore conclusion II is definitely true.
Conclusion I (Q = N) is not guaranteed because N ≤ M allows N to be less than, equal to, or (if equal to M) possibly different from Q. A concrete counterexample shows it can be false:
Example: Let M = 3, Q = 2, N = 1, P = 3. Then M > Q (3 > 2), P ≥ M (3 ≥ 3), and N ≤ M (1 ≤ 3) all hold, but Q ≠ N. Thus conclusion I is not definitely true.
Conclusion: Only conclusion II is definitely true; conclusion I is not necessarily true.