Question

Choose the statement/statements required to answer the question by selecting the right option.
Question: Is X a positive integer?
Statements:
I. X² = 49
II.X < 8

• A. Statement I alone is sufficient but statement II alone is insufficient
• B. Statement II alone is sufficient but statement I alone is insufficient
• C. Both statements I and II together are sufficient
• D. The question can't be answered even by using both the statements

Answer 1

The Correct Option is D

Step 1: Analyze Statement I:

• It states that X² = 49. 
• Solving for X, we get: X = ±7.
• This means X can be either +7 or −7, but we do not know if X is positive.

Conclusion: Statement I alone is insufficient.

Step 2: Analyze Statement II:

• It states that X < 8.
• This condition does not give any information about whether X is positive or not.

Conclusion: Statement II alone is insufficient.

Step 3: Combine both statements:

• From Statement I, X = ±7.
• From Statement II, X < 8.
• The possible values of X are still +7 and −7, both of which satisfy X < 8.

Since we still have ambiguity (both positive and negative values are possible), we cannot conclusively say X is positive.

Final Conclusion: Even using both statements together, we cannot determine whether X is a positive integer.