Question

Is 'b' positive?

1. a + b is positive.
2. a - b is positive.

• A. Statement I alone is sufficient to answer the question.
• B. Statement II alone is sufficient to answer the question.
• C. Both statements I and II together are necessary to answer the question.
• D. Both statements I and II together are not sufficient to answer the question.

Answer 1

The Correct Option is D

To determine whether 'b' is positive, let's analyze the given statements:

1. The statement a + b is positive implies that a + b > 0. However, this alone does not provide definitive information about the sign of 'b'. For instance, if a = 1 and b = -1, the sum is still zero, and 'b' is not positive.

2. The statement a - b is positive implies that a - b > 0. Again, this statement by itself does not confirm whether 'b' is positive. Consider a = 1 and b = 0.5; 'b' is positive. Alternatively, a = 3 and b = 2.5 also validates the condition without verifying 'b' is positive.

Combining both statements:

• If we solve the equations a + b > 0 and a - b > 0 simultaneously:

  • From a + b > 0, rearrange to get b > -a.

  • From a - b > 0, rearrange to get b < a.

  The critical range for 'b' is -a < b < a, which gives no definitive conclusion on whether 'b' is positive or negative, as 'b' could still have either sign within this range.

Thus, neither statement alone nor both combined are sufficient to conclude if 'b' is positive.

Conclusion: The correct answer is: Both statements I and II together are not sufficient to answer the question.