Question

Is 'b' positive?
(I) a + b is positive.
(II) 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 statement I and II together are necessary to answer the question.
• D. Both statements I and II together are not sufficient to answer the question.

Hint:

Pick numbers to test both statements together; b's sign is not fixed even then.

Answer 1

The Correct Option is D

Step 1: Understand what needs to be established.
The question asks whether b is positive, that is, whether b > 0. We must check if statement (I), statement (II), or both together let us decide this with certainty.
Step 2: Test statement (I) alone.
Statement (I) says a + b > 0. Try a = 10, b = 5: a + b = 15 > 0, and b is positive. Now try a = 10, b = -5: a + b = 5 > 0, but b is negative. Both cases satisfy statement (I), yet b has a different sign in each, so statement (I) alone is not sufficient.
Step 3: Test statement (II) alone.
Statement (II) says a - b > 0. Try a = 10, b = 5: a - b = 5 > 0, and b is positive. Now try a = 10, b = -5: a - b = 15 > 0, but b is negative. Again both cases satisfy statement (II) while b changes sign, so statement (II) alone is not sufficient.
Step 4: Test both statements together.
Combine a + b > 0 and a - b > 0. Try a = 10, b = 5: both conditions hold (15 > 0 and 5 > 0), and b is positive. Now try a = 10, b = -5: a + b = 5 > 0 and a - b = 15 > 0, both conditions still hold, but b is negative. So even together, the two statements allow b to be either positive or negative.
Step 5: Conclude.
Since neither statement alone, nor both statements together, can fix the sign of b, the data is not sufficient to answer the question. This corresponds to option (4).