What is the value of a + b? a) a = b b) 2a = 6

Concept: In a Data Sufficiency question, a statement (or combination of statements) is sufficient only if it pins down a single, unique value for the quantity asked — here, a + b. If a statement is consistent with more than one possible value of that quantity, it is insufficient, no matter how much algebra it allows.

Application:

1. Statement (a) alone: a = b relates the two variables but fixes no numbers — a = b = 1 gives a sum of 2, a = b = 5 gives a sum of 10, and so on. The sum is not unique, so statement (a) alone is insufficient.

2. Statement (b) alone: 2a = 6 gives a = 3, but b is unconstrained, so a + b can take infinitely many values. Statement (b) alone is insufficient.

3. Combine both: from statement (b), a = 3. Substituting into statement (a) (a = b) gives b = 3. So a + b = 3 + 3 = 6, a single determined value.

Cross-check: Since neither statement alone pins the sum to one value, but the pair together does, the correct classification is that both statements together are required — not either statement alone, and not one statement alone.