What is the value of x? a) 2x + 3y = 8 b) y = 1

Concept: In data-sufficiency questions, a statement (or combination of statements) is sufficient only if it pins down a single, unique value of the quantity asked for. A single linear equation in two unknowns has infinitely many solutions, and knowing only one unrelated variable's value does not by itself determine another variable - both are treated as not sufficient alone unless they can be combined to isolate the target quantity.

Application:

1. Statement A gives 2x + 3y = 8 - one equation with two unknowns (x and y). Infinitely many (x, y) pairs satisfy it, so x cannot be pinned to a single value from A alone.

2. Statement B gives y = 1 - this fixes y but says nothing about x directly, so x still cannot be determined from B alone.

3. Combining both: substitute y = 1 into 2x + 3y = 8, giving 2x + 3(1) = 8.

4. Solve: 2x = 8 - 3 = 5, so x = 5/2.

Cross-check: substituting x = 5/2 and y = 1 back into Statement A gives 2(5/2) + 3(1) = 5 + 3 = 8, which matches - confirming the unique value. Since neither statement alone fixes x, but both together do, both statements are required.