Who is the slowest among the three builders A, B, and C? Statements: I. A and…

Concept: In data-sufficiency work-rate problems, a statement that gives only the combined rate of a group of workers fixes that group's total rate, but it does not fix each worker's individual rate unless enough independent equations exist to solve for every unknown separately. With n unknown individual rates, you need n independent equations to pin all of them down; fewer equations leave some unknowns tied together only by a sum.

Application: Statement I gives the combined rate of A and B (one equation in two unknowns, rate(A) and rate(B)). Statement II gives the combined rate of A, B, and C (one equation in three unknowns). Subtracting statement I's combined rate from statement II's combined rate isolates rate(C) exactly. But that leaves only rate(A) + rate(B) known as a single sum — two unknowns tied to one equation. This has infinitely many valid splits (for example, A could be much faster than B, or the reverse, or they could be equal), and different splits can change whether A or B is the slowest of the three.

Cross-check: Since rate(C) is fixed but rate(A) and rate(B) individually are not, you cannot always tell whether A, B, or C is slowest — the answer would change depending on how the A+B sum is actually split between them. Because at least two genuinely different splits are consistent with both statements and would name different builders as slowest, the two statements together do not sufficiently determine who is the slowest builder.