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

Concept: A data-sufficiency statement (or combination of statements) is sufficient only if it pins down a single, unique answer to the question asked — not merely a plausible one. For a work-rate problem, the governing identity is rate = 1 / time, and when two or more people work together their combined rate is simply the sum of their individual rates.

Application: let the hourly work rates of A, B, and C (fraction of the wall completed per hour) be a, b, and c.

1. Statement I gives the combined rate of A and B: a + b = 1/5.

2. Statement II gives the combined rate of all three together: a + b + c = 1/3.

3. Subtracting the first equation from the second isolates C's individual rate: c = 1/3 - 1/5 = 2/15, so C alone would take 7.5 hours to build the wall.

4. However, a + b = 1/5 is only a single combined figure. It does not split into unique individual values of a and b, so A and B's individual rates — and hence which of the two is slower — remain undetermined even after using both statements together.

Cross-check: two different splits of a + b = 1/5 both satisfy the statements but hand the wall to a different 'slowest builder' each time.

Both splits satisfy a + b = 1/5 (Statement I) and c = 2/15 (both statements together), yet they name a different builder as slowest. Since two scenarios that are both consistent with the given statements produce different answers, the two statements together fail to fix a unique answer.

It can also be shown that C alone can never be the unique slowest: if both A and B individually took less than 7.5 hours each, their combined rate would exceed 1/5, contradicting Statement I. So the slowest builder is always A or B — but exactly which one depends entirely on the unknown split, so the question still cannot be answered. Both the statements, put together, are not sufficient.