A question and two statements are given below. You have to decide which…

Concept:

A statement (or combination of statements) is SUFFICIENT only if it lets you pin down a single, unique numerical value for the quantity asked, using strictly the relationships that are given. If, after combining every given relation, the target expression still contains a free (unrestricted) unknown, that unknown cannot be removed by inventing a new equation of your own — the judgement must rest only on what is stated.

Application:

Let T denote the amount of money T has.

• From Statement I: S = T − 200, so S is known only in terms of T; R is not mentioned at all. R + S cannot be pinned down.

• From Statement II: R = T + 300, so R is known only in terms of T; S is not mentioned at all. R + S cannot be pinned down.

• Combining both: R + S = (T + 300) + (T − 200) = 2T + 100. This still contains the free variable T, so R + S is not a fixed number — for example, T = 0 gives R + S = 100, while T = 50 gives R + S = 200.

Cross-check:

A common trap is to set 2T + 100 = 0 (i.e., to assume R + S = 0) and solve T = -50. That step is not valid: nothing in either statement says R + S = 0 — that equation would be an assumption invented by the solver, not a fact given in the problem. Data sufficiency must be judged strictly from the given relationships; a solver is never allowed to manufacture an extra equation just to force a unique value. Since T is genuinely unconstrained by the given information, R + S has no fixed value.

Result:

Statement I alone is not sufficient, Statement II alone is not sufficient, and even both together are not sufficient, because the combined relation R + S = 2T + 100 still depends on the unknown T.