P, Q, R, S are four friends. Who is the youngest among them? Statements: I.…

Concept: To determine a UNIQUE minimum (the youngest) among several quantities, a statement or combination of statements is "sufficient" only if it proves ONE specific quantity is strictly smaller than every other quantity being compared — it does NOT require fixing the mutual order among the remaining (non-minimum) quantities. If no single quantity can be shown to be smaller than all the others, the information is not sufficient to identify who is youngest.

Application:

1. Statement I gives P + Q > R.

2. Statement II gives P + S < R, i.e. R > P + S.

3. Since every age is positive, R > P + S automatically gives R > S and R > P (each of P and S alone is smaller than their own sum, which is itself smaller than R).

4. From Statement I, Q > R − P. Using R > P + S from the previous step, R − P > S, so Q > R − P > S — i.e. Q > S.

5. So combining both statements establishes only R > P, R > S, and Q > S. Both R and Q are shown to be older than at least one friend, so neither R nor Q can be the youngest.

6. That leaves only P and S as possible candidates for youngest — but neither statement relates P and S to each other directly, so their relative order is still open.

Cross-check (two valid age sets, both satisfying Statement I and Statement II):

Both examples satisfy P + Q > R and P + S < R, yet the youngest friend is different in each — P in Example A, S in Example B. This confirms the two statements never pin down a unique youngest.

Result: Both statements together do not determine who is youngest — the data is not sufficient.