PP is a two-digit number with the same digits: $11P$. Similarly, PQ is the two-digit number: $(10P + Q)$. RRSS is a four-digit number with first two digits R and last two digits S and S.

Given: $PP \times PQ = RRSS$ $\Rightarrow (11P) \times (10P + Q) = RRSS$

Step 2: Since $P \le 3$ and $Q \le 4$, test values for $P = 1, 2, 3$ and $Q = 1$ to $4$.

Check $P = 3$: $PP = 33$

Now compute $33 \times (30 + Q)$: $Q = 1 \rightarrow 33 \times 31 = 1023$ (not of form RRSS) $Q = 2 \rightarrow 33 \times 32 = 1056$ (not RRSS) $Q = 3 \rightarrow 33 \times 33 = 1089$ (not RRSS) $Q = 4 \rightarrow 33 \times 34 = 1122$ (this is RRSS form)

So: $RRSS = 1122 \rightarrow R = 1$ and $S = 2$, and $Q = 4$.

Step 3: Did we need the statements? We derived the solution directly using the main condition.
The statements ($R = 1$ and $S = 2$) merely confirm what we already found.

Therefore, the question can be solved without using either statement.