Data sufficiency - PP x PQ = RRSS cryptarithm
Question
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: Let P, Q, R, S be distinct non-zero digits. If PP × PQ = RRSS, where P ≤ 3 and Q ≤ 4, then what is Q equal to ? Statement I: R = 1. Statement II: S = 2. Which one of the following is correct in respect of the above Question and the Statements?
Options
The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
The Question can be answered by using either Statement alone.
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
The Question can be answered even without using any of the Statements.
Explanation
Evaluate the core equation PP × PQ = RRSS under the constraints P \le 3 and Q \le 4. Since P is a digit up to 3, PP can only be 11, 22, or 33. If P=1, max product is 11 × 14 = 154 (Not 4 digits). If P=2, max product is 22 × 24 = 528 (Not 4 digits). Therefore, ⟨MATH⟩P⟨/MATH⟩ must be 3. PP is 33. Q is a distinct digit \le 4, so Q can be 1, 2, or 4 (since Q \ne P). Check Q=1: 33 × 31 = 1023 (Does not match RRSS pattern). Check Q=2: 33 × 32 = 1056 (Does not match RRSS pattern). Check Q=4: 33 × 34 = 1122. This perfectly matches the RRSS format where R=1, S=2. The value of Q is forced to be 4 by the mathematical constraints alone, rendering both statements unnecessary.
Answer: (d).
Question details
Year
2025
Paper
CSAT
Question
Q79
Section
Data Interpretation & Sufficiency
Sub-topic
Data Sufficiency
Type
Data sufficiency
Difficulty
Hard
Source hint
Data sufficiency
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