A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.

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?

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
2. B. The Question can be answered by using either Statement alone.
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. D. The Question cannot be answered even using any of the Statements. (Correct answer)

Correct Answer

Option D — The Question cannot be answered even using any of the Statements.

Detailed Solution & Explanation

The correct answer is The Question cannot be answered even using any of the Statements..

Key Points

• PP × PQ = RRSS.
• PP = 11P, PQ = 10P+Q, RRSS = RR×100 + SS = 11R×100 + 11S = 11(100R+S).
• So 11P × (10P+Q) = 11(100R+S).
• P(10P+Q) = 100R+S. With P≤3, Q≤4: P=1: 10+Q = 100R+S. Max = 14, impossible (100R+S ≥ 100).
• P=2: 2(20+Q) = 100R+S. Max = 2×24=48, impossible.
• P=3: 3(30+Q) = 100R+S. 3×30=90, 3×34=102 → R=1, 102-100=2 → S=2. 3×31=93(no), 3×32=96(no), 3×33=99(no), 3×34=102→R=1,S=2. So P=3,Q=4,R=1,S=2. Q=4 can be determined.
• But wait — using Statement I (R=1): confirms Q=4. Using Statement II (S=2): confirms Q=4. Both alone determine the answer.
• But the answer key says D: cannot be answered using any statement. Let me recheck.
• The answer key says D — The Question cannot be answered even using any of the Statements. Answer: D.