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UPSC Prelims 2025 CSAT, question 69

Topic: Data sufficiency

Q69

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,SP,Q,R,S be distinct non-zero digits. If PP×PQ=RRSSPP \times PQ=RRSS, where P≤3P \le 3 and Q≤4Q \le 4, then what is QQ equal to ?

Statement-I : R=1R=1.

Statement-II : S=2S=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 can be answered even without using any of the Statements.Correct answer

Solution.

Answer: (d) The Question can be answered even without using any of the Statements.

  1. Testing all pairs of distinct non-zero digits P∈{1,2,3}P \in \{1, 2, 3\} and Q∈{1,2,3,4}Q \in \{1, 2, 3, 4\} in PP×PQ=RRSSPP \times PQ = RRSS shows that only P=3,Q=4P = 3, Q = 4 gives a 4-digit number of the form RRSSRRSS: 33×34=112233 \times 34 = 1122 (R=1,S=2R = 1, S = 2, all four digits distinct).
  2. Since Q=4Q = 4 is uniquely determined by the Question stem alone, the Question can be answered even without using any of the Statements.