Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits…

Quantitative Aptitude ·Previously asked in UPSC Civil Services Examination 2025

View the full solved paper: GS Paper II

Question

Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR − PS = PPT. If Q = 3 and T < 6, then what is the number of possible values of (R, S)?

  1. A. 2
  2. B. 3 (Correct answer)
  3. C. 4
  4. D. More than 4

Correct Answer

Option B — 3

Detailed Solution & Explanation

The correct answer is 3.

Key Points

  • PQR − PS = PPT, Q=3. P3R − PS = PPT.
  • Working through digit constraints with T<6: P=1 gives 13R−1S=11T.
  • Testing valid digit combinations where R,S,T are distinct non-zero digits and T<6, there are 3 valid (R,S) pairs. Answer: 3.