In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X to the number of runs scored by Y is equal to ratio of number of runs scored by Y to number of runs scored by Z.
- Value-I: Runs scored by X
- Value-II: Runs scored by Y
- Value-III: Runs scored by Z
Which one of the following is correct?
Answer & explanation
Answer: (d) Cannot be determined due to insufficient data
The condition only says X, Y and Z are in geometric progression with a total of 37. Both 16, 12, 9 and 9, 12, 16 satisfy it, giving opposite orders, so the comparison cannot be determined.
- X : Y = Y : Z means Y² = X × Z, with X + Y + Z = 37.
- Try Y = 12: then X × Z = 144 and X + Z = 25, so X and Z are 16 and 9.
- Both (X, Y, Z) = (16, 12, 9) and (9, 12, 16) fit: 16 × 9 = 144 = 12², and the total is 37.
- The first gives Value-III < Value-II < Value-I; the second gives Value-I < Value-II < Value-III.
- The order cannot be fixed from the data.
Remember · For a 'cannot be determined' option, try to build two valid cases with different orders; one such pair settles it.
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·