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 ?
- (a) Value-I < Value-II < Value-III
- (b) Value-III < Value-II < Value-I
- (c) Value-I < Value-III < Value-II
- (d) Cannot be determined due to insufficient data ✓ UPSC's answer
Why the answer is (d)
• X : Y = Y : Z means Y² = X × Z, so the runs X, Y, Z form a geometric progression with Y in the middle.
• With X + Y + Z = 37 and whole-number runs, the only solution is the numbers 9, 12, 16 (12² = 144 = 9 × 16 and 9 + 12 + 16 = 37); equal scores are impossible because 37 is not divisible by 3.
• These can be taken in either order: X = 9, Y = 12, Z = 16, or X = 16, Y = 12, Z = 9 — both satisfy every condition.
• So X could be less than or greater than Y; the order of the three values cannot be fixed — option (d).
Why the other options are wrong
- (a) Value-I < Value-II < Value-III
- This option assumes the GP is increasing, but a decreasing GP (e.g., 16, 12, 9) is also a valid solution.
- (b) Value-III < Value-II < Value-I
- This option assumes the GP is decreasing, but an increasing GP (e.g., 9, 12, 16) is also a valid solution.
- (c) Value-I < Value-III < Value-II
- This option suggests an order that does not correspond to a standard Geometric Progression where the middle term is the geometric mean of the other two.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.