Comparative - three players' runs in T20
Question
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?
Options
Value-I < Value-II < Value-III
Value-III < Value-II < Value-I
Value-I < Value-III < Value-II
Cannot be determined due to insufficient data
Explanation
We are given X + Y + Z = 37 and X/Y = Y/Z, which means Y² = XZ. The runs must be positive integers. Testing possible integer values for Y where Y² can be factored into X and Z such that X+Z = 37-Y, we find Y = 12. Y² = 144. The remaining sum is 37 - 12 = 25. The factors of 144 that sum to 25 are 9 and 16. This gives two equally valid sets of scores: (X=9, Y=12, Z=16) where X < Y < Z, and (X=16, Y=12, Z=9) where Z < Y < X. Since both sequences perfectly satisfy the ratios, a definitive order cannot be determined.
Answer: (d).
Question details
Year
2025
Paper
CSAT
Question
Q55
Section
Data Interpretation & Sufficiency
Sub-topic
Comparative Quantitative
Type
Comparative quantitative
Difficulty
Medium
Source hint
Quantitative comparison
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