UPSC Prelims 2025·CSAT·Quantitative Aptitude·Arithmetic

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?

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  1. AValue-I < Value-II < Value-III
  2. BValue-III < Value-II < Value-I
  3. CValue-I < Value-III < Value-II
  4. DCannot be determined due to insufficient dataCorrect

Explanation

To solve this problem, let the runs scored by X, Y, and Z be x, y, and z respectively. The total runs are x plus y plus z equals 37. The given ratio condition is x divided by y equals y divided by z, which means y squared equals x times z.

This indicates that x, y, and z form a geometric progression. Since the number of runs must be non negative integers, we can test possible sets of numbers.

Case 1: If x equals 9, y equals 12, and z equals 16, the sum is 37 and the ratio is 3 to 4. In this case, x is less than y is less than z.

Case 2: If x equals 16, y equals 12, and z equals 9, the sum is 37 and the ratio is 4 to 3. In this case, z is less than y is less than x.

Case 3: If x, y, and z are all equal, the sum 37 is not divisible by 3, so this is not possible with integers.

Because both increasing and decreasing sequences satisfy the given conditions, we cannot determine the specific order of the values. Therefore, the answer cannot be determined due to insufficient data. Choice D is correct.

Quantitative Aptitude: 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 t
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