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UPSC Prelims 2025 CSAT, question 75

Topic: Arithmetic

Q75

In a T20 cricket match, three players X,YX,Y and ZZ scored a total of 37 runs. The ratio of number of runs scored by XX to the number of runs scored by YY is equal to ratio of number of runs scored by YY to number of runs scored by ZZ.

Value−I=RunsscoredbyXValue-I=Runs scored by X

Value−II=RunsscoredbyYValue-II=Runs scored by Y

Value−III=RunsscoredbyZValue-III=Runs scored by Z

Which one of the following is correct ?

  1. (a) Value−I<Value−II<Value−IIIValue-I<Value-II<Value-III
  2. (b) Value−III<Value−II<Value−IValue-III<Value-II<Value-I
  3. (c) Value−I<Value−III<Value−IIValue-I<Value-III<Value-II
  4. (d) Cannot be determined due to insufficient dataCorrect answer

Solution.

Answer: (d) Cannot be determined due to insufficient data

  1. The condition XY=YZ\frac{X}{Y} = \frac{Y}{Z} means X,Y,ZX, Y, Z are in geometric progression with X+Y+Z=37X + Y + Z = 37.
  2. Both (X,Y,Z)=(9,12,16)(X, Y, Z) = (9, 12, 16) (common ratio 43\frac{4}{3}, where Value-I<Value-II<Value-III\text{Value-I} < \text{Value-II} < \text{Value-III}) and (X,Y,Z)=(16,12,9)(X, Y, Z) = (16, 12, 9) (common ratio 34\frac{3}{4}, where Value-III<Value-II<Value-I\text{Value-III} < \text{Value-II} < \text{Value-I}) satisfy all given conditions.
  3. Because the direction of the geometric progression is not specified, the ordering cannot be determined.