Xavier Aptitude Test 2025 Paper

Concept:The five consecutive distances between dustbins form a closed cycle. Adding the two-gap and three-gap distances for all five starting points gives bounds on the total circumference.Explanation:Let $x_1,x_2,\dots,x_5$ be the five consecutive distances between dustbins, measured in steps. Indices are taken cyclically, so $x_6=x_1$.The total circumference is $C=x_1+x_2+x_3+x_4+x_5$ steps.To reach every second dustbin, the distance is the sum of two consecutive gaps: $x_i+x_{i+1}$.Since the minimum such distance is 800 steps, every two-gap distance is at least 800:$$x_i+x_{i+1}\ge 800$$Summing these five inequalities gives:$$2C\ge 5\times 800=4000$$So $C\ge 2000$ steps.Similarly, to reach every third dustbin, the distance is the sum of three consecutive gaps: $x_i+x_{i+1}+x_{i+2}$.Since the maximum such distance is