CAT 2025 Number System Question (Hard)

Question

Let and , where is the greatest integer not exceeding . If set represents all feasible values of , then a possible subset of is

Accepted Answer

Given and , where is the greatest integer not exceeding . Goal Determine the solution set and verify that option D is a possible subset of . 1. Partition by the integer part . For the possible values are . Treat each case on the interval where . 2. Case so then , so . This means , hence . The endpoi

CAT 2025

Quantitative

Number System

Hard

Let $3 \leq x \leq 6$ and $\lfloor x^2 \rfloor = \lfloor x \rfloor^2$ , where $\lfloor x \rfloor$ is the greatest integer not exceeding $x$ . If set $S$ represents all feasible values of $x$ , then a possible subset of $S$ is:

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