TANCET 2025 Solved Papers

Concept:For $m$ to be divisible by $12$, it must be divisible by both $3$ and $4$.Being divisible by $6$ only gives factors $2$ and $3$, not $4$.Explanation:Statement (1): $m$ is divisible by $6$.So, $m$ could be $6$, $12$, $18$, etc.These are not always divisible by $12$.Thus, Statement (1) alone is not sufficient.Statement (2): $m$ is divisible by $3$.So, $m$ could be $3$, $6$, $9$, $12$, etc.Again, these are not always divisible by $12$.Thus, Statement (2) alone is not sufficient.Combining both statements: $m$ is divisible by $6$ and by $3$.Since divisibility by $6$ already includes divisibility by $3$, the second statement adds no new condition.For example, $m=6$ or $m=18$ satisfies both, yet is not divisible by $12$.So, even together the statements are not sufficient.Answer:Option D — Statements (1) and (2) TOGETHER are NOT sufficient.