NIMCET 2025 — Reasoning PYQ

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Question

NIMCET 2025 — Reasoning PYQ

NIMCET | Reasoning | 2025

"In order to be a teacher one must graduate from college. All poets are poor. Some Mathematicians are poets. No college graduate is poor." Based on these statements, which of the following must be true?

Choose the correct answer:

Explanation

1. Logical Statements:

$T \implies G$

(Teacher $\rightarrow$ Graduate)
$P \implies R$

(Poet $\rightarrow$ Poor)
$M \cap P \neq \emptyset$

(Some Mathematicians are Poets)
$G \cap R = \emptyset$

(No Graduate is Poor)

2. Deduction Steps:

From

$G \cap R = \emptyset$

and

$T \subseteq G \implies T \cap R = \emptyset$

(Teachers are not Poor).
From

$P \subseteq R$

and

$T \cap R = \emptyset \implies T \cap P = \emptyset$

(No Teacher is a Poet).
From

$M \cap P \neq \emptyset$

, there exists a group of Mathematicians who are Poets ( $M_p$ ).
Since

$M_p \subseteq P$

and

$P \cap T = \emptyset \implies M_p \cap T = \emptyset$

.

3. Final Conclusion:

(\text{Some Mathematicians}) \notin \text{Teachers}

Correct Answer: Option A