CUET PG 2021 — Reasoning PYQ

1. Logical Analysis

In a typical group such as $\{13,17,19,21\}$:

• 13, 17, and 19 are Prime Numbers (they have exactly two factors: 1 and themselves).

• 21 is a Composite Number (it has more than two factors: 1, 3, 7, and 21).

2. Mathematical Definition

The set of Prime Numbers $P$ is defined as:

For the number 21, we find its prime factorization:

Since $21$ has divisors other than $1$ and itself:

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3. Alternative Logic (Divisibility)

If the other numbers are not prime, 21 might be different based on a divisibility rule (e.g., being the only number divisible by $3$ or $7$).

If the group is $\{14,28,35,21\}$, all follow the rule:

In that case, you would look for the one number that cannot be divided by $7$.

Final Answer:

The number 21 is usually the correct answer because it is Composite, whereas the others are Prime.