Odd number basic definition – UGC NET Question

This option is correct because an odd number is defined as an integer that is not divisible by 2. When an odd number is divided by 2, it always leaves a remainder of 1. This matches exactly the condition given in the question. Therefore, an integer not divisible by 2 is called an odd number.

Option A:
An odd number has the form 2k+1 for some integer k and is not divisible by 2. Dividing any odd number by 2 leaves a remainder of 1, which fits the description in the stem. Hence, this option correctly names the type of number described.

Option B:
An even number is divisible by 2 and leaves no remainder on division by 2. The question specifies numbers that are not divisible by 2, so this property does not match. Therefore, this option is not correct here.

Option C:
A prime number is defined by having exactly two distinct positive divisors, 1 and the number itself. Some primes are odd but the concept of primality does not directly refer to divisibility by 2 alone. Hence, prime is not the specific term required by the question.

Option D:
A composite number has more than two positive divisors. It can be even or odd, and its definition is unrelated to divisibility by 2 alone. Therefore, composite is not the best term for numbers that are simply not divisible by 2.