Are a and b relatively prime numbers? I. The HCF of a and b is 1. II. Either a or b is a prime number.

Statement I ALONE is sufficient but statement II ALONE is not sufficient.
Statement II ALONE is sufficient but statement I ALONE is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.

Correct answer: Statement I ALONE is sufficient but statement II ALONE is not sufficient.

Solution

Statement I directly says the HCF of a and b is 1, which means they are relatively prime, so it is sufficient. Statement II is not sufficient because one number being prime does not ensure the pair is relatively prime.

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