Question

Directions: In Question Numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct option from the following:
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.

Assertion (A): For any two prime numbers $p$ and $q$, their HCF is 1 and LCM is $p + q$.
Reason (R): For any two natural numbers, HCF × LCM = product of numbers.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

Remember: LCM of primes $p$ and $q$ is $p \cdot q$, not $p + q$.

Answer 1

The Correct Option is D

Solution: To determine the correctness of the Assertion (A) and Reason (R), we need to analyze each statement separately and see if the Reason logically explains the Assertion.

Assertion (A): For any two prime numbers $p$ and $q$, their HCF is 1 and LCM is $p + q$.

Prime numbers have no common factors other than 1, so their Highest Common Factor (HCF) is indeed 1. However, the Least Common Multiple (LCM) of two prime numbers is not their sum. Instead, it is their product because there is no smaller common multiple other than that. Therefore, Assertion (A) is false.

Reason (R): For any two natural numbers, HCF × LCM = product of numbers.

This is a well-known arithmetic property and holds true for any two numbers. Therefore, Reason (R) is true.

Conclusion: Since Assertion (A) is false and Reason (R) is true, the correct option is:

Assertion (A) is false, but Reason (R) is true.