Question 19 Statement A (Assertion): HCF of any two consecutive even natural numbers is always 2. Statement R (Reason): Even natural numbers are divisible by 2. (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 and 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.Checking Assertion
HCF of any two consecutive even natural numbers is always 2.
Two consecutive even natural numbers is 2, 4 OR 6, 8 OR 18, 20
Finding HCF of 6 & 8
6 = 2 × 3
8 = 2 × 2 × 2
∴ H.C.F = 13
Finding HCF of 18 & 20
18 = 2 × 3 × 3
20 = 2 × 2 × 5
∴ H.C.F = 2
Since HCF is 2 in both cases
Hence, the Assertion is true
Checking Reason
Even natural numbers are divisible by 2.
Since even numbers are always divisble by 2
Thus, Reason is true.
Is Reason correct explanation for Assertion?
It is true that HCF of two consecutive even natural numbers is 2. But, it is not just because they are divisible by 2.
Like, HCF of two even natural numbers is not always 2 (like HCF of 10 & 20 is 10). But for consecutive even natural numbers it is 2.
Therefore, Reasoning is NOT a correct explanation for Assertion
So,
Assertion is true
Reasoning is true
But, Reasoning is NOT a correct explanation for Assertion
So, the correct answer is (b)
Made by
Davneet Singh
Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.
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