Let x = n(n + 1)(n+2), where n is an even natural number. Which of the following statements is/are correct? I. x is always divisible by 48. II. x^2 is always divisible by 144. Select the answer using the code given below.

Explanation

Let n = 2. Then x = 2 \times 3 \times 4 = 24. Since 24 is not divisible by 48, Statement I is incorrect. However, since n is even, n(n+1)(n+2) is a product of three consecutive integers (always divisible by 6) and contains at least an additional factor of 4, making it divisible by 24. Thus, x^2 is divisible by 24^2 = 576, which is a multiple of 144. So Statement II is correct.

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