Consider the following statements: 1 The sum of 5 consecutive integers can be 100. 2 The product of three consecutive natural numbers can be equal to their sum. Which of the above statements is/are correct?

Statement 1: The sum of 5 consecutive integers can be 100. Let the 5 consecutive integers be x-2, x-1, x, x+1, x+2. Their sum is (x-2) + (x-1) + x + (x+1) + (x+2) = 5x. If 5x = 100, then x = 20. Since 20 is an integer, this is possible. The integers would be 18, 19, 20, 21, 22, and their sum is indeed 100. So, statement 1 is correct. Statement 2: The product of three consecutive natural numbers can be equal to their sum. Let the three consecutive natural numbers be n-1, n, n+1 (where n is a natural number and n >= 2 for n-1 to be a natural number). Their product is (n-1) * n * (n+1) = n(n^2 - 1) = n^3 - n. Their sum is (n-1) + n + (n+1) = 3n. We need to check if n^3 - n = 3n. n^3 - 4n = 0 n(n^2 - 4) = 0 n(n-2)(n+2) = 0 The possible values for n are 0, 2, -2. Since n must be a natural number (n >= 2), n=2 is a valid solution. If n=2, the three consecutive natural numbers are 1, 2, 3. Their product is 1 * 2 * 3 = 6. Their sum is 1 + 2 + 3 = 6. Since the product (6) equals the sum (6), this is possible. So, statement 2 is correct. Both statements are correct. The final answer is C