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 ?

Correct Option: (c) Both 1 and 2

Let's check 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 5x. If 5x = 100, then x = 20. The integers are 18, 19, 20, 21, and 22. Their sum is indeed 100. Thus, Statement 1 is correct. Let's check Statement 2: 'The product of three consecutive natural numbers can be equal to their sum.' Let the three consecutive natural numbers be x-1, x, and x+1 (where x >= 2). Their product is (x-1)x(x+1) = x(x^2 - 1) = x^3 - x. Their sum is (x-1) + x + (x+1) = 3x. Setting product equal to sum: x^3 - x = 3x => x^3 - 4x = 0 => x(x^2 - 4) = 0. Since x is a natural number (x >= 2), x^2 - 4 = 0 => x = 2. The numbers are 2-1 = 1, 2, and 2+1 = 3. Let's check: Product = 1 * 2 * 3 = 6. Sum = 1 + 2 + 3 = 6. Both product and sum are equal to 6! Thus, Statement 2 is also correct. Therefore, both 1 and 2 are correct, making option (c) correct.