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…

Correct Option (C)

Statement 1: Let the five consecutive integers be represented as $x - 2, x - 1, x, x + 1, x + 2$x−2,x−1,x,x+1,x+2. The sum of these integers is $(x - 2) + (x - 1) + x + (x + 1) + (x + 2) = 5x$(x−2)+(x−1)+x+(x+1)+(x+2)=5x. If the sum is 100, then $5x = 100$5x=100, which yields $x = 20$x=20. The integers are consequently 18, 19, 20, 21, 22. Therefore, the sum of 5 consecutive integers can be 100. Statement 1 is correct.

Statement 2: Consider the three consecutive natural numbers 1, 2, and 3. Their sum is calculated as $1 + 2 + 3 = 6$1+2+3=6. Their product is calculated as $1 \times 2 \times 3 = 6$1×2×3=6. Since the sum equals the product in this specific case, the product of three consecutive natural numbers can be equal to their sum. Statement 2 is correct.

As both Statement 1 and Statement 2 are correct, Option C is the correct answer.

Incorrect Options:

Options A, B, and D are incorrect because both Statement 1 and Statement 2 have been demonstrated to be factually correct. Option A is incorrect as it excludes the correctness of Statement 2. Option B is incorrect as it excludes the correctness of Statement 1. Option D is incorrect as it asserts that neither statement is correct, which contradicts the derived conclusions.