Consider the following statements: 1. The sum of 5 consecutive integers can be 100. 2. The product of three…
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?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Solution
Statement 1: Let the 5 consecutive integers be $x-2, x-1, x, x+1, x+2$; their sum is $5x = 100$, giving $x = 20$. The integers 18, 19, 20, 21, 22 sum to 100, so Statement 1 is correct. Statement 2: For 1, 2, 3, the sum is $1+2+3 = 6$ and the product is $1 \times 2 \times 3 = 6$, so Statement 2 is also correct.