Graduate Management Admission Test (GMAT) Practice Test

The sum of what type of integers is always a multiple of the quantity of integers involved?

1. Consecutive integers

2. Even integers

3. Odd integers

4. Prime integers

The correct answer is: Consecutive integers

The sum of consecutive integers is always a multiple of the quantity of integers involved because of the arithmetic properties of these integers. When considering \( n \) consecutive integers, you can express them generally as \( x, x+1, x+2, \ldots, x+n-1 \). The sum of these integers can be computed as: \[ S = x + (x + 1) + (x + 2) + \ldots + (x + n - 1) = nx + \frac{(n - 1)n}{2} \] This simplifies to: \[ S = nx + \frac{n(n - 1)}{2} \] To see why this sum aligns with the number of integers \( n \), observe that: - The first part, \( nx \), is clearly a multiple of \( n \). - The second part consists of \( \frac{n(n - 1)}{2} \). For any integer \( n \), this quantity will also be divisible by \( n \) when \( n \) is greater than 1. Thus, regardless of the specific values of \( x \) and \( n \), due to the