Question

An integer is subtracted from its square. The result could be which of the following?

• A. A negative even integer
• B. An odd integer
• C. The product of two consecutive even integers
• D. The product of two consecutive odd integers
• E. The product of two consecutive integers

Answer 1

Answer: (E)

The product of two consecutive integers

Suppose that the integer is $n$.
Square of that integer is $n^2$.
The result of subtracting $n$ from its square $=n^2-n=n(n-1)$,
which is the product of two consecutive integers $n$ and $n-1$.
If we assume any integers for $n$, we will get an integer because if we subtract $1$ from an integer, it will remain an integer.
So, option E is correct.